Simple Machines
Senior 2 · Physics
Simple Machines
Lesson 3 of 4
20 min
Let's begin
The roads that climb Rwanda's hills do not go straight up. They zigzag back and forth. Workers loading heavy sacks onto a lorry push them up a sloping plank instead of lifting them. A mechanic raises a car with a screw jack. All three use the same idea: a gentle slope lets a small force do a big job over a longer distance.
An inclined plane is a sloping surface used to raise a load. You push the load along the slope (length l) instead of lifting it straight up through the height h.
VR = length of slope ÷ vertical height = l ÷ h
A longer, gentler slope has a bigger VR and needs less effort, but you must push further. Zigzag mountain roads, ramps for wheelchairs and loading planks are all inclined planes. A wedge (an axe head or a hoe blade) is a double inclined plane that is pushed into the material.
A 500 N sack of cement is pushed up a plank 3.0 m long onto a lorry bed 1.0 m high. The effort along the plank is 200 N.
A screw is an inclined plane wrapped round a cylinder. The distance between neighbouring threads is the pitch (p). In one full turn, the screw moves forward by one pitch, while the effort, applied at the end of a handle of radius r, moves round a circle of 2πr. So:
VR = 2πr ÷ p
Examples: bolts and nuts, wood screws, bottle tops, the bench vice and the car screw jack.
A screw jack has a handle of radius 0.30 m and a thread pitch of 5.0 mm (0.0050 m).
That high friction is useful: it stops the car from sinking back down when you let go of the handle.
Tip
Plane: VR = l ÷ h. Screw: VR = 2πr ÷ p
Put the pitch and the radius in the SAME unit (convert mm to m) before you divide. That is the most common slip in screw questions.
A ramp 5.0 m long rises 1.2 m. Find its VR, the ideal effort to push a 600 N load up it, and the efficiency if the real effort is 180 N.
Solution: VR = 5.0 ÷ 1.2 ≈ 4.2. Ideal effort = 600 ÷ 4.17 = 144 N. MA = 600 ÷ 180 = 3.33, so η = 3.33 ÷ 4.17 × 100% = 80%.
Why do roads up steep hills zigzag?
Solution: The zigzag makes the road longer for the same height gain. That makes the slope gentler (a larger VR), so vehicles need a smaller driving force to climb.
A bench vice has a handle of radius 0.15 m and a pitch of 2.0 mm. Find its VR.
Solution: VR = 2π × 0.15 ÷ 0.0020 ≈ 470.
Why is a screw described as an "inclined plane"?
Solution: Its thread is a sloping ramp wound round a cylinder. Turning the screw pushes the load up this spiral ramp.
Summary
Sources and credits
Written by Ganzaa.
