   Chapter 13, Problem 5P

Chapter
Section
Textbook Problem

A biologist hangs a sample of mass 0.725 kg on a pair of identical, vertical springs in parallel and slowly lowers the sample to equilibrium, stretching the springs by 0.200 m. Calculate the value of the spring constant of one of the springs.

To determine
The spring constant of one of the springs.

Explanation

Given information: The mass of the sample is 0.725 kg. The springs stretch by 0.200 m.

Explanation:

Given information: The mass of the sample is 0.725 kg. The springs stretch by 0.200 m.

From Hooke’s law, the formula for the restoring force is,

F=kx (I)

• F is the force
• k is force constant of the spring
• x is the displacement of the spring

The force on the sample is equal to the force of gravity.

F=mg (II)

• m is the mass of the object
• g is the acceleration due to gravity

The force applied on the sample will be exactly equal to the negative of the restoring force. So from Equations (I) and (II),

kx=mgk=mgx

The sample is hung by two similar springs

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