Two identical blocks, A and B, on a surface of negligible friction are connected

Question

Two identical blocks, A and B, on a surface of negligible friction are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left. During the interval from t1, to t2: Is the work done on block A by the hand positive, negative, or zero? Explain. Is the work done on block B by the wall positive, negative, or zero? Explain. Let system X consist of block A, block B, and the spring. Write an expression for the net work done on system X by external forces in terms of the given quantities. Explain. Tutorials in Introductory Physics , Pearson McDermott, Shaffer, and the P.E.G., U. Wash. Work and changes in kinetic energy Block B is now removed, so that the right end of the spring is now directly in contact with the wall, as shown. During the interval from to t4, block A is again pushed a distance dA by a hand exerting a constant force FA. The wall exerts a force on the spring that varies with time but is always directed to the left. Consider the interval from t3 to t4: Let system Y consist of block A and the spring. Would you expect the net work on system Y by external forces during this interval to be greater than, less than, or equal to the net work by external forces on system X between t1 and t2? Explain. Write an expression for the work done on block A by the hand during this interval in terms of the given quantities. Explain. What is the displacement of the left end of the spring during this interval? W hat is the displacement of the right end of the spring during this interval? Which of these displacements should be used to calculate the work done on the spring by the wall? Explain. Is the work on the spring by the wall positive, negative, or zero? Write an expression for the net work done on system Y by external forces in terms of the given quantities. Explain. Is your answer for question b.iv consistent with your answers for questions b.i and a.iii? If it is consistent, explain how. If it is not consistent, resolve the inconsistency.

Explanation / Answer

a) We know that work done, w = F.s, where is the force and s is the displacement.

Here, displacement, dA and work done is in the same direction.

Hence, work done on the block A by the hand is positive.

b) Here, the displacement is zero as the block B is held in place by the wall.

Hence, work done is zero.

c) Net work done on the system = Fada.

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