Section 6.6

Work

In physics, Work is Force * Distance. But what if the Force changes as you move? Or what if you are moving many things different distances (like water in a tank)? We use integrals.

Variable Force

For pumping liquids: Sum (Weight of Slice * Lift Distance).

Work Calculator

Worked Example: Springs

Hooke's Law

Force . It takes 10 N to stretch 0.1 m. Find work to stretch from 0 to 0.2 m.

1. Find k

2. Integral

3. Calculate

Joules.

Level Up Examples

Example A: Pumping Water

Cylindrical tank (r=2, h=5) full of water. Pump to top.

1. Slice Weight:

. Weight =

2. Lift Distance:

Slice at

(from bottom) must go to

. Dist =

3. Integrate:

Example B: Lifting a Chain

10m chain, 2 kg/m, hanging from roof. Lift to roof.