A force of 1300 lb compresses a spring from its natural length of 16 in to a length of 10 in. How much work is done in compressing it from 10 in to 6 in?
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To find the work done in compressing the spring from 10 inches to 6 inches, we can use the formula:
Work = (1/2)k(x_final^2 - x_initial^2)
Where:
- Work is the amount of work done in compressing the spring
- k is the spring constant (a measure of the stiffness of the spring)
- x_final is the final displacement of the spring from its natural length
- x_initial is the initial displacement of the spring from its natural length
Given that the spring is initially compressed from its natural length (16 inches) to 10 inches, and the force applied is 1300 pounds, we can calculate the spring constant as follows:
Force = k * (x_final - x_initial)
1300 lb = k * (10 in - 16 in)
1300 lb = k * (-6 in)
Dividing both sides by -6 inches, we get:
-216.67 lb/in = k
Now we can calculate the work done in compressing the spring from 10 inches to 6 inches using the formula:
Work = (1/2)k(x_final^2 - x_initial^2)
Work = (1/2) * (-216.67 lb/in) * (6 in^2 - 10 in^2)
Work = (1/2) * (-216.67 lb/in) * (-36 in^2)
Work = 3888.06 lb*in
Therefore, the work done in compressing the spring from 10 inches to 6 inches is 3888.06 lb*in.