Work & Machines — Problem set, Grade 8

Explain how machines transfer energy, trade force for distance, and improve useful output.

Review the key ideas

Work: Transferring Energy with a Force

Work transfers energy when a force acts through a displacement. For aligned force and motion, W = F × d.

Levers, Ramps & Pulleys

Simple machines trade force for distance or change force direction; they do not create energy.

Mechanical Advantage

Mechanical advantage compares forces; energy accounting also requires distances.

Efficiency & Improving a Design

Efficiency is the useful share of input energy. Improving it means reducing unwanted transfers, not creating energy.

Power: The Rate of Energy Transfer

Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy. Useful powers are 30 W for A and 20 W for B.

Problem 1

Which condition is needed for simply using W=Fd?
Answer and explanation

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

The force must be constant and aligned with displacement for this simple positive-work calculation. Other directions require considering the component along displacement.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 2

Would the same horizontal displacement give work by a vertical force?
Answer and explanation

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work.

Not in this simple perpendicular-force case. Only the component along displacement contributes to that mechanical work.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 3

Visual-model chapter review: A box moves 4 m right under a constant 12 N rightward push and 3 N leftward resistance. Find each work contribution and net work.
Answer and explanation

Push +48 J; resistance −12 J; net +36 J in the stated aligned-force comparison.

Multiply each force by the common displacement and include direction.

Add the work contributions rather than adding force and energy units.

Push +48 J; resistance −12 J; net +36 J in the stated aligned-force comparison.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 4

Why can pushing farther from the pivot reduce the needed force?
Answer and explanation

A larger perpendicular distance gives a larger turning effect for the same force. A smaller force can then balance the same load turning effect.

A larger perpendicular distance gives a larger turning effect for the same force. A smaller force can then balance the same load turning effect.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 5

Why are these ramps not a scale drawing?
Answer and explanation

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning.

The drawn slopes and heights are arranged for readability. Use the stated 1 m, 2 m and 0.5 m dimensions for quantitative reasoning.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 6

Visual-model chapter review: For an ideal balanced lever, the load exerts 180 N at an arm 0.2 m long. The effort arm is 0.6 m. Find the effort force and explain its distance tradeoff.
Answer and explanation

Effort is 180×0.2/0.6 = 60 N. The effort end travels about three times the load-end distance for the small-motion ideal comparison; the lever does not create energy.

Match turning effects F×arm on opposite sides.

Connect the 3:1 arm ratio to effort travel as well as force.

Effort is 180×0.2/0.6 = 60 N. The effort end travels about three times the load-end distance for the small-motion ideal comparison; the lever does not create energy.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 7

Why distinguish ideal and actual mechanical advantage?
Answer and explanation

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

Ideal MA comes from a loss-free geometry model. Actual MA uses measured forces and can be lower because real machines have friction and other losses.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 8

Does force ratio 4 mean energy efficiency 400%?
Answer and explanation

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work.

No. Force is gained by trading displacement. The ideal energy efficiency here is 100%, with equal 12 J input and output work.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 9

Visual-model chapter review: A measured machine uses effort 20 N through 0.9 m to lift a 60 N load by 0.2 m. Find actual mechanical advantage and useful efficiency.
Answer and explanation

MA = 60/20 = 3. Input work 18 J; useful output 12 J; efficiency = 12/18×100 ≈ 66.7%.

Keep force ratio separate from work ratio.

Include both travel distances in the energy account.

MA = 60/20 = 3. Input work 18 J; useful output 12 J; efficiency = 12/18×100 ≈ 66.7%.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 10

What should you investigate after calculating efficiency above 100%?
Answer and explanation

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

Check units, boundaries, intervals, measurement errors, and any previously stored energy or omitted input. The calculation may not account for the complete energy supply.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 11

What should change if the purpose is heating rather than lifting?
Answer and explanation

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task.

Define the useful output again. Some thermal pathways previously called waste may count as useful for a heating task.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 12

Visual-model chapter review: A device receives 240 J, delivering 150 J to its defined useful output and 90 J to other changes. Find efficiency and explain what is wrong with calling the 90 J destroyed.
Answer and explanation

Efficiency = 150/240×100 = 62.5%. The other 90 J remains in other stores/transfers included in a complete account; usefulness is a job definition, not conservation.

Divide useful output by total input.

Account for every supplied contribution with the same energy units.

Efficiency = 150/240×100 = 62.5%. The other 90 J remains in other stores/transfers included in a complete account; usefulness is a job definition, not conservation.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 13

What information is missing to find input power?
Answer and explanation

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

The input energy or input power and the losses. Useful lifting power alone does not describe all energy entering the device.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 14

If A receives 400 J and B 300 J, which is more efficient?
Answer and explanation

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison.

A is 60% and B 80%. A has higher useful power but lower efficiency for this stated output and input comparison.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 15

Visual-model chapter review: A device transfers a useful 180 J in 3 s while receiving 240 J in that interval. Find useful average power and efficiency, then explain which changes if the same energy transfers take 6 s.
Answer and explanation

Useful power is 60 W and efficiency 75%. Taking 6 s reduces useful power to 30 W while the same energy ratio stays 75%.

Use energy/time for power and useful/input for efficiency.

Change only the interval in the second comparison.

Useful power is 60 W and efficiency 75%. Taking 6 s reduces useful power to 30 W while the same energy ratio stays 75%.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.
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