# A force of 250 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 20 centimeters to 50 centimete

Question

A force of 250 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 20 centimeters to 50 centimeters?

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1 year 2021-09-02T02:20:27+00:00 1 Answers 0 views 0

Work done = 87.5 J

Explanation:

Given:

Force required to stretch the spring (F) = 250 N

Extension of the spring (x) = 30 cm = 0.30 m     [1 cm = 0.01 m]

So, spring constant (k) of the spring is given as:

$$k=\frac{F}{x}\\\\k=\frac{250\ N}{0.30\ m}=833.33\ N/m$$

Also given:

Initial length of the spring (x₁) = 20 cm = 0.20 m

Final length of the spring (x₂) = 50 cm = 0.50 m

Now, work done in stretching the spring from an initial length (x₁) to final length (x₂) is given as:

$$W=\frac{1}{2}k(x_2^2-x_1^2)$$

Plug in the given values and solve for ‘W. This gives,

$$W=\frac{1}{2}\times \frac{250}{0.3}\times (0.50^2-0.20^2)\\\\W=\frac{1250}{3}\times (0.25-0.04)\\\\W=\frac{1250\times 0.21}{3}=87.5\ J$$

Therefore, work is done in stretching the spring from 20 centimeters to 50 centimeters is 87.5 J