Suppose that 4 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 47 cm. (a) How much work is needed to stretch the spring from 41 cm to 45 cm? (Round your answer to two decimal places.) J (b) How far beyond its natural length will a force of 15 N keep the spring stretched? (Round your answer one decimal place.)

Explanation:

Work done on a spring is expressed as

k is the elastic constant

e is the extension of the material

If 4 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 47 cm, then;

Work done = 4J and the extension e = 47 cm - 36 cm; e = 11 cm

11cm = 0.11m

Substituting the given values into the equation above to get the elastic constant;

a) In order to determine the amount of work needed work is needed to stretch the spring from 41 cm to 45 cm, wre will use the same formula as above.

b) According to hooke's law, F = ke where F is the applied force

We are to get the extension when a force of 15N is applied to the original length of the material.

e = F/k

e = 15/661.16

e = 0.02 m (to 1 d.p)

This means that the natural length of the spring will be stretched by 0.02 m when a force of 15N is applied to it.

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