   Chapter 5, Problem 34P

Chapter
Section
Textbook Problem

A 35.0-cm long spring is hung vertically from a ceiling and stretches to 41.5 cm when a 7.50-kg weight is hung from its free end. (a) Find the spring constant. (b) Find the length of the spring if the 7.50-kg weight is replaced with a 195-N weight.

(a)

To determine
The spring constant.

Explanation

Given Info:

The actual length of the spring is 35.0cm .

The length of the spring after stretching is 41.5cm .

The weight hung on the spring is 7.50kg

The length that the spring stretched is the difference of length of stretched spring with actual length of the spring.

Thus,

The length to which the spring is stretched is 6.5cm .

The force acting upward on the spring is,

F=kx

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

The force acting down ward on the spring is,

F=mg

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

After hanging the weight on the spring, the force experienced on the spring is equal to the weight of the object hung on it.

Thus,

kx=mg

On re-arranging,

k=mgx

Substitute 7

(b)

To determine
The total length of the spring after stretching.

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