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8.5 More About Levers and Gears

GCSE Physics · AQA · Chapter 8: Forces in Balance

A free GCSE Physics lesson for AQA (8463) from OBA School: levers as force multipliers, gears and the wheel and axle (physics only). Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Explain how a lever acts as a force multiplier and how to tell whether it does
  • Calculate the force a lever exerts by equating moments
  • Describe how gears transmit a turning effect and calculate the moment on each gear (M = F × radius)
  • Explain why a small gear driving a large gear gives a bigger turning effect but a lower speed

Key words

  • Force multiplier: A device that exerts a larger force than the force applied to it.
  • Gear: A wheel with teeth that meshes with another gear to pass on a turning effect.
  • Driver gear: The gear that is turned by the motor, engine or pedals; it turns the driven gear.
  • Driven gear: The gear turned by the driver gear; it is on the output shaft.
  • Low gear: A small driver gear turning a larger driven gear: low output speed, large turning effect.
  • High gear: A large driver gear turning a smaller driven gear: high output speed, small turning effect.
  • Wheel and axle: A large wheel fixed to a narrow shaft (axle) so they turn together.

Levers as force multipliers

A lever multiplies a force when the effort acts further from the pivot than the force it has to overcome. Bottle openers, nutcrackers, scissors, pliers and wheelbarrows all work this way. Because the effort has a long perpendicular distance, a small effort produces a large moment; the lever then exerts a large force where the distance to the pivot is short.

Worked example: force on the nut

The nutcracker below is squeezed with an effort of 20 N, 15 cm from the hinge. The nut is 3.0 cm from the hinge.
Moment of the effort about the hinge = 20 N × 0.15 m = 3.0 N m
This moment is passed on to the nut, which is 0.030 m from the hinge:
force on nut × 0.030 m = 3.0 N m, so force on nut = 3.0 ÷ 0.030 = 100 N

Answer: 100 N – five times the effort, because the distance ratio is 15 cm : 3.0 cm = 5 : 1

Key fact: force exerted by lever × its distance from pivot = effort × distance of effort from pivot. The bigger the ratio of the distances, the bigger the multiplying effect.

How gears pass on a turning effect

Gears are toothed wheels that mesh together. Where the teeth touch, the two gears push on each other with equal and opposite forces (Newton’s third law). Each force acts along the edge of the gear (at right angles to the radius), so the perpendicular distance from each gear’s shaft is its radius:

moment on a gear = force at the teeth × radius of the gear (M = F d with d = radius, in metres)

Worked example: moments on two gears

The teeth push on each other with a force of 120 N. Radii: small gear 15 mm = 0.015 m; large gear 45 mm = 0.045 m.
Moment on small gear = 120 × 0.015 = 1.8 N m
Moment on large gear = 120 × 0.045 = 5.4 N m

Answer: the large gear has 3 times the turning effect (5.4 N m) but turns only once for every 3 turns of the small gear

Gears turn in opposite directions when they mesh directly. The larger gear has more teeth, so it turns more slowly: a 30-tooth gear turns once for every three turns of a 10-tooth gear.

Low gear and high gear

  • Arrangement; Low gear small gear on the engine shaft drives a large gear on the output shaft; High gear large gear on the engine shaft drives a small gear on the output shaft
  • Output speed; Low gear output shaft turns slower than the engine; High gear output shaft turns faster than the engine
  • Turning effect; Low gear larger moment on the output shaft; High gear smaller moment on the output shaft
  • Used for; Low gear starting off, climbing steep hills, towing; High gear cruising at high speed on a level road

A bicycle works the same way: the pedals turn the front sprocket and the chain pulls on a rear sprocket. Choosing a large rear sprocket puts the chain force further from the rear axle, giving a bigger moment on the back wheel for climbing hills.

Exam tip: To increase the turning effect, a small gear must drive a larger gear. You gain turning effect but lose speed.

The wheel and axle

A wheel and axle is like a pair of gears joined on one shaft. An effort pulling on the rim of the wheel (radius R) turns the axle (radius r), which winds up a rope carrying the load. If friction is negligible, effort × R = load × r, so the load can be much larger than the effort.

Worked example: a well winch

A winch has a handle (wheel) radius of 0.30 m and an axle radius of 0.050 m. It lifts a bucket of weight 240 N.
Ideal effort = load × r ÷ R = 240 × 0.050 ÷ 0.30 = 40 N

Answer: 40 N (a real winch needs a little more because of friction)

To investigate a wheel and axle, add known weights to the effort hanger until the load just starts to rise, then calculate load ÷ effort. Repeat for several loads. Wear eye protection and keep feet clear of falling masses.

Common mistakes

  • Saying a lever “creates energy” or “reduces the load”. It changes the size of a force by changing the distance from the pivot.
  • Using the diameter of a gear instead of its radius when calculating the moment.
  • Forgetting to change mm to m: 15 mm = 0.015 m.
  • Mixing up low and high gear: low gear means a small driver turning a large driven gear – slow but powerful turning.

Revision questions

Try these, then check your answers below each one.

Question 1. The teeth of a gear wheel of radius 0.050 m are pushed with a force of 60 N. Calculate the moment of the force on the gear.

Answer: 3 N m

Working: M = F × r = 60 × 0.050 = 3.0 N m.

Question 2. A force of 200 N acts at the edge of a gear wheel of radius 25 mm. Calculate the moment of the force in N m.

Answer: 5 N m

Working: r = 25 mm = 0.025 m. M = 200 × 0.025 = 5.0 N m.

Question 3. A car needs the biggest possible turning effect on its wheels to climb a steep hill. Which gear arrangement gives this? (Choose from: a small gear on the engine shaft turning a large gear on the output shaft, a large gear on the engine shaft turning a small gear on the output shaft, two gears of equal size.)

Answer: a small gear on the engine shaft turning a large gear on the output shaft

Working: Low gear: a small driver turns a large driven gear. The force acts at a larger radius on the driven gear, so its moment is larger (but it turns more slowly).

Related lessons

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This lesson is section 8.5 (AGCPH0805) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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