Chapter 13, Problem 16P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A 0.250-kg block attached to a light spring oscillates on a frictionless, horizontal table. The oscillation amplitude is A = 0.125 m and the block moves at 3.00 m/s as it passes through equilibrium at x = 0. (a) Find the spring constant, k. (b) Calculate the total energy of the block-spring system. (c) Find the block’s speed when x = A/2.

a)

To determine
The spring constant of the spring.

Explanation

Given information: The mass of the block is 0.250 Kg. The amplitude is 0.125 m. The maximum velocity when it crosses the equilibrium position is 3.00â€‰ms-1 .

Explanation:

The total energy of the object-spring system at any instance is given by:

E=KE+PEs

Here,

E is the total energy of the system

KE is the kinetic energy of the system

PEs is the elastic potential energy of the system

The kinetic energy of the system is given by:

KE=12mv2

Here,

m is the mass of the system

v is the velocity of the system

The elastic potential of the system is given by:

PEs=12kx2

Here,

k is the force constant of the spring

x is the displacement of the spring from its equilibrium position

At the equilibrium position, the entire energy is stored as kinetic energy of the block and at the turning points the entire energy is stored in the form of elastic potential energy

b)

To determine
The total energy of the block-spring system.

c)

To determine
The block’s speed when x=A2 .

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