   Chapter 13, Problem 15P

Chapter
Section
Textbook Problem

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m. (a) What is the spring constant? (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? (d) What is the speed of the block when its displacement is 0.160 m? (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.240 m on a rough surface so that it loses 14.0 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?

a)

To determine
The spring constant of a spring.

Explanation

Given info: The total mechanical energy of the block-spring system is 47.0 J. The maximum displacement from equilibrium is 0.240 m.

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 maximum displacement point the total energy is stored as elastic potential energy

b)

To determine
The kinetic energy of the system at equilibrium position.

c)

To determine
The mass of the block.

d)

To determine
The speed of the block.

e)

To determine
The kinetic energy of the block.

f)

To determine
The potential energy stored in the spring.

g)

To determine
The position of the first turning point of the block.

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