The apparatus shown in the figure below uses a spring to launch a small block al

Question

The apparatus shown in the figure below uses a spring to launch a small block along a track. A latch holds the block of mass M in place against the compressed spring (spring constant k) as shown. When the ring is raised the block is launched along the track. The parts of the track from A to B and from C to D can be considered frictionless for this problem. The part from B to C has significant friction (coefficient of sliding friction, ).

When the block is launched, it gets through the frictional part, rises up the ramp to the point D, a height h above the straight part of the ramp. It then slides back down. On its return, it gets to the point B and stops. For the items below choose the symbol that best completes the sentence: greater than (>); less than (<); equals (=), positive (+), negative (), zero (0). If none complete the sentence correctly, choose N.

(a) The potential energy stored in the spring just before the mass is released is  ---Select--- greater than (>) less than (<) equals (=) positive (+) negative (-) zero (0) none (N) the kinetic energy of the mass as it is reaches the point B for the first time.

(b) The potential energy stored in the spring just before the mass is released is  ---Select--- greater than (>) less than (<) equals (=) positive (+) negative (-) zero (0) none (N) the gravitational potential energy of the mass as it is reaches the point D. (Take the zero of gravitational PE at the level of the straight part of the track.)

(c) In the overall motion, the magnitude of the total work done by the frictional force is  ---Select--- greater than (>) less than (<) equals (=) positive (+) negative (-) zero (0) none (N) the magnitude of the total work done by the spring force.

(d) The total work done by the gravitational force throughout the whole motion is  ---Select--- greater than (>) less than (<) equals (=) positive (+) negative (-) zero (0) none (N) .

(e) The total work done by the friction force throughout the whole motion is ---Select--- greater than (>) less than (<) equals (=) positive (+) negative (-) zero (0) none (N) .

Explanation / Answer

(a) The potential energy stored in the spring just before the mass is released is equals (=) positive (+) the kinetic energy of the mass as it is reaches the point B for the first time.

(b) The potential energy stored in the spring just before the mass is released is greater than positive the gravitational potential energy of the mass as it is reaches the point D. (Take the zero of gravitational PE at the level of the straight part of the track.)

(c) In the overall motion, the magnitude of the total work done by the frictional force is less than negative the magnitude of the total work done by the spring force.

(d) The total work done by the gravitational force throughout the whole motion is negative.

(e) The total work done by the friction force throughout the whole motion is negative

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