Which one of the answer choices INCORRECTLY describes the system at the instant

Question

Which one of the answer choices INCORRECTLY describes the system at the instant that the block is passing through its equilibrium position ? a. the block has its maximum speed; b. the net force acting on the block is zero; c. the total mechanical energy of the system is in the form of kinetic energy; d. the acceleration of the block is zero; e. the total mechanical energy of the system is in the form of elastic (i.e. spring) potential energy; 15. Let M = 10 kg and k = 1000 N/m. At time t = 0, the block is at its equilibrium position and has a velocity of 5 m/sec in the +x direction. What is the velocity of the block at the instant t = 1 sec ? a. 4.2 m/sec in the +x direction b. 2.7 m/sec in the -x direction c. 3.5 m/sec in the -x direction d. 4.2 m/sec in the -x direction e. 2.7 m/sec in the +x direction

Explanation / Answer

14. e

   At equilibrium position, elastic potential energy is zero.

15. d

   x = A sin(wt).
w = sqrt(K/M) = sqrt(1000/10) = 10 rad/s
   Aw = 5 m/s => A = 5/10 m= 0.5 m
V = Aw cos(wt) = 0.5x 10 cos(10x1) = - 4.195 m/s

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