Work and Friction

Force Parallel to Motion

Only the parallel force does work.W=Fd

Example: A force of 30 N is applied to a box over a distance of 15 meters. What is the work done?

Answer: W=FD; 450 J

Force Not Parallel

Ө

If Ө = 30° and the Force is 20 N. How far would the box move if 100J of work were expended?

Answer 5.77 meters.

Force going down

What is the same force is pointing down? How far will the block move? (We are neglecting friction)

Answer: 5.77 meters

Ө

Adding in Friction

Box weighs 20 N.θ = 30°F = 3 ND = 50 mIf the box is moving at a constant velocity, how much work does the Force do?How much work does friction do?

Ө

mg

F

F

How much work does the Force Do?

Remember, only the parallel forces do work. So…W = FdW = 50m ( 3N ) cos 30°W = 130 J

How much work does Friction do?

First, find Friction:F = µN = F cosθSo W = FdW = 50 ( 3N ) cos 30°W = 193.19 J

Pushing Force

Box weighs 20 N.θ = 30°F = 3ND = 50 mNow, how much work does the Force do?

Ө

mg

F

Solution

Once again, the velocity does not matter.W = FdFx = F cosθ

d = 50mW = 50m (3N) cos θW = 193.19 J

Friction Example

A 25 kg crate of chocolate is sitting on a loading. It needs to be pulled 10 meters to the store. The coefficient of kinetic friction between the box and the sidewalk is .22. How much work will a man exert if he pulls the box with a 60N force at an angle of 30°How much work will friction exert?What, if any, will be the acceleration of the box?

Solution

Ө

mg

F

N

We Start Solving

Since only the horizontal force contributes to work:Fx = F cosӨ

W = FdW = Fd cos θW = 10m (60) cos 30°W = 519.6 J

Friction’s Work

Find the normal force:N = mg – F sinӨF = μNF = μ(mg - FsinӨ)W = D *μ(mg - FsinӨ)W = 473 J

What is the acceleration?

Force going forward: F cos θFriction: µ (mg – F sinθ)Calculate each of these and find the differenceF cosθ = 60 cos 30°F = 52.0NFriction: .22 ( 25*9.8 – 60 sin 30° )Friction = 47.3NF = ma4.7 = 25 aa = .188 m/s2

Bonus Question

How fast is the box moving when it gets to the store?We get 1.93 m/s.

The End