# A few work problems

1. Dec 13, 2006

### Gauss177

We recently covered work in my calculus class, and I'm confused on how to approach these problems. I know work is the integral of force, but I just don't know how to start these problems. Thanks for the help.

1. The problem statement, all variables and given/known data
1. If 6 J of work are needed to stretch a spring from 10 cm to 12 cm and another 10 J are needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?

2. A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mineshaft 500 ft deep. Find the work done.

3. When gas expands in a cylinder with radius r, the pressure at any given time is a function of the volume: P = P(V). The force exerted by the gas on the a piston (in the cylinder) is the product of the pressure and the area: $$F = \pi r^2P$$. Show that the work done by the gas when the volume expands from volume V1 to volume V2 is: W = Integral from V1 to V2 of P dV.

2. Relevant equations
Work = integral of Force

3. The attempt at a solution

Last edited: Dec 13, 2006
2. Dec 13, 2006

### StatusX

Start by writing the force as a function of distance.