Work and Inclined Planes
Work Review
W = Fd
Example: How much work is done in the
picture below?
30 N
10 m
Answer: 300J
Going Straight Up
How much work is done lifting the small box
to the top of the tower.
●
12 m
5 kg
Solution
The force is g.
So W = mgh
W = 5 * 9.8 * 12
W = 588J
Going Down a Slide
Find the amount of work done.
●
5 kg
6m
30°
Solution (Hard Way)
Find the distance
h = d sinθ
d= h
sinθ
Find the Force
F = mg sin θ
W = Fd = mg sin θ * h
sin θ
W = mgh
Which Brings us to the Easy
Way
Just use mgh, and you will have a direct
route to the answer.
Answer: 25 * 9.8 * 3.0
= 735 J
Going up a Ramp
Which takes more work, lifting an object
straight up, or pushing an object up a ramp?
5m
5m
5 kg
5 kg
30 °
Answer Part I
Let’s calculate lifting an object straight up:
W = mgh
W = 5 * 9.8 * 5
W = 245 J
Answer Part II
Going up a ramp:
W = Fd
F = mg sin θ
d = h/sin θ
Multiply and the sin’s cancel.
We get W = mgh, which is what we had
before
Practice
Roger is loading a truck. The bed of the
truck is .75 m off the ground. If he lifts a
75kg chair into the truck, how much work
has he done?
Solution: W = mgh
W = .75 * 9.8 * 75
W = 551.25 J
In Conclusion
Bear in mind
This is without friction
With friction things get a lot more messy
But that’s a different workshop.
The End