College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 6, Problem 9CQ
As a skater forms a circle, what force is responsible for making her turn? Use a free body diagram in your answer.
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A car of mass m is negotiating a circular turn of radius R and speed v on a banked road with an angle of banking θ. The forces on the car are shown below. Ignore friction in this problem.
Draw a free body of the car.
Identify and show the radial direction. Pick coordinate axes with x pointing in the radial direction towards the center of the circle and y in the vertical direction. Show the coordinate axes on the free body diagram.
Set up Newton’s Laws in the radial and vertical direction. Which force provides the centripetal force?
Use the equations in part C to solve for the speed of the car in terms of R, Does the speed depend on the mass of the car?
If R=250.0 m, m=750.0 kg, calculate the speed of the car.
No need to solve. Just draw the free body diagram of the sphere and wedge that would help in solving the problem.
The truck in the figure is going around a circular track of radius 72 m, banked at a 60° angle. The centre of the circular track is to the left in the figure. A spider rests on the inside of the side window of the truck as shown. The coefficient of static friction between the truck window and the spider is 0.91. Find the maximum speed that the truck can have before the spider begins to slip down the window. Show your relevant free body diagram, and clearly show all your steps.
Chapter 6 Solutions
College Physics
Ch. 6 - There an analogy between rotational and physical...Ch. 6 - Can centripetal acceleration change the speed of...Ch. 6 - If you wish to reduce the stress (which related to...Ch. 6 - Define centripetal force. Can any type of force...Ch. 6 - If centripetal force is directed toward the...Ch. 6 - Pace car drivers routinely cut corners as shown in...Ch. 6 - A number of amusement parks have rides that make...Ch. 6 - What is the direction of the force exerted by the...Ch. 6 - As a skater forms a circle, what force is...Ch. 6 - Suppose a child is riding on a merry-go-round at a...
Ch. 6 - Do you feel yourself thrown to either side when...Ch. 6 - Suppose a mass is moving in a circular path on a...Ch. 6 - When a toilet is flushed or a sink is drained,...Ch. 6 - Is there a real force that throws water from...Ch. 6 - In one amusement park ride, riders enter a large...Ch. 6 - Actin at a distance, such as is the case for...Ch. 6 - Two friends are having a conversation. Anna says a...Ch. 6 - A frame of reference placed at the center of the...Ch. 6 - Action at a distance, such as is the case for...Ch. 6 - Two friends are having a conversation. Anna says a...Ch. 6 - Draw a free body diagram for a satellite in an...Ch. 6 - Newton's laws of motion and gravity were among the...Ch. 6 - In what frame(s) of reference are Kepler's laws...Ch. 6 - Semi-trailer trucks have an odometer on one hub of...Ch. 6 - Microwave ovens rotate at a rate of about 6...Ch. 6 - An automobile with 0.260 m radius tires travels...Ch. 6 - (a) What is the period of rotation of Earth in...Ch. 6 - A baseball pitcher brings his arm forward during a...Ch. 6 - In lacrosse, a ball is thrown from a net on the...Ch. 6 - A truck with 0.420-m-radius tires travels at 32.0...Ch. 6 - Integrated Concepts When kicking a football, the...Ch. 6 - Construct Your Own Problem Consider an amusement...Ch. 6 - A fairground ride spins its occupants inside a...Ch. 6 - A runner taking part in the 200 m dash must run...Ch. 6 - Taking the age of Earth to be about 4109 years and...Ch. 6 - The propeller of a World War Il fighter plane is...Ch. 6 - An ordinary workshop grindstone has a radius of...Ch. 6 - Helicopter blades withstand tremendous stresses....Ch. 6 - Olympic ice skaters are able to spin at about 5...Ch. 6 - What percentage of the acceleration at Earth's...Ch. 6 - Verify that the linear speed of an ultracentrifuge...Ch. 6 - A rotating space station is said to create...Ch. 6 - At takeoff, a commercial jet has a 60.0 m/s speed....Ch. 6 - Integrated Concepts Riders in an amusement park...Ch. 6 - Unreasonable Results A mother pushes her child on...Ch. 6 - (a) A 22.0 kg child is riding a playground...Ch. 6 - Calculate the centripetal force on the end of a...Ch. 6 - What is the ideal banking angle for a gentle turn...Ch. 6 - What is the ideal speed to take a 100 m radius...Ch. 6 - (a) What is the radius of a bobsled turn banked at...Ch. 6 - Part of riding a bicycle involves leaning at the...Ch. 6 - A large centrifuge, like the one shown in Figure...Ch. 6 - Integrated Concepts If a car takes a banked curve...Ch. 6 - Modern roller coasters have vertical loops like...Ch. 6 - Unreasonable Results (a) Calculate the minimum...Ch. 6 - (a) Calculate Earth's mass given the acceleration...Ch. 6 - (a) Calculate the magnitude of the acceleration...Ch. 6 - (a) What is the acceleration due to gravity on the...Ch. 6 - (a) Calculate the acceleration due to gravity on...Ch. 6 - The Moon and Earth rotate about their common...Ch. 6 - Solve part (b) of Example 6.6 using ac=v2/r.Ch. 6 - Astrology, that unlikely and vague pseudoscience,...Ch. 6 - The existence of the dwarf planet Pluto was...Ch. 6 - (a) The Sun orbits the Milky Way galaxy once each...Ch. 6 - Unreasonable Result A mountain 10.0 km from a...Ch. 6 - A geosynchronous Earth satellite is one that has...Ch. 6 - Calculate the mass of the Sun based on data for...Ch. 6 - Find the mass of Jupiter based on data for the...Ch. 6 - Find the ratio of the mass of Jupiter to that of...Ch. 6 - Astronomical observations of our Milky Way galaxy...Ch. 6 - Integrated Concepts Space debris left from old...Ch. 6 - Unreasonable Results (a) Based on Kepler's laws...Ch. 6 - Construct Your Own Problem On February 14, 2000,...
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- A 1600kg car moving on a flat, horizontal road negotiates a curve . If the radius of the curve is 40m and the coefficient of static friction between the tires and dry pavement is 0.65. a) Draw a free body diagram for the car . b) Calculate the maximum speed the car can have and still make the turn successfully.arrow_forwardA sport car moves around a banked curve at just the right constant speed v so that no friction is needed to make turn. During the turn, the driver (mass m) feels as though she weighs x times her actual weight. Find the magnitude of the net force on the driver during the turn in terms of m,g and x. Fnet? b) Find the radius of the turn.arrow_forwardA car making a turn on a dry, banked highway ramp is experiencing friction. The coefficient of static friction between the tires and the road is 0.60. The banking angle is 40° and the radius of the turn is 200 m. a) Draw a free-body diagram of the car. b) Determine the minimum speed at which the car can safely negotiate the turn without sliding down the ramp.arrow_forward
- A 5000 kg car is traveling in a horizontal circular path with a speed of 25 m/s on a banked curve. The radius of the curve is 60 m. Friction is negligible. a. Find the horizontal part of the normal force from the road acting on the car. b. Find the vertical part of the normal force from the road acting on the car.arrow_forwardA 55.0 Kg ice skater is moving at 4.00 m/s when she grabs the loose end of the rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.800 m around the pole. a) Determine the force exerted by the horizontal rope on her arms. b) Compare this force with her weight.arrow_forwardA car of mass m traveling at a speed vc enters a banked turn covered in ice. The road is banked at an angle theta, and there is no friction between the road and the car’s tires as shown in the figure below. You can assume that the acceleration due to gravity is given as g. Find the magnitude of the acceleration of the car around the turn.Express your answer in terms of known quantities such as m, vc, theta, and g.arrow_forward
- A car is going round a circular banked track at constant speed close to the maximum speed for the angle and friction coefficient of the track. Which of these is the correct free body diagram for the car? (a) (b) (C) (d) Select one: a. a b. b С. С d. darrow_forwardA 600 kg car is going around a banked curve with a radius of 110 m at a speed of 24.5 m/ s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction? Can you draw a free body diagram for this problem and expain it as well.arrow_forwardOn the ride “Spindletop” at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor dropped about 0.5 m. The people remained pinned against the wall without touching the floor. (a) Draw a force diagram for a person on this ride after the floor has dropped. (b) What minimum coefficient of static friction was required for the person not to slide downward to the new position of the floor? (c) Does your answer in part (b) depend on the person’s mass? (Note: When such a ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the wall to the floor.)arrow_forward
- A child of mass 25 kg rides on a Ferris wheel. The child moves in a vertical circle of radius. 10.0 m at a constant speed of 4.0 m/s. Find the normal force of the chair acting on the child when the child is at the top of the wheel. (Hint: Your answer should be smaller than mg.)arrow_forwardA car is traveling at a speed of 120 km/h and attempts to take a turn. The coefficient of friction of the tires on the dry asphalt is 0.90. Determine the difference in the radius of the turn if the road is horizontal or banked at 20º into the turn (but the car is still turning on the horizontal plane). Draw Free Body Diagrams that clearly show the components of the forces that you need. You must show how you get to any equations you use (i.e. derive them from your FBD)arrow_forwardCircular turns of radius r in a race track are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified. a.Find the y component of the normal force FN on a car going around the turn in terms of the angle θ and the magnitude of the normal vector FN. b. Find the x component of the normal force FN on a car going around the turn in terms of the angle θ and the magnitude of the normal vector FN. c. Now write the magnitude of the normal force in terms of the force of gravity Fg and the angle θ. d. Now write the magnitude of the normal force again, this time in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v. e.Now assume that the car is moving at 15 m/s and the radius of the track is 130 m. What is the angle θ in degrees?arrow_forward
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