General Notes

Work = Force x Distance

$$ W=∫(force)(distance)dx $$

• Separate what weights something down and how far that piece moves

1. Identify tiny piece of something (say a rope, water, etc)
2. Find force on that piece
3. Find distance moved
4. Multiply $dW=(force)(distance)$

EXAMPLE:

A tank is 10ft tall with a radius of 2ft and full of water. We want to pump water out of the top, find the amount of work required to do this.

1. Define x:

x= height above the bottom

• bottom is x=0
• top is x=10