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?
223
likes1114 views
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.
Frequently asked questions (FAQs)
What is the chain rule for the derivative of sin(3x^2) with respect to x?
+
What are the points of intersection between the graph of the tangent function, f(x) = tan x, and the x-axis?
+
Math question: Can the equation a^n + b^n = c^n be satisfied for integers a, b, c, and n such that n > 2?
+
New questions in Mathematics