Download Work and Friction

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
Ө
What is the same force is pointing down?
How far will the block move? (We are
neglecting friction)
Answer: 5.77 meters
Adding in Friction
F
Ө
F
mg
Box weighs 20 N.
θ = 30°
F=3N
D = 50 m
If the box is moving at a constant velocity, how much work
does the Force do?
How much work does friction do?
How much work does the Force
Do?
Remember, only the parallel forces do work.
So…
W = Fd
W = 50m ( 3N ) cos 30°
W = 130 J
How much work does Friction do?
First, find Friction:
F = µN = F cosθ
So W = Fd
W = 50 ( 3N ) cos 30°
W = 193.19 J
Pushing Force
F
Ө
mg
Box weighs 20 N.
θ = 30°
F = 3N
D = 50 m
Now, how much work does the Force do?
Solution
Once again, the velocity does not matter.
W = Fd
Fx = F cosθ
d = 50m
W = 50m (3N) cos θ
W = 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
N
Ө
F
mg
We Start Solving
Since only the horizontal force contributes to
work:
Fx = F cosӨ
W = Fd
W = Fd cos θ
W = 10m (60) cos 30°
W = 519.6 J
Friction’s Work
Find the normal force:
N = mg – F sinӨ
F = μN
F = μ(mg - FsinӨ)
W = D *μ(mg - FsinӨ)
W = 473 J
What is the acceleration?
Force going forward: F cos θ
Friction: µ (mg – F sinθ)
Calculate each of these and find the difference
F cosθ = 60 cos 30°
F = 52.0N
Friction: .22 ( 25*9.8 – 60 sin 30° )
Friction = 47.3N
F = ma
4.7 = 25 a
a = .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