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A lightweight spring with spring constant k = 225 N/m is attached to a block of mass m1 = 4.50 kg on a frictionless, horizontal table. The block–spring system is initially in the equilibrium configuration. A second block of mass m2 = 3.00 kg is then pushed against the first block, compressing the spring by x = 15.0 cm as in Figure P16.77A. When the force on the second block is removed, the spring pushes both blocks to the right. The block m2 loses contact with the spring–block 1 system when the blocks reach the equilibrium configuration of the spring (Fig. P16.77B).
a. What is the subsequent speed of block 2?
b. Compare the speed of block 1 when it again passes through the equilibrium position with the speed of block 2 found in part (a).
77. (a) The energy of the system initially is entirely potential energy.
At the equilibrium position, the total energy is the total kinetic energy of both blocks:
Therefore, the speed of each block is
(b) Once the second block loses contact, the first block is moving at the speed found in part (a) at the equilibrium position. The energy 01 this spring-block 1 system is conserved, so when it returns to the equilibrium position, it will be traveling at the same speed in the opposite direction, or
FIGURE P16.77
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Chapter 16 Solutions
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
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