Exam 7: Conservation of Energy

A conservative force on a particle moving along the x axis is given by $\overrightarrow{\mathbf{F}}=\left(3 x^{2}-2 x\right) \tilde{\mathbf{i}}$ . Which of the following is a potential that is associated with this force?

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

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

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 spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm?

A cricket wicketkeeper throws a cricket ball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30 $\degree$ . What is the kinetic energy of the cricket ball at the highest point of the trajectory?

A particle is acted upon by only two forces, one conservative and one non-conservative and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if:

For a force to be a conservative force, when applied to a single test body:

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 $\degree$ with the vertical.

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

A rain cloud contains 2.66 * 107 kg of water vapour. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2000 m?

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

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 FA and FB, while the power supplied is respectively PA and PB. Which statement is correct?

A 2.0-kg block is projected down a plane that makes an angle of 20 $\degree$ 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?

Which of the following is a conservative force? (All refer to a car on a slope.)

A pendulum bob has potential energy U0 when held taut in a horizontal position. The bob falls until it is 30 $\degree$ away from the horizontal position, when it has potential energy UA. It continues to fall until the string is vertical, when it has potential energy UB. Compare its potential energies at O, A, and B.

An astronaut tosses a ball out in space where gravitational forces may be neglected. What will happen to the ball?

The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct?