   Chapter 13, Problem 25P

Chapter
Section
Textbook Problem

A vertical spring stretches 3.9 cm when a 10.-g object is hung from it. The object is replaced with a block of mass 25 g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

To determine
The force constant of the spring and period of the motion.

Explanation

Given info: The mass of the object is 10g . The spring stretches 3.9cm .

Explanation:

From Hooke’s law, the restoring force is,

F=kx

Here,

F is the force

k is force constant of the spring

x is the displacement of the spring

The force of gravity is,

F=mg

Here,

m is the mass of the object

g is the acceleration due to gravity

The magnitude of restoring force and force due to gravity will be same.

kx=mgk=mgx

Substituting 10g for m and 3.9cm for x to find the force constant k ,

k=(10g)(9.8ms-2)3.9cm=(0.010kg)(9.8ms-2)3.9×102m=2

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