Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
1st Edition
ISBN: 9781305259836
Author: Debora M. Katz
Publisher: Cengage Learning
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Chapter 16, Problem 77PQ

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.

E 0 = U 0 = 1 2 k y max 2 = 1 2 ( 225  N/m)(0 .150 m) 2 = 2.53  J

At the equilibrium position, the total energy is the total kinetic energy of both blocks:

1 2 ( m 1 + m 2 ) v 2 = 1 2 ( 4.50  kg + 3.00  kg) v 2 = ( 3.75  kg ) v 2 = 2.53  J

Therefore, the speed of each block is

v = 2.53  J 3.75  kg = 0.822  m/s

(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 v = 0.822  m/s .

Chapter 16, Problem 77PQ, A lightweight spring with spring constant k = 225 N/m is attached to a block of mass m1 = 4.50 kg on

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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