The Inclined Plane

An inclined plane is a flat surface tilted at an angle. It reduces the force needed to lift an object by spreading the work over a longer distance.

What Is an Inclined Plane?

An inclined plane is a ramp — a flat, tilted surface. It is one of the six classical simple machines.

An object of weight W on a ramp of length L and height h. The effort F is less than W.

The Mechanical Advantage

Using a ramp reduces the required force:

Mechanical Advantage — Inclined Plane

MA = \frac{L}{h} = \frac{W}{F}

L = length of ramp, h = height, W = weight of object, F = force needed along the ramp.

A longer ramp (same height) → greater mechanical advantage → less effort needed.

Conservation of Work

Using a simple machine does not reduce the total work done:

$W_{in} = W_{out}$

$F \times L = W \times h$

Note You trade force for distance — push with less force but over a longer path. Total work is the same.

Real-World Examples

Ramps for wheelchairs
Screws (a screw is a rolled-up inclined plane)
Mountain roads that zig-zag

A ramp 5 m long rises 1 m. What force is needed to push a 200 N box to the top?

$MA = \frac{L}{h} = \frac{5}{1} = 5$

$F = \frac{W}{MA} = \frac{200}{5} = 40 \text{ N}$

Real world: Loading ramp at a warehouse

A delivery worker needs to roll a 600 N trolley into a truck bed 1.2 m above ground. The loading ramp is 4.8 m long.

$MA = \frac{L}{h} = \frac{4.8}{1.2} = 4$

$F = \frac{W}{MA} = \frac{600}{4} = 150 \text{ N}$

Instead of lifting 600 N straight up, the worker only pushes with 150 N along the ramp — four times less effort.

Real world: Wheelchair accessibility ramp

Building regulations often require a maximum ramp slope of 1:12 — for every 1 m of height, the ramp must be at least 12 m long. This gives:

$MA = \frac{12}{1} = 12$

A person in a wheelchair weighing 900 N total would require only 75 N of push force — roughly the weight of a small bag.

Real world: Wood-splitting wedge

A wedge is a double-sided inclined plane. When an axe (wedge) is driven into a log, the downward striking force is redirected outward, splitting the wood apart. A sharper, longer wedge (greater MA) splits wood with less force but requires driving deeper.

Tip Where do you see this in real life? Look for ramps everywhere — car park ramps, skateboard half-pipes, escalator bases, and even the thread of a screw. Every time a slope helps you move something upward with less effort, an inclined plane is at work.

Practice Problems

A ramp has mechanical advantage 4. How long is it if the height is 2 m?

Show answer

MA = L/h → 4 = L/2 → L = 8 m.

Why do mountain roads zig-zag instead of going straight up?

Show answer

A zig-zag path is like a longer ramp — it increases the distance, reducing the force (gradient) needed.