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A box too heavy to lift straight up can be pushed up a ramp. The ramp trades a big force over a short rise for a smaller force over a longer slope.
- An inclined plane helps move a heavy load to a higher level with less force. Pushing a load up a ramp of length L to height h : work F' × L = mgh (ignoring friction).
- So mg F' = L h , and since load = mg , effort = F' : mechanical advantage = mg F' = L h
- As L > h , the effort F' is less than mg , so the mechanical advantage is greater than 1. A longer, shallower ramp reduces the effort further.
In this Activity, we will pull a cart up planks of different steepness with a spring balance to see how the inclined plane reduces the force needed.
- Attach a spring balance to a cart. First lift the cart straight up to a stool about 0.5 m high and note the force (this equals the cart's weight).
- Now place a plank against the stool and pull the cart up slowly — is the reading smaller? Then make the plank less steep and repeat.
- The force needed decreases as the plank becomes less steep. But you must apply that smaller force over a larger distance to reach the same height.
- Inclined plane — a simple machine (a sloping surface) that helps move a heavy load to a higher or lower level with less force; mechanical advantage = L / h.
- The work done (force × displacement) is the same in all cases. If the force decreases, the displacement increases, so the total work done stays constant.
A ramp raises an object over a step 30 cm high and is 40 cm wide. What is its mechanical advantage?
By the right-angled triangle, ramp length
L
=
30
2
+ 40
2
= 50
cm
.
mechanical advantage
=
L
h
=
50
30
= 1.67
.
