A 1440-kg crate of cabbages is laid on a level, frictionless track at the end of a heavy spring. The spring is compressed a distance of 0.100 m by a force of 83500 N. When the spring is released, it propels the crate. the spring constant of the spring equals 835000 N/m.
What is the total amount of work done by the spring on the crate during the launch in J?
To find the total amount of work done by the spring on the crate during the launch, we need to calculate the work done by the spring force.
The work done by a force is given by the formula:
Work = Force * Distance * cos(theta)
In this case, the force exerted by the spring is the spring force, which is defined by Hooke's Law:
Force = k * displacement
where k is the spring constant and displacement is the distance the spring is compressed or stretched.
Given that the spring constant is 835000 N/m and the spring is compressed by 0.100 m, we can calculate the force applied by the spring as:
Force = 835000 N/m * 0.100 m = 83500 N
The distance over which the spring force acts is the same as the distance the spring is compressed, which is 0.100 m.
So, the work done by the spring force is:
Work = Force * Distance * cos(theta)
= 83500 N * 0.100 m * cos(0°)
= 8350 J
Therefore, the total amount of work done by the spring on the crate during the launch is 8350 J.