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Gauss177

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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. 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: [tex]F = \pi r^2P[/tex]. 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.

Work = integral of Force

## Homework Statement

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: [tex]F = \pi r^2P[/tex]. 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.

## Homework Equations

Work = integral of Force

## The Attempt at a Solution

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