Speed (m/s) 6.00 8.00 10.0 12.0 14.0 16.0 Force (N) 8100 7690 7050 6100 5200 4200
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A road heading due east passes over a small hill. You
drive a car of mass m at constant speed v over the top of the hill, where
the shape of the roadway is well approximated as an arc of a circle with
radius R. Sensors have been placed on the road surface there to measure
the downward force that cars exert on the surface at various speeds. The
table gives values of this force versus speed for your car: Treat the car as a particle. (a) Plot the values in such a way that they
are well fitted by a straight line. You might need to raise the speed, the
force, or both to some power. (b) Use your graph from part (a) to calculate
m and R. (c) What maximum speed can the car have at the top of the
hill and still not lose contact with the road?
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- A student pushes a physics textbook of mass 1.15 kg across a table with a horizontal force of 5.48 Newtons. If the frictional force between the table and the textbook is 3.38 Newtons and the textbook was initially at rest, what is the speed of the textbook after 2.3 seconds? Remember to give your answer in metres per second and to at least 3 significant figures.A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.23 N/m3, i.e. the magnitude of the force on a particle can be written as 0.23r3, when the particle is at a distance r from the force center. Find the magnitude of the potential energy, in joules, of a particle subjected to this force when the particle is at a distance 0.21 m from point P assuming the potential energy to be zero when the particle is at P. PE= ?The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick mass was 0.14 g, its speed before entering the branch was 221 m/s, and its penetration depth was 17 mm. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick?
- A light plane of mass 1000kg makes an emergency landing on a short runway. With its engine off, it lands on the runway at a speed of 40m⋅s-1 . A hook on the plane snags a cable attached to a 120kg sandbag and drags the sandbag along. If the coefficient of friction between the sandbag and the runway is µk = 0.4, and if the plane’s brakes give an additional retarding force of magnitude 1400N, how far does the plane go before it comes to a stop?A cyclist competes in a one-lap race around a flat, circular course of radius 140 m. Starting from rest and speeding up at a constant rate throughout the race, the cyclist covers the entire course in 60 s. The mass of the bicycle (including the rider) is 76 kg. Find Ff,net, the magnitude of the net force acting on the cyclist at the finish line. What is the magnitude of the net force Fnet acting on the bicycle as it crosses the finish line?A woman at an airport is rolling her suitcase (mass = 20 kg) at an initial velocity of 1 m/s by pulling on a strap at an angle of 30° above the horizontal with a force of 33 N. The woman starts to speed up when she realizes that she is late for her flight. She pulls the suitcase over a distance of 50 m as she walks to her gate. What is the speed of the suitcase when she reaches her gate? (You can neglect friction in this problem. Give your answer in m/s.)
- A jet dives vertically at a speed v = 174 m/s, before pulling out of the dive along a circular arc. The pilot can survive an acceleration of a = 8.6 g. His mass is m = 91 kg. What is the minimum radius of the circular arc, in meters, that the pilot can make without injury? (Watch you sigfigs) I understand how to calculate this answer, but I need help determining the correct number of sig figs for the answer.Under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. When the drive force is shut off, the snowmobile coasts to a halt. The snowmobile and its rider have a mass of 143 kg. Under the influence of a drive force of 220 N, it is moving at a constant velocity whose magnitude is 4.38 m/s. The drive force is then shut off. Find (a) the distance in which the snowmobile coasts to a halt and (b) the time required to do so. (a) s= (b) t = i i + +In the very Dutch sport of Fierljeppen, athletes run up to a long pole and then use it to vault across a canal as shown in (Figure 1). At the very top of his arc, a 70 kg vaulter is moving at 2.9 m/s and is 5.5 m from the bottom end of the pole. What is the magnitude of the vertical force that the pole exerts on the vaulter? Express your answer with the appropriate units.
- A box, initially at rest, is pushed up a ramp that makes an angle of 15◦ with the horizontal as shown in the diagram. The magnitude of the pushing force is 8m newtons, where m is the mass of the box in kilograms. The force is in a direction parallel to and up the ramp. The coefficient of sliding friction between the box and the ramp is 0.25. Model the box as a particle and take the magnitude of the acceleration due to gravity to be g = 9.8 m s−2 . Express the four forces in component form in terms of unknown magnitudes where appropriate and find an expression for the resultant force acting on the box. Hence find the magnitude of the acceleration of the box, in m s−2The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick mass was 0.15 g, its speed before entering the branch was 212 m/s, and its penetration depth was 17 mm. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick? Number UnitsAir track: two objects tied together by a string. The figure shows a glider with mass my that moves on a level, frictionless air track in a physics lab. It is connected by a string passing over a small frictionless pulley to a hanging weight with total mass m₂. The string is light and flexible, and it doesn't stretch. (a) Find the acceleration of each object and the tension in the string. (b) What happens to the acceleration when m, is two times heavier than that of m₂? (c) Now my is four times heavier than that of m₂. Calculate the distance between it traveled during the initial period of two (2) seconds after the glider started moving. The tract is long enough for the travel. Show your work that leads to your answer. Explain each step in your work to explanation -quation WILIT T