   Chapter 13, Problem 18P

Chapter
Section
Textbook Problem

A 0.40-kg object connected to a light spring with a force constant of 19.6 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine (a) the maximum speed of the object, (b) the speed of the object when the spring is compressed 1.5 cm, and (c) the speed of the object as it passes the point 1.5 cm from the equilibrium position. (d) For what value of x does the speed equal one-half the maximum speed?

a)

To determine
The maximum speed of the object.

Explanation

Given info: The mass of the block is 0.40kg . The force constant of the spring is 19.6Nm-1 . The spring is compressed to 4.00cm .

Explanation:

The total energy of the system is stored as kinetic energy when the system is in equilibrium position. When the block is in the turning points, the total energy is stored as the elastic potential energy of the system.

Hence, from the conservation of energy

12mvmax2=12kA2

Here,

vmax is the maximum velocity of the block

A is the amplitude of the oscillation

k is the force constant of the spring

m is the mass of the block

On re-arranging

vmax=kA2m

Substituting 19.6Nm-1 for k , 0.40kg for m and 4

b)

To determine
The speed of the object when the spring is compressed to 1.5cm .

c)

To determine
The speed of the object as it passes the point 1.5cm from the equilibrium position.

d)

To determine
The value of x for which the velocity is half the maximum velocity.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Children who don't drink milk often have lower bone density than than those who do? T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Describe four structural characteristics exhibited by most fatty acids.

Chemistry for Today: General, Organic, and Biochemistry

Describe how bone first develops.

Human Biology (MindTap Course List) 