Question
A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
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Answer to a math question A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
Jett
4.797 Answers
To determine the work done to compress the spring an additional 3 inches, we can utilize the formula for the elastic potential energy of a spring:
U = 1/2 * k * x^2
where:
U is the elastic potential energy (in inch-pounds)
k is the spring constant (in pounds per inch)
x is the compression or extension of the spring (in inches)
We know that a force of 750 pounds compresses the spring 3 inches, so we can deduce the spring constant:
750 pounds = k * 3 inches
k = 250 pounds per inch
Now, let's calculate the work done to compress the spring an additional 3 inches (from 3 inches to 6 inches):
U = 1/2 * 250 pounds per inch * (3 inches)^2
U = 1125 inch-pounds
Therefore, the work done to compress the spring an additional 3 inches is 1125 inch-pounds.
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