A spring exerts a force of 4x lbs when it is compressed a distance of x feet. How much work is required to compress the spring a distance of one inch?
The answer is 2
a = 0 (start of the spring)
b = 1
integrate 4x then plug in the limits (0 and 1)
Correction its not 2. It's 1/72 ft lbs
To find the work required to compress the spring a distance of one inch, we'll use the formula for work:
Work = Force × Distance
In this case, the force exerted by the spring is given as 4x pounds, and the distance to be compressed is given as x feet. However, we need to convert the distance to inches before calculating the work.
1 foot is equal to 12 inches, so x feet would be 12x inches.
Therefore, the work required to compress the spring a distance of one inch is:
Work = Force × Distance
= (4x pounds) × (12x inches)
= 48x^2 inch-pounds
So, the work required to compress the spring a distance of one inch is 48x^2 inch-pounds.