Exam 8: Conservation of Energy

Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μ_k. At the highest point,

A 3.0-kg block is on a horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 12 N) acting parallel to the surface is applied to the block causing it to accelerate. The coefficient of kinetic friction between the block and the surface is 0.20. At what rate is the force P doing work on the block at t = 2.0 s?

A 2.0-kg mass is projected from the edge of the top of a 20-m tall building with a velocity of 24 m/s at some unknown angle above the horizontal. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass just before it strikes the ground?

A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m. The maximum angle the string makes with the vertical as the pendulum swings is 30°. What is the speed of the object at the lowest point in its trajectory?

A spring with spring constant k = 800 N/m is extended 12 cm from its equilibrium position. A spring with 6.0 cm extension from equilibrium will have the same potential energy as the first spring if its spring constant is

A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction?

A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800 kg mass along a frictionless surface. The mass reaches a surface area where μ_k = 0.400 and comes to a stop. The following student solution contains at least one error. What is the error?

The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in s. At what rate is the resultant force on this object doing work at t = 1 s?

A 2.0-kg block is projected down a plane that makes an angle of 20° with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest?

A large spring is used to stop the cars after they come down the last hill of a roller coaster. The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero. Compare the compression of the spring, x_A, for a fully loaded car with that, x_B, for a lightly loaded car when m_A = 2m_B.

As an object moves from point A to point B only two forces act on it: one force is nonconservative and does −30 J of work, the other force is conservative and does +50 J of work. Between A and B,

Starting from rest at t = 0, a 5.0-kg block is pulled across a horizontal surface by a constant horizontal force having a magnitude of 12 N. If the coefficient of friction between the block and the surface is 0.20, at what rate is the 12-N force doing work at t = 5.0 s?

A skier weighing 0.70 kN goes over a frictionless circular hill as shown. If the skier's speed at point A is 9.2 m/s, what is his speed at the top of the hill (point B)?

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50° with the vertical.

When an automobile moves with constant velocity the power developed is used to overcome the frictional forces exerted by the air and the road. If the power developed in an engine is 50.0 hp, what total frictional force acts on the car at 55 mph (24.6 m/s)? One horsepower equals 746 W.

A single conservative force F_x = (6.0x − 12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m?

Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μk. At the highest point,

Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are F_A and F_B, while the power supplied is respectively P_A and P_B. Which statement is correct?

A 1.6-kg block slides down a plane (inclined at 25° with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block?

As a result of friction between internal parts of an isolated system