Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for University Physics Volume 1
An electron is moving in a straight line with a velocity of 4.0105m/s . It enters a region 5.0 cm long where it undergoes an acceleration of 6.01012m/s2 along the same straight line. (a) What is the electron’s velocity when it emerges from this region? b) How long does the electron take to cross the region?An ambulance driver is rushing a patient to the hospital. While traveling at 72 km/h, she notices the traffic light at the upcoming intersections has turned amber. To reach the intersection before the light turns red, she must travel 50 m in 2.0 s. (a) What minimum acceleration must the ambulance have to reach the intersection before the light turns red? (b) What Is the speed of the ambulance when it reaches the intersection?A motorcycle that is slowing down uniformly covers 2.0 successive km in 80 s and 120 s, respectively. Calculate (a) the acceleration of the motorcycle and (b) its velocity at the beginning and end of the 2-km trip.A cyclist travels from point A to point B in 10 mm. During the first 2.0 mm of her trip, she maintains a uniform acceleration of 0.090m/s2 . She then travels at constant velocity for the next 5.0 nun. Next, she decelerates at a constant rate so that she cons to a rest at point B 3.0 mm later. (a) Sketch the velocity-versus-tine graph for the trip. (b) What is the acceleration during the last 3 mm? (c) How far does the cyclist travel?Two trains are moving at 30 m/s in opposite directions on the same track. The engineers see simultaneously that they are on a collision course and apply the brakes when they are 1000 m apart. Assuming both trains have the same acceleration, what must this acceleration be if the trains are to stop just short of colliding?A 10.0-m-long truck moving with a constant velocity of 97.0 km/h passes a 3.0-m-long car moving with a constant velocity of 80.0 km/h. How much time elapses between the moment the front of the truck is even with the back of the car and the moment the back of the truck is even with the front of the car?A police car waits in hiding slightly off the highway. A speeding car is spotted by the police car doing 40 m/s. At the instant the speeding car passes the police car, the police car accelerates from rest at 4m/s2 to catch the speeding car. How long does it take the police car to catch the speeding car?Pablo is running in a half marathon at a velocity of 3 m/s. Another runner, Jacob, is 50 meters behind Pablo with the same velocity. Jacob begins to accelerate at 0.5m/s2 . (a) How long does it take Jacob to catch Pablo? (b) What is the distance covered by Jacob? (C) What is the final velocity of Jacob?Unreasonable results A runner approaches the finish line and is 75 m away; her average speed at this position is 8 m/s. She decelerates at this point at 0.5m/s2 . How long does it take her to cross the finish line horn 75 m away? Is this reasonable?An airplane accelerates at 5.0m/s2 for 30.0 s. During this time, it covers a distance of 10.0 km. What are the initial and final velocities of the airplane?Compare the distance traveled of an object that undergoes a change in velocity that Is twice its initial velocity with an object that changes its velocity by four times its initial velocity over the same time period. The accelerations of both objects are constant.An object is moving east with a constant velocity and is at position x0 at time t0=0 . (a) With what acceleration must the object have for its total displacement to be zero at a later time t ? (b) What is the physical interpretation of the solution in the case for t ?A ball is thro straight up. It passes a 2.00-m-high window 7.50 m off the ground on its path up and takes 1.30 s to go past the window. What was the ball’s initial velocity?A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) Its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.A soft tennis ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.10 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after It leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms (3.50103s) (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?Unreasonable results. A raindrop falls from a cloud 100 m above the ground. Neglect air resistance. What is the speed of the raindrop when it hits the ground? Is this a reasonable number?Compare the time in the air of a basketball player who jumps 1.0 m vertically off the floor with that of a player who jumps 0.3 m vertically.Suppose that a person takes 0.5 s to react and move his hand to catch an object he has dropped. (a) How far does the object tall on Earth, where g=9.8m/s2 ? (b) How far does the object fall on the Moon, where the acceleration due to gravity is 1/6 of that on Earth?A hot-air balloon rises from ground level at a constant velocity of 3.0 m/s. One minute after liftoff, a sandbag is dropped accidentally from the balloon. Calculate (a) the time it takes for the sandbag to reach the ground and (b) the velocity of the sandbag when it hits the ground.(a) A world record was se for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt “coasted” across the finish line with a time of 9.69 s. If we assume that Bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of the race, calculate his maximum speed and his acceleration. (b) During the same Olympics, Bolt also set the world record in the 200-rn dash with a time of 19.30 s. Using the some assumptions as for the 100-m dash, what was his maximum speed for this race?An object is dropped from a height of 75.0 m above ground level. (a) Determine the distance traveled during the first second. (b) Determine the final velocity at which the object hits the ground. (c) Determine the distance traveled during the last second of motion before hitting the ground.A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 0.0800ms(8.0010-5s) (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?An object is dropped from a roof of a building of height h . During the last second of its descent, it drops a distance h/3 . Calculate the height of the building.In a 100-rn race, the winner is timed at 11.2 s. The second-place finisher’s time Is 11.6 s. How far Is the second-place finisher behind the winner when she crosses the finish line? Assume the velocity of each runner is constant throughout the race.The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 . Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t=2.0s , (c) the time at which the position is a maximum, (d) the time at which the velocity Is zero, and (e) the maximum position.A cyclist sprints at the end of a race to clinch a victory. She has an initial velocity of 11.5 m/s and accelerates at a rate of 0.500m/s2 for 7.00 s. (a) What is her final velocity? (b) The cyclist continues at this velocity to the finish. If she is 300 m from the finish line when she starts to accelerate, how much time did she save? (c) The second-place winner was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at 11.8 m/s until the finish line. What was the difference in finish time in seconds between the winner and runner-up? How far back was the runner-up when the winner crossed the finish line?In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, of 295.38 km/h. The one-way course was 8.00 km long. Acceleration rates are often described by the time it takes to reach 96.0 km/h from rest. If this time was 4.00 s and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the course?4.1CYU4.2CYUCheck Your Understanding A rock is thrown horizontally off a cliff 100.0 m high with a velocity of 15.0 m/s. (a) Define the origin of the coordinate system (b) Which equation describes the horizontal motion? (c) Which equation describe the vertical motion (d) What is the rock’s velocity at the point of impact?Check Your Understanding If the two golf shots in Example 4.9 were bunched at the same speed, which shot would have the greatest range? When we speak of the range of a projectile on level ground, we assume R is very small compared with the circumference of Earth. If, however, the range is large, Earth curves away below the projectile and the acceleration resulting from gravity changes direction along the path. The range is larger than predicted by the range equation given earlier because the projectile has father to fail than it would on level ground, as shown in Figure 4.17, which is based on a drawing in Newton’s Principia. If the initial speed is great enough, the projectile goes into orbit. Earth’s surface drops every 8000 m. In 1 s an object falls 5 m without a resistance. Thus, if an object is given a horizontal velocity of 8000 m/s (or 18,000 mi/hr) near Earth’s surface, it will go into orbit around the planet because, the surface continuously falls away from object Thu is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. These and other aspects of orbital motion, such as Earth’s rotation, are covered in greater depth in Gravitation. Figure 4.17 Projectile to satellite. In each case shown here, a projectile is launched from a very high tower to avoid air resistance. With increasing initial speed, the range increases and becomes longer than t would be on level ground because Earth curves away beneath its path. With a speed of 8000 m/s, orbit is achieved.Check Your Understanding A flywheel has a radius of 20.0 cm What is the speed of a point on the edge of the flywheel if it experiences a centripetal acceleration of 900.0cm/s2 ?Check Your Understanding A boat heads north in still water at 4.5m/s directly across a river that is running east at 3.0 m/ s. What is the velocity o the boat with respect to Earth?What form does the trajectory of a particle have if the distance from any point Ato point Bis equal to the magnitude of the displacement from Ato B ?Give an example of a trajectory in two or three dimensions caused by independent perpendicular motions.If the instantaneous velocity is zero, what can be said about the slope of the position function?If the position function of a particle is a linear function of time, what can be said about its acceleration?If an object has a constant x -component of the velocity and suddenly experiences an acceleration in the y direction, does the x -component of its velocity change?If an object has a constant x -component of velocity and suddenly experiences an acceleration at an angle of 70 in the x direction, does the x -component of velocity change?Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 nor 90 : (a) Is the velocity ever zero? (b) When Is the velocity a minimum? A maximum? (c) Can the velocity ever be the same as the initial velocity at a time other than at t=0 ? (d) Can the speed ever be the same as the initial speed at a time other than at t=0 ?Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 nor 90 : (a) Is the acceleration ever zero? (b) Is the vector v ever parallel or antiparallel to the vector a? (c) Is the vector v ever perpendicular to the vector a? If so, where is this located?A dime is placed at the edge of a table so it hangs over slightly. A quarter is slid horizontally on the table surface perpendicular to the edge and hits the dime head on. Which coin hits the ground first?Uniform Circular Motion Can centripetal acceleration change the speed of a particle undergoing circular motion?Can tangential acceleration change the speed of a particle undergoing circular motion?Dimensions What frame or frames of reference do you use instinctively when driving a car? When flying in a commercial jet?A basketball player dribbling down the court usually keeps his eyes fixed on the players around him. He is moving fast. Why doesn’t he need to keep his eyes on the ball?If someone is riding in the back of a pickup thick and throws a softball straight backward, is it possible for the ball to fall straight down as viewed by a person standing at the side of the road? Under what condition would this occur? How would the motion of the ball appear to the person who threw it?The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger’s frame of reference. Draw its path as viewed by a stationary observer. Neglect air resistance.A clod of dirt falls from the bed of a moving thick. It strikes the ground directly below the end of the truck. (a) What is the direction of its velocity relative to the truck just before it hits? (b) Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answer.The coordinates of a particle in a rectangular coordinate system are (1.0,4.0,6.0) . What is the position vector of the particle?18P19PA bird files straight northeast a distance of 95.0 km for 3.0 h. With the x -axis due east and the y -axis due north, what is the displacement in unit vector notation for the bird? What is the average velocity for the trip?A cyclist rides 5.0 km due east, then 10.0 km 20 west of north. From this point she rides 8.0 km due west. What is the final displacement from where the cyclist started?New York Rangers defenseman Daniel Girardi stands at the goal and passes a hockey puck 20 m and 45 from straight down the ice to left wing Chris Kreider waiting at the blue line. Kreider waits for Giran:li to reach the blue line and passes the puck directly across the ice to him 10 m away. What is the final displacement of the puck? See the following figure.23PClay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 45 with respect to the 50-yard line and covers 8.0 m in 1 s. He then fins straight down the field at 90 with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews’ final displacement from the start of the play? (b) What is his average velocity?The F-35B Lighting II is a short-takeoff and vertical landing fighter jet. If it does a vertical takeoff to 20.00-rn height above the ground and then follows a flight path angled at 30 with respect to the ground for 20.00 km, what is the final displacement?26PA particles acceleration is (4.0i+3.0j)m/s2. At t=0, its position and velocity are zero. (a) What are the particles position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x and y-axes and sketch the trajectory of the particle.28PThe position of a particle for t0 is given by r(t)=(3.0t2i7.0t3j5.0t2k)m. (a) What Is the velocity as a function of time? (b) What is the acceleration as a function of time? (c) What is the particle’s velocity at t=2.0s? (d) What is its speed at t=1.0s and t=3.0s? (e) What is the average velocity between t=1.0s and t=2.0s?30P31PA Lockheed Martin F-35 II lighting jet takes off from an aircraft carrier with a runway length of 90 m and a takeoff speed 70 m/s at the end of the runway. Jets are catapulted into airspace from the deck of an aircraft carrier with two sources of propulsion: the jet propulsion and the catapult. At the point of leaving the deck of the aircraft carrier, the F-35’s acceleration decreases to a constant acceleration of 5.0m/s2 at 30 with respect to the horizontal. (a) What is the initial acceleration of the F-35 on the deck of the aircraft carrier to make it airborne? (b) Write the position and velocity of the F-35 in unit vector notation from the point it leaves the deck of the aircraft carrier. (c) At what altitude is the fighter 5.0 s after it leaves the deck of the aircraft carrier? (d) What is its velocity and speed at this time? (e) How far has it traveled horizontally?Projectile Motion A bullet is shot horizontally from shoulder height (1.5 m) with an initial speed 200 m/s. (a) How much time elapses before the bullet hits the ground? (b) How far does the bullet travel horizontally?A marble rolls off a tabletop 1.0 m high and hits the floor at a point 3.0 m away from the table’s edge in the horizontal direction. (a) How long is the marble in the air? (b) That is the speed of the marble when it leaves the table’s edge? (c) What is its speed when it hits the floor?A dart is thrown horizontally at a speed of 10 m/s at the bull’s-eye of a dartboard 2.4 m away, as in the following figure. (a) How far below the Intended target does the dart hit? (b) What does your answer tell you about how proficient dart players throw their darts?An airplane flying horizontally with a speed of 500 km/h at a height of 800 m drops a crate of supplies (see the following figure). If the parachute fails to open, how far in front of the release point does the crate hit the ground?Suppose the airplane in the preceding problem fires a projectile horizontally in its direction of motion at a speed of 300 m/s relative to the plane. (a) How far in front of the release point does the projectile hit the ground? (b) What is its speed when it hits the ground?A fastball pitcher can throw a baseball at a speed of 40 m/s (90 mi/b). (a) Assuming the pitcher can release the ball 16.7 m from home plate so the ball is moving horizontally, how long does it take the ball to reach bone plate? (b) How far does the ball drop between the pitcher’s hand and home plate?A projectile is launched at an angle of 30 and lands 20 s later at the same height as it was launched. (a) What is the initial speed of the projectile? (b) What is the maximum altitude? (c) What is the range? (d) Calculate the displacement from the point of launch to the position on its trajectory at 15 s.A basketball player shoots toward a basket 6.1 m ay and 3.0 m above the floor. If the ball is released 1.8 m above the floor at an angle of 60 above the horizontal, what must the initial speed be if it were to go through the basket?At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. When she lands, where will she find the ball? Ignore air resistance.A man on a motorcycle traveling at a uniform speed of 10 m/s throws an empty can straight upward relative to himself with an initial speed of 3.0 m/s. Find the equation of the trajectory as seen by a police officer on the side of the road. Assume the initial position of the can is the point where it is thrown. Ignore air resistance.An athlete can jump a distance of 8.0 m in the broad jump. What is the maximum distance the athlete can jump, on the Moon, where the gravitational acceleration is one-sixth that of Earth?The maximum horizontal distance a boy can throw a ball is 50 m. Assume he can throw with the same initial speed at all angles. How high does he throw the ball when he throws it straight upward?A rock is thrown off a cliff at an angle of 53 with respect to the horizontal. The cliff is 100 m high. The initial speed of the rock is 30 m/s. (a) How high above the edge of the cliff does the rock rise? (b) How far has it moved horizontally when it is at maximum altitude? (c) How long after the release does it hit the ground? (d) What is the range of the rock? (e) What are the horizontal and vertical positions of the rock relative to the edge of the cliff at t=2.0s,t=4.0s , and t=6.0s ?Trying to escape his pursuers, a secret agent skis off a slope inclined at 30 below the horizontal at 60 km/h. To survive and land on the snow 100 m below, he must clear a gorge 60 m wide. Does he make it? Ignore air resistance.A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40 with an initial speed of 20 m/s, how close to the green does she come?A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60 above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20 to the horizontal. Relative to the coordinate system shown in the figure, the equation of this straight y=(tan20)x109 . Where on the hill does the projectile land?An astronaut on Mars kicks a soccer ball at an angle of 45 with an initial velocity of 15 m/s. If the acceleration of gravity on Mars is 3.7m/s2 , (a) what is the range of the soccer kick on a flat surface? (b) What would be the range of the same kick on the Moon, were gravity is one-sixth that of Earth?Mike Powell holds the record for the long jump of 8.95 m, established in 1991. If he left the ground at an angle of 15 . What was his initial speed?MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h. (a) If the robot launches itself at an angle of 60 at this speed, what is its maximum height? (b) What would the launch angle have to be to reach a height of 46 cm?Mt. Asama, Japan, is an active volcano. In 2009, an eruption threw solid volcanic rocks that landed 1 km horizontally from the crater. If the volcanic rocks were launched at an angle of 40 with respect to the horizontal and landed 900 m below the crater, (a) what would be their initial velocity and (b) what is their time of flight?Drew Brees of the New Orleans Saints can throw a football 23.0 m/s (50 mph). If he angles the throw at 10 from the horizontal, what distance does it go if it is to be caught at the same elevation as it was thrown?The Lunar Roving Vehicle used In NASA’s late Apollo missions reached an unofficial lunar land speed of 5.0 m/ s by astronaut Eugene Cernan. If the rover was moving at this speed on a flat lunar surface and hit a small bump that projected it off the surface at an angle of 20 , how long would it be “airborne” on the Moon?A soccer goal is 2.44 m high. A player kicks the ball at a distance 10 m from the goal at an angle of 25 . The ball hits the crossbar at the top of the goal. What is the initial speed of the soccer ball?Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?You throw a baseball at an initial speed of 15.0 m/s at an angle of 30 with respect to the horizontal. What would the ball’s initial speed have to be at 30 on a planet that has twice the acceleration of gravity as Earth to achieve the same range? Consider launch and impact on a horizontal surface.Aaron Rodgers throws a football at 20.0 m/s to his wide receiver, who runs straight down the field at 9.4 m/s for 20.0 m. If Aaron throws the football when the wide receiver has reached 10.0 m, what angle does Aaron have to launch the ball so the receiver catches it at the 20.0 m mark?A flywheel is rotating at 30 rev/s. What is the total angle, in radians, through which a point on the flywheel rotates in 40 s?A particle travels in a circle of radius 10 m at a constant speed of 20 m/s. What is the magnitude of the acceleration?Cam Newton of the Carolina Panthers throws a perfect football spiral at 8.0 rev/s. The radius of a pro football is 8.5 cm at the middle of the short side. What is the centripetal acceleration of the laces on the football?A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has an 8.00-m radius, at how many revolutions per minute are the riders subjected to a centripetal acceleration equal to that of gravity?A runner taking part in the 200-m dash must run around the end of a track that has a circular arc with a radius of curvature of 30.0 m. The runner starts the race at a constant speed. If she completes the 200-m dash in 23.2s and rum at constant speed throughout the race, what is her centripetal acceleration as she runs the curved portion of the track?What is the acceleration of Venus toward the Sun, assuming a circular orbit?An experimental jet rocket travels around Earth along its equator just above its surface. At what speed must the jet travel if the magnitude of its acceleration is g ?A fan is rotating at a constant 360.0 rev/min. What is the magnitude of the acceleration of a point on one of its blades 10.0 cm from the axis of rotation?A point located on the second hand of a large clock has a radial acceleration of 0.1cm/s2 . How far is the point from the axis of rotation of the second hand?69P70P71PRaindrops fall vertically at 43 m/s relative to the earth. What does an observer in a car moving at 22.0 m/s a straight line measure as the velocity of the raindrops?A seagull can fly at a velocity of 9.00 m/s in still air. (a) If it takes the bird 20.0 mm to travel 6.00 kin straight into an oncoming wind, what is the velocity of the wind? (b) If the bird turns around and flies with the wind, how long will it take the bird to return 6.00 km?A ship sets sail from Rotterdam, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0 north of east. What is the velocity of the ship relative to Earth?A boat can be rowed at 8.0 km/h in still water. (a) How much time is required to row 1.5 km downstream in a river moving 3.0 km/h relative to the shore? (b) How much time is required for the return trip? (c) In what direction must the boat be aimed to row straight across the river? (d) Suppose the river is 0.8 km wide. What is the velocity of the boat with respect to Earth and how much time is required to get to the opposite shore? (e) Suppose, instead, the boat is aimed straight across the river. How much time is required to get across and how far downstream is the boat when it reaches the opposite shore?A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?A cyclist traveling southeast along a road at 15 km/h feels a wind blowing from the southwest at 25 km/h. To a stationary observer, what are the speed and direction of the wind?A river is moving east at 4 m/s. A boat starts from the dock heading 30 north of west at 7 m/s. If the river is 1800 m wide, (a) what is the velocity of the boat with respect to Earth and (b) how long does it take the boat to cross the river?A Formula One race car is traveling at 89.0 m/s along a straight track enters a turn on d race track with radius of curvature of 200.0 m. What centripetal acceleration must the car have to gay on the track?A particle travels m a circular orbit of radius 10 m. Its speed is changing at a rate of 15.0m/s2 at an instant when its speed is 40.0 m/s. What is the magnitude of the acceleration of the particle?The driver of a car moving at 90.0km/h presses down on the brake as the car enters a circular curve of radius 150.0 m. If the speed of the car is decreasing at a rate of 9.0 km/h each second, what is the magnitude of the acceIeration of the car the instant its speed is 60.0 km/h?A race car entering the curved part of the track at the Daytona 500 drops its speed from 85.0 m/s to 80.0 m/ s in 2.0 s. If the radius of the curved part of the track is 316.0 m, calculate the total acceleration of the race car at the beginning and ending of reduction of speed.An elephant is located on Earth’s surface at a latitude . Calculate the centripetal acceleration of the elephant resulting from the rotation of Earth around is polar axis. Express your answer in terms of , the radius REof Earth and time T for one rotation of Earth. Compare your answer with g for =40 .A proton in a synchrotron is moving in a circle of radius 1 km and increasing its speed by v(t)=c1+c2t2 , where c1=2.0105m/s,c2=105m/s3 . (a) What is the proton’s total acceleration at t=5.0s ? (b) At what tine does the expression for the velocity become unphysical?A propeller blade at rest starts to rotate from t=0 to t=5.0s with a tangential acceleration of the tip of the blade at 3.00m/s2 . The tip of the blade is 1.5 m from the axis of rotation. At t=5.0s , what is the total acceleration of the tip of the blade?A particle is executing circular motion with a constant angular frequency of =4.00rad/s . If time t=0 corresponds to the position of the particle being located at y=0m and x=5m , (a)what is the position of the particle at t=10s ? (b) What is its velocity at this time? (c) What is its acceleration?A particle’s centripetal acceleration is aC=4.0m/s2 at t=0s . It is executing uniform circular motion about an axis at a distance of 5.0 m. What is its velocity at t=10s ?A rod 3.0 m in length is rotating at 2.0 rev/s about an axis at one end. Compare the centripetal accelerations at radii of (a) 1.0 m, (b) 2.0 m, and (c) 3.0 m.89AP90AP91APA crossbow is aimed horizontally at a target 40 m away. The arrow hits 30 cm below the spot at which it was aimed. What is the initial velocity of the arrow?A long jumper can jump a distance of 8.0 m when he takes off at an angle of 45 with respect to the horizontal. Assuming he can jump with the same initial speed at all angles, how much distance does he lose by taking off at 30 ?On planet Arcon, the maximum horizontal range of a projectile launched at 10 m/s is 20 m. What is the acceleration of gravity on this planet?A mountain biker encounters a jump on a race course that sends him into the air at 60 to the horizontal. If he lands at a horizontal distance of 450 m and 20 m below his launch point, what is his initial speed?Which has the greater centripetal acceleration, a car with a speed of 15.0 m/s along a circular track of radius 100.0 m or a car with a speed of 12.0 m/s along a circular track of radius 75.0 m?A geosynchronous satellite orbits Earth at a distance of 42,250.O km and has a period of 1 day. What is the centripetal acceleration of the satellite?Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at 4.0 m/s and 5.0 m/s. (a) What is the speed of the boats relative to the river? (b) How fast is the river moving relative to the shore?World’s Longest Par 3. The tee of the world’s longest par 3 sits atop South Africa’s Hanglip Mountain at 400.0 m above the green and can only be reached by helicopter. The horizontal distance to the green is 359.0 in. Neglect air resistance and answer the following questions. (a) If a golfer launches a shot that is 40 with respect to the horizontal, what initial velocity must she give the ball? (b) What is the time to reach the green?When a field goal kicker kicks a football as hard as he can at 45 to the horizontal, the ball just clears the 3-m- high crossbar of the goalposts 45.7 m away. (a) What is the maximum speed the kicker can impart to the football? (b) In addition to clearing the crossbar, the football must be high enough in the air early during its flight to clear the reach of the onrushing defensive lineman. If the lineman is 4.6 m away and has a vertical reach of 2.5 m, can he block the 45.7-m field goal attempt? (c) What if the lineman is 1.0 m away?A truck is traveling east at 80 km/h. At an intersection 32 km ahead, a car is traveling north at 50 km/h. (a) How long after this moment will the vehicles be closest to each other? (b) How far apart will they be at that point?Check Your Understanding Find the magnitude and direction of the net force in the ice skater example just given.Check Your Understanding A skydiver opens his parachute, and shortly thereafter, he is moving at constant velocity. (a) What forces are acting on him? (b) Which force is bigger?Check Your Understanding At the time of its launch, the HMS Titanic was the most massive mobile object ever built, with a mass of 6.0107kg . If a force of 6 MN (6106N) was applied to the ship, what acceleration would it experience?Check Your Understanding A 550-kg sports car collides with a 2200-kg truck, and during the collision, the net force on each vehicle is the force exerted by the other. If the magnitude of the truck’s acceleration is 10m/s2 , what is the magnitude of the sports car’s acceleration?Check Your Understanding A car gas forces acting on it, as shown below. The mass of the car is 1000.0 kg. The rode is slick, so friction can be ignored. (a) What is the net force on the car? (b) What is the acceleration of the car?Check Your Understanding For Example 5.8, find the acceleration when farmer’s applied force is 230.0 N.Check Your Understanding Two blocks are at rest and in contact on a frictionless surface as shown below, with m1=2.0kg,m2=6.0kg , and applied force 24 N. (a) Find the acceleration of the system of blocks. (b) Suppose that the blocks are later separated. What force will give the second block, with the mass of 6.0 kg, the same acceleration as the system of blocks?Check Your Understanding A force of 1150 N acts parallel to a ramp to push a 250-kg gun safe into a moving van. The ramp is frictionless and inclined at 17 . (a) What is the acceleration of the safe up the ramp? (b) If we consider friction in this problem, with a friction force of 120 N, what is the acceleration of the safe?Check Your Understanding One end of a 3.0-m rope is tied to a tree; the other, end is tied to a car stuck in the mud. The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. If he exerts a force of 200.0 N under these conditions, determine the force exerted on the car.Check Your Understanding (a) Draw the free-body diagram for the situation shown. (b) Redraw it showing components; use x -axes parallel to the two ramps.What properties do forces have that allow us to classify them as vectors?Taking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames? (a) A car moving at constant velocity (b) A car that is accelerating (c) An elevator in free fall (d) A space capsule orbiting Earth (e) An elevator descending uniformlyA woman was transporting an open box of cupcakes to a school party. The car in front of her stopped suddenly; she applied her brakes immediately. She was wearing her seat belt and suffered no physical harm (just a great deal of embarrassment), but the cupcakes flew into the dashboard and became “smushcakes.” Explain what happened.Why can we neglect forces such as those holding a body together when we apply Newton’s second law?A rock is thrown straight up. At the top of the trajectory, the velocity is momentarily zero. Does this imply that the force acting on the object is zero? Explain your answer.What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?Which of the following statements is accurate? (a) Mass and weight are the same thing expressed In different units. (b) If an object has no weight, it must have no mass. (c) If the weight of an object vanes, so must the mass. (d) Mass and inertia are different concepts. (e) Weight is always proportional to mass.When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?How would you give the value of g in vector form?Newton’s Third Law Identity the action and reaction forces in the following situations: (a) Earth attracts the Moon, (b) a boy kicks a football, (c) a rocket accelerates upward, (d) a car accelerates forward, (e) a high jumper leaps, and (f) a bullet is shot from a gun.Suppose that you are holding a cup of coffee in your hand. Identify all forces on the cup and the reaction to each(a) Why does an ordinary rifle recoil (kick backward) when fired? (b) The barrel of a recoilless rifle is open at both ends. Describe how Newton’s third law applies when one is fired. (c) Can you safely stand close behind one when it is fired?Common Forces A table is placed on a rug. Then a book is placed on the table. What does the floor exert a normal force on?A particle is moving to the right. (a) Can the force on it be acting to the left? If yes, what would happen? (b) Can that force be acting downward? If yes, why?Drawing Free-Body Diagrams In completing the solution for a problem involving forces, what do we do after constructing the tree-body diagram? That is, what do we apply?If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.If the book in the previous question is in free fall, how many forces should be shown in a free-body diagram of the book? Describe them.Two ropes are attached to a tree, and forces of and are applied. The forces are coplanar (In the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.A telephone pole has three cables pulling as shown from above, with and (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force.Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30 . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N. (a) Find the component form of the net force. (b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David’s rope.Two forces of and act on an object. Find the third force that is needed to balance the first two forces.While sliding a couch across a floor, Andrea and Jennifer exert forces FA and FJ on the couch. Andrea’s force is due north with a magnitude of 130.0 N and Jennifer’s force is 32 east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer’s housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined forceFDS should they push so that the couch does not move?Newton’s Second Law Andrea, a 63.0-kg sprinter, starts a race with an acceleration of 4.200m/s2 . What is the net external force on her?If the sprinter from the previous problem accelerates at that rate for 20.00 m and then maintains that velocity for the remainder of a 100.00-m dash, what will her time be for the race?A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of his cart’s acceleration.Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted, and an astronaut’s acceleration is measured to be 0.893m/s2 . (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method by which recoil of the vehicle is avoided.In Figure 5.12, the net external force on the 24-kg mower is given as 51 N. If the force of friction opposing the motion is 24 N, what force F(in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force Fis removed. How far will the mower go before stopping?The rocket sled shown below decelerates at a rate of 196m/s2 . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2.10103kgIf the rocket sled shown in the previous problem starts with only one rocket burning, what is the magnitude of this acceleration? Assume that the mass of the system is 2.10103kg , the thrust Tis 2.40104N , and the force of friction opposing the motion is 650.0 N. (b) Why is the acceleration n one-fourth of what it is with all rockets burning?What is the deceleration of the rocket sled if it comes to rest in 1.10 s from a speed of 1000.0 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second exerts a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (See the free-body diagram.) (b) Calculate the acceleration. (c) What would the acceleration be if friction were 15.0 N?A powerful motorcycle can produce an acceleration of 3.50m/s2 while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, total 400.0 N. (Air resistance is analogous to air fiction. It always opposes the motion of an object.) What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?A car with a mass of 1000.0 kg accelerates from 0 to 90.0 km/h in 10.0 s. (a) What is its acceleration? (b) What is the net force on the car?The driver in the previous problem applies the brakes when the car is moving at 90.0 km/h, and the car comes to rest after traveling 40.0 m. What is the net force on the car during its deceleration?An 80.0-kg passenger in an SUV traveling at 1.00103km/h is wearing a seat belt. The driver slams on the brakes and the SUV stops in 45.0 m. Find the force of the seat belt on the passenger.A particle of mass 2.0 kg is acted on by a single force (a) What is the particle’s acceleration? (b) If the particle starts at rests how far does it travel in the first 5.0 s?Suppose that the particle of the previous problem also experiences forces and What is its acceleration in this case?Find the acceleration of the body of mass 5.0 kg shown below.In the following figure, the horizontal surface on which this block slides is frictionless. If the two forces acting on it each have magnitude F=30.0Nand M=10.0kg, what is the magnitude of the resulting acceleration of the block?Mass and Weight The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 1.00104kg . The thrust of its engines is 3.00104N . (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.A rocket sled accelerates at a rate of 49.0m/s2 . Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of 201m/s2 . In this problem, the forces are exerted by the seat and the seat belt.A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?A car weighing 12,500 N stalls from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.A body with a mass of 10.0 kg is assumed to be in Earth’s gravitationaI field with g=9.80m/s2 . What is its acceleration?A fireman has mass m ; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is 90.0 kg and he accelerates at 5.00m/s2 , what is the magnitude of his applied force?A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. His glove stops the ball in 0.0100 s. What is the force exerted by his glove on the ball?When the Moon is directly overhead at sunset, the force by Earth on the Moon FEM , is essentially at 90 to the force by the Sun on the Moon, FSM, as shown below. Given that FEM=1.981020N and FSM=4.361020N , all other forces on the Moon are negligible, and the mass of the Moon is 7.351022kg, determine the magnitude of the Moon’s acceleration.(a) What net external force is exerted on a 1100.0-kg artillery shell fired from a battleship if the shell is accelerated at 2.40104m/s2 ? (b) What is the magnitude of the force exerted on the ship by the artillery shell, and why?A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800.0 N on him. The mass of the losing player plus equipment is 90.0 kg, and he is accelerating backward at 1.20m/s2 . (a) What is the force of friction between the losing player’s feet and the grass? (b) What force does the winning player exert on the ground to move forward if his mass plus equipment is 110.0 kg?A history book is lying on top of a physics book on a desk, as shown below a free-body diagram is also shown. The history and physics books weigh 14 N and 18 N, respectively. Identify each force on each book with a double subscript notation (for instance, the contact force of the history book pressing against physics book can be described as F HP), and determine the value of each of these forces, explaining the process used.A truck collides with a car, and during the collision, the net force on each vehicle is essentially the force exerted by the other. Suppose the mass of the car is 550 kg, the mass of the truck Is 2200 kg, and the magnitude of the truck’s acceleration is 10m/s2 . Find the magnitude of the car’s acceleration.Common Forces A leg is suspended in a traction system, as shown below (a) Which pulley in the figure is used to calculate the force exerted on the foot? (b) What is the tension In the rope? Here T is the tension, wleg is the weight of the leg, and w is the weight of the load that provides the tension.Suppose the shinbone in the preceding image was a femur in a traction setup for a broken bone, with pulleys and rope available. How might we be able to increase the force along the femur using the same weight?Two teams of nine members each engage in tug-of-war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally. (a) What is magnitude of the acceleration of the two teams, and which team sins? (b) What is the tension in the section of rope between the teams?What force does a trampoline have to apply to Jennifer, a 45.0-kg gymnast, to accelerate her straight up at 7.50m/s2 ? The answer is independent of the velocity of the gymnast—she can be moving up or down or can be instantly stationary.(a) Calculate the tension in a vertical strand of spider web if a spider of mass 2.00105kg hangs motionless on it. (b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 5.26. The strand sags at an angle of 12 below the horizontal. Compare this with the tension in the vertical strand (find their ratio).Suppose Kevin, a 60.0-kg gymnast, climbs a rope. (a) What Is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of 1.50m/s2 ?Show that, as explained in the text, a force F exerted on a flexible medium at its center and perpendicular to its length (such as on the tightrope wire in Figure 5.26) gives rise to a tension of magnitude T=F/2sin() .Consider Figure 5.28. The driver attempts to get the car out of the mud by exerting a perpendicular force of 610.0 N, and the distance she pushes in the middle of the rope is 1.00 m while she stands 6.00 m away from the car on the left and 6.00 m away from the tree on the right. What is the tension Tin the rope, and how do you find the answer?A bird has a mass of 26g and perches in the middle of a stretched telephone line. (a) Show that the tension in the line can be calculated using the equation T=mg2sin . Determine the tension when (b) =5 and (c) =0.5. Assume that each half of the Line is straight.-m rope is tied to a tree; the other end is tied to a car stuck in the mud. The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 2 m. If he exerts a force of 80 N under these conditions, determine the force exerted on the car.Consider the baby being weighed in the following figure. (a) What is the mass of the infant and basket if a scale reading of 55 N is observed? (b) What is tension T1in the cord attaching the baby to the scale? (c) What is tension T2, In the cord attaching the scale to the ceiling, If the scale has a mass of 0.500 kg? (d) Sketch the situation, indicating the system of interest used to solve each part. The masses of the cords are negligible.What force must be applied to a 100.0-kg crate on a frictionless plane inclined at 30 to cause an acceleration of 2.0m/s2 up the plane?A 2.0-kg block is on a perfectly smooth ramp that makes an angle of 30 with the horizontal. (a) What is the block’s acceleration down the ramp and the force of the ramp on the block? (b) What force applied upward along and parallel to the ramp would allow the block to move with constant velocity?Drawing Free-Body Diagrams A ball of mass m hangs at rest, suspended by a sting. (a) Sketch all forces. (b) Draw the free-body diagram for the ball.A car moves along a horizontal road. Draw a free- body diagram; be sure to include the friction of the road that opposes the forward motion of the car.A runner pushes against the track, as shown. (a) Provide a free-body diagram showing all the forces on the runner. (Hint: Place all forces at the center of his body, and include his weight.) (b) Give a revised diagram showing the xy -component form. (credit: modification of work by “Greenwich Photography”/Flicke)The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for this situation.Two small forces, F1=2.40i6.10tj N and F2=8.50i9.70j N , are exerted on a rogue asteroid by a pair of space tractors. (a) Find the net force. (b) What are the magnitude and direction of the net force? (c) If the mass of the asteroid is 125 kg, what acceleration does it experience (in vector form)? (d) What are the magnitude and direction of the acceleration?Two forces of 25 and 45 N act on an object. Their directions differ by 70 . The resulting acceleration has magnitude of 10.0m/s2 . What is the mass of the body?A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at 20 . (a) What is the acceleration of the piano up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest?Draw a free-body diagram of a diver who has entered the water, moved downward, and is acted on by an upward force due to the water which balances the weight (that is, the diver is suspended).For a swimmer who has just jumped off a diving board, assume air resistance is negligible. The swimmer has a mass of 80.0 kg and jumps off a board 10.0 m above the water. Three seconds after entering the water, her downward motion is stopped. What average upward force did the water exert on her?(a) Find an equation to determine the magnitude of the net force required to stop a car of mass m, given that the initial speed of the car is v0 and the stopping distance is x . (b) Find the magnitude of the net force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 m.A sailboat has a mass of 1.50103kg and is acted on by a force of 2.00103N toward the east, while the wind acts behind the sails with a force of 3.00103N in a direction 45 north of east. Find the magnitude and direction of the resulting acceleration.Find the acceleration of the body of mass 10.0 kg shown below.A body of mass 2.0 kg is moving along the x -axis with a speed of 3.0 m/s at the instant represented below. (a) What is the acceleration of the body? (b) What is the body’s velocity 10.0 s later? (c) What is its displacement after 10.0 s.Force FBhas twice the magnitude of force FA. Find the direction in which the particle accelerates in this figure.Shown below is a body of mass 1.0 kg under the influence of the forces FA,FB ,and mg . If the body accelerates to the left at 20m/s2 , what are FA and FB?A force acts on a car of mass m so that the speed v of the car increases with position x as v=kx2 where kis constant and all quantities are in SI units. Find the force acting on the car as a function of position.A 7.0-N force parallel to an incline is applied to a 1.0-kg crate. The ramp is tilted at 20 and is frictionless. (a) What Is the acceleration of the crate? (b) If all other conditions are the same but the ramp has a friction force of 1.9 N, what is the acceleration?Two boxes, A and B, are at rest Box A is on level ground, while box B rests on an inclined plane tilted at angle with the horizontal. (a) Write expressions for the normal force acting on each block (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is 10 , which force is greater?A mass of 250.0 g is suspended from a spring hanging vertically. The spring stretches 6.00 cm. How much will the spring stretch if the suspended mass is 530.0 g?As shown below, two identical springs, each with the spring constant 20 N/m, support a 15.0-N weight. (a) What is the tension in spring A? (b) What is the amount of stretch of spring A from the rest position?Shown below is a 30.0-kg block resting on a frictionless ramp inclined at 60 to the horizontal. The block is held by a spring that is stretched 5.0 cm. What is the force constant of the spring?In building a house, carpenters use nails from a large box. The box is suspended from a spring twice dining the day to measure the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the end of the day, the spring stretches 30 cm. What fraction or percentages of the nails have been used?A force is applied to a block to move it up a 30 incline. The incline is frictionless. If F=65.0Nand M=5.00kg , what is the magnitude of the acceleration of the block?Two forces are applied to a 5.0-kg object, and it accelerates at a rate of 2.0m/s2 in the positive y -direction. If one of the forces acts in the positive x -direction with magnitude 12.0 N, find the magnitude of the other force.The block on the tight shown below has more mass than the block on the left (m2m1). Draw free-body diagrams for each block.If two tugboats pull on a disabled vessel, as shown here in an overhead view, the disabled vessel will be pulled along the direction indicated by the result of the exerted forces. (a) Draw a free-body diagram for the vessel. Assume no friction or drag forces affect the vessel. (b) Did you include all forces in the overhead view in your free-body diagram? Why or why not?A 10.0-kg object is initially moving east at 15.0 m/ s. Then a force acts on it for 2.00 s, after which it moves northwest, also at 15.0 m/s. What are the magnitude and direction of the average force that acted on the object over the 2.00-s interval?On June 25, 1983, shot-putter Udo Beyer of East Germany threw the 7.26-kg shot 22.22 m, which at that time was a world record. (a) If the shot was released at a height of 2.20 m with a projection angle of 45.00, what was its initial velocity? (b) If while in Beyer’s hand the shot was accelerated uniformly over a distance of 1.20 m, what was the net force on it?A body of mass m moves in a horizontal direction such that at time t its position is given by x(t)=at4+bt3+ct , where a,b ,and c are constants.(a) What is the acceleration of the body? (b) What is the time-dependent force acting on the body?A body of mass m has initial velocity v0 in the positive x -direction. It is acted on by a constant force F for time t until the velocity becomes zero; the force continues to act on the body until its velocity becomes v0 in the same amount of time. Write an expression for the total distance the body travels in terms of the variables Indicated.The velocities of a 3.0-kg object at and are and respectively. If the object is moving at constant acceleration, what is the force acting on it?A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of 5.0m/s2 and a downward component of 3.8m/s2 . Calculate the magnitude of the force on the rider by the sled. (Hint: Remember that gravitational acceleration must be considered.)Two forces are acting on a 5.0-kg object that moves with acceleration 2.0m/s2 in the positive y -direction. If one of the forces acts in the positive x -direction and has magnitude of 12 N, what is the magnitude of the other?Suppose that you are viewing a soccer game from a helicopter above the playing field. Two soccer players simultaneously kick a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 N at north of west. At the same instant, the second player kicks with force 215 N at east of south. Find the acceleration of the ball in and form.A 10.0-kg mass hangs from a spring that has the spring constant 535 N/m. Find the position of the end of the spring away from its rest position. (Use g=9.80m/s2 .)A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of 3.20 from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?At a circus, a donkey pulls on a sled carrying a small clown with a force given by . A horse pulls on the same sled, aiding the hapless donkey, with a force of The mass of the sled is 575 kg. Using and from for the answer to each problem, find (a) the net force on the sled when the two animals act together, (b) the acceleration of the sled, and (c) the velocity after 6.50 s.Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled . Let T1 be the tension in the leftmost section of the string, T2 , be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m,g , and . (b) Find the angle in terms of the angle . (c) If =5.10 , what is the value of ?(d) Find the distance x between the endpoints in terms of d and .A bullet shot from a rifle has mass of 10.0 g and travels to the right at 350 m/s. It strikes a target, a large bag of sand, penetrating it a distance of 34.0 cm. Find the magnitude and direction of the retarding force that slows and stops the bullet.An object is acted on by three simultaneous forces: F1=(3.00i+2.00j)N , F2=(6.00i4.00j)N , and F3=(2.00i+5.00j)N . The object experiences acceleration of 4.23m/s2 . (a) Find the acceleration vector in terms of m. (b) Find the mass of the object. (c) If the object begins from rest, find its speed after 5.00 s. (d) Find the components of the velocity of the object after 5.00 s.In a particle accelerator, a proton has mass 1.6710-27kg and an initial speed of 2.00105m/s . It moves in a straight line, and its speed increases to 9.00105m/s in a distance of 10.0 cm. Assume that the acceleration Is constant. Find the magnitude of the force exerted on the proton.A drone is being directed across a frictionless ice- covered lake. The mass of the drone is 1.50 kg, and its velocity is 3.00i m/s . After 10.0 s, the velocity is 9.00i+4.00j m/s . If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.Check Your Understanding Now calculate the scale reading when the elevator accelerates downward at a rate of 1.20m/s2 .Check Your Understanding Calculate the acceleration of the system, and the tension in the string, when the masses are andCheck Your Understanding Determine a general formula in terms of and for calculating the tension in the string for the Atwood machine shown above.Check Your Understanding The soccer player stops after completing the play described above, but now notices that the ball is in position to be stolen. If she now experiences a force of 126 N attempts to steal the ball, which is 2.00 m away from her, how long will it take her to get to the ball?Check Your Understanding Find the direction of the resultant for the 1.50-kg model helicopter.Check Your Understanding If atmospheric resistance is neglected find the maximum height for the mortar shell. Is calculus required for this solution?Check Your Understanding A block of mass 1.0 kg rests on a horizontal surface. The frictional coefficients for the block and surface are s=0.50and k=0.40 . (a) What is the minimum horizontal force required to move the block? (b) What is the block’s acceleration when this force is applied?Check Your Understanding The snowboarder is now moving down a hill with incline 10.0 . What is the skier’s acceleration.Check Your Understanding A car moving at 96.8 km/h travels around a circular curve of radius 182.9 m on a flat county road. What must be the minimum coefficient of static friction to keep the car from slipping?Check Your Understanding Find the terminal velocity of a 50-kg skydiver falling in spread-eagle fashion.Check Your Understanding suppose the resistive force the air on a skydiver can be approximated f=bv2 . If the terminal velocity of a 100-kg skydiver is 60 m/s, what is the value of b ?Solving Problems with Newton’s Laws To sirmulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at Why do they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness on orbit and in the aircraft?Friction The glue on a piece of tape can exert forces. Can these forces be a type of simple friction? Explain, considering especially that tape can stick to vertical walls and even to ceilings.When you learn to drive, you discover that you need to let up slightly on the brake pedal as you come to a stop or the car will stop with a jerk. Explain this in terms of the relationship between static and kinetic friction.When you push a pices of chalk across a chalkboard. It sometimes screeches because it rapidly altemates between slipping and sticking to the board. Describe this process in more detail, in particular, explaining how it is related to the face that kinetic is less than static friction. (The same slip-grap process occurs when tires screech on pavament.)A physics major is cooking breakfast en she notices that the frictional force between her steel spatula and Teflon trying pan is only 0.200 N. Knowing the coefficient of kinetic friction between the two materials, she quickly calculates the normal force. What is it?Centripetal Force If you wish to reduce the stress (which is related to centripetal force) on high-speed tires, would you use large- or small-diameter tires? Explain.Define centripetal force. Can any type of force (for example, tension, gravitational force, friction, and so on) be a centripetal force? Can any combination of forces be a centripetal force?If centripetal force is directed toward the center, why do you feel that you are ‘thrown’ away from the center as a car goes around a curve? Explain.Race car drivers routinely cut corners, as shown below (Path 2). Explain how this allows the curve to be taken at the greatest speed.Many amusement parks have rides that make vertical loops like the one shown below. For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What other force acts and what is its direction if: (a) The car goes over the top at faster than this speed? (b) The car goes over the top at slower than this speed?What causes water to be removed from clothes in a spin-dryer?As a skater forms a circle, what force is responsible for making his turn? Use a free-body diagram in your answer.Suppose a child is riding on a merry-go-round at a distance about halfway between its center and edge. She has a lunch box resting on wax paper, so that there is very little friction between it and the merry-go-round. Which path shown below will the lunch box take s1wn she lets go? The lunch box leaves a trail in the dust on the merry-go-round. Is that trail straight, curved to the left, or curved to the right? Explain your answer.Do you feel yourself thro to either side when you negotiate a curve that is ideally banked for your car’s speed? What is the direction of the force exerted on you by the car seat?Suppose a mass is moving in a circular path on a frictionless table as shown below. In Earth’s frame of reference, there is no centrifugal force pulling the mass away from the center of rotation, yet there is a force stretching the siring attaching the mass to the nail. Using concepts related to centripetal force and Newton’s third law; explain that force stretches the string, identifying its physical origin.When a toilet is flushed or a sink Is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the Northern Hemisphere. (Note that this is a small effect and in most toilets the rotation is caused by directional water jets.) Would the direction of rotation reverse if water were forced up the drain?A car rounds a curve and encounters a patch of ice with a very low coefficient of kinetic fiction. The car slides off the road. Describe the path of the car as it leaves the road.In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is an inertial force sensed and used by the riders to explain events in the rotating frame of reference of the barrel. Explain in an inertial frame of reference (Earth is nearly one) what pins the riders to the wall, and identify all forces acting on them.Two friends are having a conversation. Anna says a satellite in orbit is in free tall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in free fall because the acceleration due to gravity is not 9.80m/s2 . Who do you agree with and why?A nonrotating frame of reference placed at the center of the Sun is very nearly an inertial one. Why is it not exactly an Inertial frame?Athletes such as swimmers and bicyclists wear body suits In competition. Formulate a list of pros and cons of such suits.Two expressions were used for the drag force experienced by a moving object in a liquid. One depended upon the speed, while the other was proportional to the square of the speed. In which types of motion would each of these expressions be more applicable than the other one?As cars travel, oil and gasoline leaks onto the road surface. If a light rain falls, what does this do to the control of the car? Does a heavy rain make any difference?Why can a squirrel jump from a tree branch to the ground and nm away undamaged, while a human could break a bone in such a fall?Solving Problems with Newton’s Laws A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force Fso that the swing ropes are 30.0with respect to the vertical. (a) Calculate the tension in each of the two ropes supporting the swing under these conditions. (b) Calculate the magnitude of F .Find the tension in each of the three cables supporting the traffic light if it weighsThree forces act on an object, considered to be a particle, which moves with constant velocity . Two of the forces are and . Find the third force.A flea jumps by exerting a force of 1.2010-5Nstraight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 0.50010-6Non the flea while the flea is still in contact with the ground. Find the direction and magnitude of the acceleration of the flea if Its mass is 6.0010-7kg . Do not neglect the gravitational force.Two muscles in the back of the leg pull upward on the Achilles tendon, as shown below. (These muscles are called the mediaI and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?After a mishap, a 76.0-kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown here. Calculate the tension in the two ropes If the person is momentarily motionless. Include a free- body diagram in your solution.A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/ s in 2.30 s to join another dolphin in play. What average force was exerted to slow the first dolphin if it was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s. (a) What is his final speed? (b) How far does he travel?A large rocket has a mass of 2.00106kgat takeoff, and its engines produce a thrust of 3.50107N . (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust?A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110.0 kg.A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110.0 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as It goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.A 0.500-kg potato is fired at an angle of 80.0 above the horizontal from a PVC pipe used as a “potato gun” and reaches a height of 110.0 m. (a) Neglecting air resistance, calculate the potato’s velocity when it leaves the gun. (b) The gun itself is a tube 0.430 m long. Calculate the average acceleration of the potato in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the potato in the gun? Express your answer in newtons and as a ratio to the weight of the potato.