Chapter 7

A potential energy function for system 1 is given by U1(x) = Cx2 + Bx3. The potential energy function for system 2 is given by U2(x) = A + Cx2 + Bx3, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

The force is identical on the two systems

Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct?

) Ball B will go four times as high as ball A because it had four times the initial kinetic energy

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

All of the above statements are true

Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true?

At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy.

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Block 2 is faster.

Is it possible for a system to have negative potential energy?

Yes, since the choice of the zero of potential energy is arbitrary.

Two objects are moving at equal speed along a level, frictionless surface. The second object has twice the mass of the first object. They both slide up the same frictionless incline plane. Which object rises to a greater height?

The two objects rise to the same height.

When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not change

True

A ball drops some distance and loses 30 J of gravitational potential energy. Do NOT ignore air resistance. How much kinetic energy did the ball gain?

less than 30 J

A ball drops some distance and gains 30 J of kinetic energy. Do NOT ignore air resistance. How much gravitational potential energy did the ball lose?

more than 30 J

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2m

the lighter box will go twice as high up the incline as the heavier box.