Question

A spring has a natural length of 8 in. If it takes a force of 10 lb to compress the spring to a length of 6 in., how much work is required to compress the spring from its natural length to 7 in.

Answer 1

The work required to compress the spring from its natural length to 7 inches is 2.5 lb*in.

Step-by-step explanation:

To calculate the work required to compress the spring from its natural length to 7 inches, we need to determine the spring constant, k.

Since we know that it takes a force of 10 lb to compress the spring to a length of 6 inches, we can use the formula F = -kx (where F is the force, k is the spring constant, and x is the displacement) to find the spring constant.

Plugging in the values, we have -10 lb = k * (6 in - 8 in), which simplifies to -10 lb = -2k lb*in. Solving for k, we get k = 5 lb/in.

Next, we can calculate the work required to compress the spring from its natural length to 7 inches using the formula for work done by a spring force: W = (1/2)kx^2. Plugging in the values, we have W = (1/2) * 5 lb/in * (7 in - 8 in)^2 = (1/2) * 5 lb/in * (-1 in)^2 = 2.5 lb*in.

Therefore, it takes 2.5 lb*in of work to compress the spring from its natural length to 7 inches.

Answer 2

Answer: Required workdone is 5 lb.in

Explanation: Force acting on a spring is given by the relation,

F = -Kx

Here, K is the spring constant

x is the compression or expansion in spring

- Ve sign shows the direction of spring force is opposite to the externally applied force.

Natural length of spring = 8 inches

For final position of spring after compression = 6 inches

Force required to compress the spring by 2 inches (8 - 6 inches) is 10 lb

F = -Kx

10 = -K
`*` 2

K = 5 lb/in

If the final position is 7 in i.e. compression by 1 in (8 - 7 in)

F = -Kx = - 5
`*` 1 = - 5 lb (-Ve sign shows the direction of spring force is outward)

Work done = Force
`*` Displacement

WD = 5
`*` 1 = 5 lb.in