Aforce of 6 lb is required to hold a spring stretched 4 in. beyond its natural length. how much work w is done in stretching it from its natural length to 8 in. beyond its natural length?

Force causes motion in a body. The amount of work needed to stretch the spring  8 in. beyond its natural length is 48 lb·in.

Force is defined as the influence under which a body is in motion. It is given by the formula,

F = m x a

m = mass of the object,

a = acceleration of the object

Given to us

Force required, F = 6 lb

displacement, x = 4 in.

We know that the force for spring is given by the formula,

F = k · x

where F is the force,

k is the spring constant

x = displacement of the spring from its initial position

Substitute the values,

F = k · x

6 = k · 4

k = 1.5 lb\in

We know that work is written as the amount of force that is needed to distance an object,

W = F · dx

As we know the spring constant of the spring now, substitute all the values,

Hence, the amount of work needed to stretch the spring 8 in. beyond its natural length is 48 lb·in.

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Explanation and

Given:

6 lb is needed to stretch 4 inches beyond natural length.

Need work done to stretch same string from natural length to 8 inches.

Solution:

string stiffness, K

= Force / stretched distance

= 6 lb / 4 inches

= 1.5 lb/inch

Work done on a string of stiffness K

= (Kx^2)/2 lb-in

= 1.5 lb/in *(8 in)^2)/2

= 48 lb-in.