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š¬ A gentler climb
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.
What is the mechanical advantage of an inclined plane?
- 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 \(F' \times L = mgh\) (ignoring friction).
- So \( \dfrac{mg}{F'} = \dfrac{L}{h} \), and since load \(= mg\), effort \(= F'\): $$\text{mechanical advantage} = \dfrac{mg}{F'} = \dfrac{L}{h}$$
- 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.
Steps
- 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.
What you observe
- 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.
Important Definitions
- 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.
ā Note
- 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.
ā Example 7.12 — A person uses an inclined
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 \(L = \sqrt{30^2 + 40^2} = 50\ \text{cm}\).
\( \text{mechanical advantage} = \dfrac{L}{h} = \dfrac{50}{30} = 1.67 \).
