Simple Machines
Senior 2 · Physics
Simple Machines
Lesson 4 of 4
22 min
Let's begin
In many villages, water is drawn from a deep well by turning a handle that winds a rope round a drum. On a building site, a worker hauls a bucket of mortar up to the second floor with a rope over a pulley. A screwdriver, a steering wheel and a door handle hide the same machine. This lesson explains the wheel and axle and the pulley.
A wheel and axle is a large wheel (or handle) fixed to a smaller axle, so that both turn together. The effort is applied at the wheel (radius R), and the load is attached to the axle (radius r). In one turn, the effort moves 2πR and the load moves 2πr, so:
VR = R ÷ r
Worked example 1
a well windlass. The handle of a windlass turns in a circle of radius 0.40 m. The rope winds round an axle of radius 0.080 m. A bucket of water weighing 150 N is raised with an effort of 40 N.
Other examples include the screwdriver (handle = wheel, blade = axle), the steering wheel, the door knob and the bicycle pedal crank.
A pulley is a grooved wheel with a rope running over it.
A block and tackle with 4 pulleys (4 supporting rope sections) lifts an 800 N engine with an effort of 250 N.
The efficiency is below 100% because of friction in the pulley axles and because the effort must also lift the lower block. Adding more pulleys raises the VR, but it also adds friction and weight, so the efficiency usually falls.
Tip
Count the ropes that hold up the moving block: that number is the VR
For a wheel and axle, VR = big radius ÷ small radius. You can use diameters instead, as long as you use them for both.
A screwdriver handle has a radius of 1.5 cm and its shaft a radius of 0.30 cm. Find its VR.
Solution: VR = 1.5 ÷ 0.30 = 5.
A single movable pulley lifts a 400 N load with an effort of 250 N. Find the MA and the efficiency.
Solution: MA = 400 ÷ 250 = 1.6. VR = 2, so η = 1.6 ÷ 2 × 100% = 80%.
A pulley system has VR = 5 and efficiency 70%. What effort lifts a 700 N load?
Solution: MA = 0.70 × 5 = 3.5, so E = 700 ÷ 3.5 = 200 N.
What is the advantage of a single fixed pulley if it does not reduce the effort?
Solution: It changes the direction of the force. You can pull down, using your own weight, to raise a load up to a high floor.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
