Question

A force of 13 lb is required to hold a spring stretched 6 in. beyond its natural length. How much work W is done in stretching it from its natural length to 9 in. beyond its natural length?

Answer 1

To calculate the work done by a spring force, we can use the formula W = (1/2) k (x2^2 - x1^2), where W is the work done, k is the spring constant, x2 is the final displacement, and x1 is the initial displacement. Given that a force of 13 lb is required to hold the spring stretched 6 in. beyond its natural length, the spring constant can be calculated as k = 13/6 lb/in. We can then use this spring constant to calculate the work done in stretching the spring from its natural length to 9 in. beyond its natural length.

Step-by-step explanation:

To calculate the work done by a spring force, we can use the formula:

W = (1/2) k (x22 - x12)

Where W is the work done, k is the spring constant, x2 is the final displacement, and x1 is the initial displacement.

Given that a force of 13 lb is required to hold the spring stretched 6 in. beyond its natural length, we can calculate the spring constant as follows:

13 lb = k * 6 in.

Converting lb to lb/in., we have:

13 lb/in. = k * 6 in.

Solving for k, we get:

k = 13/6 lb/in.

Now, we can calculate the work done in stretching the spring from its natural length to 9 in. beyond its natural length:

W = (1/2) * (13/6 lb/in.) * ((9 in.)2 - (6 in.)2)

Using the given conversions:

1 lb/in. = 386.088 N/m

1 in. = 0.0254 m

We can convert the units and calculate the value of W.