Work & Machines — Chapter Practice, Grade 8

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

Problem 1

A 5 N force moves a cart 4 m in the same direction. Find its work.
Answer and explanation

20 J

5 × 4 = 20.

Problem 2

You push a wall that remains still. Mechanical work on the wall is…
  1. zero
  2. equal to your mass
  3. always 100 J
  4. infinite
Answer and explanation

zero

The wall has no displacement.

Problem 3

Why can you feel tired while holding a heavy bag still although no mechanical work is done on the stationary bag?
Answer and explanation

Your body uses chemical energy, but the bag has no displacement. The objects and energy transfers being considered differ.

Problem 4

A horizontal 15 N force moves a box 4 m in the same direction. Find the work; compare with holding it still. Explain the reasoning in your own words.
Answer and explanation

60 J while moving; 0 J on the stationary box by the supporting force.

Use W=Fd=15×4=60 J.

With zero displacement, mechanical work on the stationary box is zero.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 5

A 12 N aligned force moves a toy 3 m. Find work. Show the reasoning, not just the conclusion.
Hints

A force without displacement transfers no mechanical work to the object in this simple model.

Answer and explanation

W=12×3=36 J.

Problem 6

A box moves horizontally while its weight acts vertically. What work does weight do over that horizontal displacement?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Zero in this ideal case, because force and displacement are perpendicular.

Problem 7

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 8

A supplied object moves 3 m horizontally while a 4 N force acts in that direction. In another case a person holds the object still with an upward force. Find the work in the first case and explain the ideal mechanical work in the second. Clarify the everyday meaning of effort.
Answer and explanation

The first force transfers 4×3=12 J through the aligned displacement. For the chosen held object, no displacement means zero ideal mechanical work by the holding force. The person may still use metabolic energy to maintain muscle activity. Everyday effort and the technical force–displacement quantity answer different questions.

The first force transfers 4×3=12 J through the aligned displacement. For the chosen held object, no displacement means zero ideal mechanical work by the holding force. The person may still use metabolic energy to maintain muscle activity. Everyday effort and the technical force–displacement quantity answer different questions.

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

Opposite forces make different contributions to workOpposite forces make different contributions to workmoving boxDisplacement: 3 m rightPush: 10 NResistance: 4 NPush work: +30 J. Resistance work: −12 J. Net work: +18 J.Forces and displacement are distinct arrows with distinct units.
For the stated constant aligned forces over 3 m rightward displacement, the push does +30 J of work and resistance does −12 J on the box. Their net contribution is +18 J. A red force arrow is not the same quantity as the blue displacement arrow. The diagram omits vertical interactions that do no work in this horizontal idealization.
For this unit’s illustrated case, if resistance becomes 6 N over the same 3 m, what happens to its work and to the net work?
Answer and explanation

Resistance work becomes −18 J; the push remains +30 J, so net work is +12 J. Work signs depend on the force direction relative to displacement.

Positive work transfers energy into the chosen object through that force; negative work transfers energy out through that force in this account. Add contributions only after their directions and common displacement are clear.

Resistance work becomes −18 J; the push remains +30 J, so net work is +12 J. Work signs depend on the force direction relative to displacement.

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

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 11

A longer ramp to the same height usually trades…
  1. more force for less distance
  2. less force for more distance
  3. zero work for motion
  4. mass for energy
Answer and explanation

less force for more distance

The force acts over a longer distance.

Problem 12

A lever pivots around a…
  1. battery
  2. fulcrum
  3. magnetic pole
  4. wavelength
Answer and explanation

fulcrum

The fulcrum is its pivot.

Problem 13

Does a fixed pulley necessarily reduce the size of the force needed?
Answer and explanation

No. An ideal fixed pulley can redirect the force while leaving its size unchanged.

Problem 14

An ideal ramp raises a 60 N load by 0.5 m over a 3 m path. Find output work and ideal input force. Explain the reasoning in your own words.
Answer and explanation

30 J of output work and 10 N ideal effort, ignoring friction.

Output work=60×0.5=30 J.

Ideal input work is also 30 J; force=30/3=10 N.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 15

An ideal pulley uses two supporting rope segments for a 60 N load. Find pulling force during a slow lift. Show the reasoning, not just the conclusion.
Hints

Both ideal methods transfer 100 J; the ramp does not create energy.

Answer and explanation

60/2=30 N, with the free end moving twice the load's distance.

Problem 16

Why does a real rough ramp require more than the ideal predicted force?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Friction transfers some input energy to thermal energy, so input work must exceed the load's gravitational-energy increase.

Problem 17

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 18

Illustrative ideal ramps raise the same load by 0.5 m. Ramp A is 1 m long and B 2 m long; measured input forces are 20 and 10 N under the simplified no-loss model. Compare input work and explain the force–distance trade-off. State why actual friction would change the required input.
Answer and explanation

Both have modeled input work 20 J: 20×1 and 10×2. The longer ramp reduces force while increasing travel distance for the same lift; it does not make energy. Actual friction can require greater input work and introduce thermal transfers. The simple along-ramp calculation uses the stated force direction and ideal model.

Both have modeled input work 20 J: 20×1 and 10×2. The longer ramp reduces force while increasing travel distance for the same lift; it does not make energy. Actual friction can require greater input work and introduce thermal transfers. The simple along-ramp calculation uses the stated force direction and ideal model.

Response criteria

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

Problem 19

A lever trades force against its distance from the pivotA lever trades force against its distance from the pivotEffort: 75 N downLoad on lever: 300 N downPivot support upArm: 4 m1 mTurning effects: 75×4 = 300×1. Forces shown act on the lever.
The ideal lever is balanced when the 75 N effort acts 4 m from the pivot and the 300 N load force acts 1 m from it. The turning effects match even though the forces differ. Both downward red arrows are forces on the lever; its upward force on the load is a different receiver’s force. Arrow lengths are qualitative here, while the arm distances and force labels supply the calculation.
For this unit’s illustrated case, why can the smaller effort balance the larger load force? Would moving the effort closer to the pivot keep the same balance?
Answer and explanation

Its arm is four times as long: 75×4 = 300×1. Moving the effort closer reduces its turning effect, so a larger effort would be needed under the same ideal conditions.

The pivot is the turning point. A force’s perpendicular distance from it affects turning. The lever does not create energy; during a small movement the long effort end travels farther than the short load end.

Its arm is four times as long: 75×4 = 300×1. Moving the effort closer reduces its turning effect, so a larger effort would be needed under the same ideal conditions.

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 20

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 21

A machine provides 45 N output for 15 N input. Find actual mechanical advantage.
Answer and explanation

3

45 ÷ 15 = 3.

Problem 22

An ideal ramp is 3 m long and 1 m high. Find ideal mechanical advantage.
Answer and explanation

3

Length ÷ height = 3 ÷ 1.

Problem 23

Why might a real ramp need more force than an ideal calculation predicts?
Answer and explanation

Friction opposes movement and transfers some energy to thermal energy.

Problem 24

A machine lifts a 120 N load with 40 N effort. Find actual mechanical advantage. Explain the reasoning in your own words.
Answer and explanation

Mechanical advantage is 3; this does not specify efficiency without distances.

Mechanical advantage=output force/input force.

120/40=3; the force units cancel.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 25

A device delivers 96 N using 24 N input. Calculate actual mechanical advantage. Show the reasoning, not just the conclusion.
Hints

It describes force multiplication, not energy creation.

Answer and explanation

96/24=4.

Problem 26

Two devices have MA=3, but one wastes more energy. Must their efficiencies be equal?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

No. MA alone lacks the input and output displacement or work needed to determine efficiency.

Problem 27

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 28

An illustrative ideal machine takes a 15 N input through 0.8 m and applies a 60 N output through 0.2 m. Compute mechanical advantage and both works. Explain how all results fit one energy account.
Answer and explanation

Mechanical advantage is 60/15=4. Input and output works are each 12 J. The fourfold force is paired with one-quarter the distance, so this ideal model conserves work. Real machines can have losses; a force ratio alone does not establish energy efficiency without displacement or other energy information.

Mechanical advantage is 60/15=4. Input and output works are each 12 J. The fourfold force is paired with one-quarter the distance, so this ideal model conserves work. Real machines can have losses; a force ratio alone does not establish energy efficiency without displacement or other energy information.

Response criteria

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

Problem 29

A ratio and an absolute force answer different questionsA ratio and an absolute force answer different questionsMachine AEffort 25 N; output 100 NMA = 100/25 = 4Machine BEffort 40 N; output 120 NMA = 120/40 = 3A has greater force advantage; B supplies a greater absolute output force.Keep the test loads and task comparable before ranking performance.
In the supplied records, A multiplies effort force by four while B multiplies it by three. B’s output force is nonetheless larger because the input force also differs. The records distinguish ratio from total output and do not establish one machine as universally better. A fair test of the same task needs matched requirements and measurements of travel and energy.
For this unit’s illustrated case, which has greater mechanical advantage, and which has larger output force in the supplied records?
Answer and explanation

A has MA 4, greater than B’s MA 3. B has output 120 N, larger than A’s 100 N. These are different comparisons.

Actual mechanical advantage is measured output force divided by measured effort force. A high ratio cannot by itself establish high efficiency, faster work or suitability for a particular job.

A has MA 4, greater than B’s MA 3. B has output 120 N, larger than A’s 100 N. These are different comparisons.

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 30

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 31

Input energy is 80 J; useful output is 60 J. Find efficiency.
Answer and explanation

75 %

60 ÷ 80 × 100 = 75.

Problem 32

Input energy is 120 J; useful output is 90 J. Find energy transferred elsewhere.
Answer and explanation

30 J

120 − 90 = 30.

Problem 33

Why does low efficiency not violate conservation of energy?
Answer and explanation

All input energy is accounted for, including thermal energy and other outputs that are not useful for the task.

Problem 34

A lift takes in 200 J and gives the load 150 J. Find efficiency and account for the remaining energy. Explain the reasoning in your own words.
Answer and explanation

75% efficient; 50 J went to other parts of the system and surroundings.

Efficiency=(150/200)×100=75%.

Remaining energy=200−150=50 J in other transfers such as thermal energy and sound.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 35

A device receives 400 J and delivers 300 J useful output. Find efficiency. Show the reasoning, not just the conclusion.
Hints

Divide the useful 300 J by the supplied 400 J, then multiply by 100%. Account for the remaining 100 J separately.

Answer and explanation

300/400×100%=75%.

Problem 36

A report claims 120 J useful output from 100 J total input in a complete energy account. What should you check?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

The 120% result indicates an omitted energy source, incorrect boundary or measurement/calculation error; a complete account cannot produce energy from nothing.

Problem 37

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 38

Illustrative machine A receives 250 J and delivers 150 J useful output; B receives 200 J and delivers 150 J. Their task and measurement boundary match. Compare efficiencies and account for each remaining energy amount. Explain why purpose matters to the useful fraction.
Answer and explanation

A is 60% efficient and B 75% for the stated task. The remaining modeled outputs are 100 J and 50 J in other pathways, such as thermal changes or sound. These amounts are not destroyed. An output called waste for lifting might be useful for heating, so usefulness must be defined before comparing fractions.

A is 60% efficient and B 75% for the stated task. The remaining modeled outputs are 100 J and 50 J in other pathways, such as thermal changes or sound. These amounts are not destroyed. An output called waste for lifting might be useful for heating, so usefulness must be defined before comparing fractions.

Response criteria

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

Problem 39

Locate the other energy pathways before improving a deviceLocate the other energy pathways before improving a deviceInput: 100 JUseful job: 70 JThermal / sound: 30 JImprovement may redirect more of the input to the defined useful job.
A supplied 100 J input gives 70 J to the stated useful output and 30 J to other changes such as thermal motion and sound. The branch arrows show pathways qualitatively, not a calibrated Sankey width. Energy in the other branch is not destroyed; whether a pathway is useful depends on the actual job.
For this unit’s illustrated case, if the intended job is heating, must thermal output be counted as a loss? Explain why the job definition matters.
Answer and explanation

No. Thermal output can be the useful output for a heater. Define the job first, then classify each pathway for that job rather than always calling heat wasted.

Useful is a design judgment about the intended result, not a different kind of physical energy. An improvement should name the unwanted mechanism it reduces and measure whether more energy reaches the intended output.

No. Thermal output can be the useful output for a heater. Define the job first, then classify each pathway for that job rather than always calling heat wasted.

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 40

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 41

Does the slower motor necessarily transfer less energy?
Answer and explanation

No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

No. It transfers the same stated 120 J over a longer interval, so its average power is smaller.

Response criteria

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

Problem 42

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 43

Does 60% efficiency mean the input power is 60 W?
Answer and explanation

No. Efficiency is a ratio. The power also depends on the energy amount and time interval.

No. Efficiency is a ratio. The power also depends on the energy amount and time interval.

Response criteria

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

Problem 44

Why can rated power alone fail to predict a daily energy bill?
Answer and explanation

The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

Response criteria

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

Problem 45

Illustrative lifting devices each deliver 240 J; A takes 8 s and B 12 s. A receives 400 J and B receives 300 J. Compare useful power and efficiency, then explain why the higher-power device is not automatically more efficient.
Answer and explanation

Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.

Useful powers are 30 W for A and 20 W for B. Efficiencies are 240/400=60% and 240/300=80%. A delivers useful energy faster but B directs a larger fraction of input to that output. Power and efficiency answer different questions, and both require the same defined useful output.

Response criteria

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

Problem 46

A 50 W model device operates steadily for 20 s. Find the transferred energy and identify an assumption.
Answer and explanation

Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.

Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.

Response criteria

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

Problem 47

Evaluate and correct: Watts measure the total energy a device uses.
Answer and explanation

Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy.

Watts measure energy per time; multiply an appropriate average power by operating time to obtain energy.

Response criteria

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

Problem 48

Choose one prediction from this unit. Explain a comparison that could test it, specifying observations, changed and matched conditions, and a result that would challenge it.
Answer and explanation

A hypothetical 0.5 kW device operating at that average power for 2 h transfers 1 kWh, or 3.6 million J. This is an illustrative arithmetic case, not a current price or an actual appliance guarantee. The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

A hypothetical 0.5 kW device operating at that average power for 2 h transfers 1 kWh, or 3.6 million J. This is an illustrative arithmetic case, not a current price or an actual appliance guarantee. The operating duration, actual average power, cycling and energy price are also needed. A rating describes a condition rather than every day’s use.

Response criteria

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

Problem 49

A model device has average input power 80 W over 10 s and supplies 600 J useful work. Find input energy and efficiency; state a condition behind the arithmetic.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

Input is 800 J and useful efficiency 600/800=75%. The 80 W must be the applicable average over the interval; the other 200 J needs an energy pathway or stored-change account.

Input is 800 J and useful efficiency 600/800=75%. The 80 W must be the applicable average over the interval; the other 200 J needs an energy pathway or stored-change account.

Problem 50

A 50 W model device operates steadily for 20 s. Find the transferred energy and identify an assumption. Explain a condition that would change this conclusion.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.

Energy is 50 J/s × 20 s = 1,000 J. This uses a constant or appropriately averaged 50 W over the entire interval; real varying operation requires interval data.

Problem 51

Same lifting work, different average powerSame lifting work, different average power3 m height gain4 kg object; g = 10 N/kg; ideal steady liftingWork = 4×10×3 = 120 J. If time = 2 s, average power = 60 W.Another device taking 6 s does the same 120 J at only 20 W.
The stated 4 kg object gains 3 m in height, receiving 120 J of gravitational energy in the ideal steady-lift model. Completing that lift in 2 s gives average useful power 60 W; taking 6 s gives 20 W. More power describes a faster energy transfer, not more energy required for the same ideal height change.
For this unit’s illustrated case, if the lift takes 4 s instead, what are work and average useful power?
Answer and explanation

The ideal lifting work stays 120 J; average useful power is 120/4 = 30 W. Conditions and any additional acceleration or losses must be accounted for separately.

A watt is one joule per second. Separate how much useful energy changes from how long the change takes. Do not infer efficiency from timing alone without measuring input energy as well.

The ideal lifting work stays 120 J; average useful power is 120/4 = 30 W. Conditions and any additional acceleration or losses must be accounted for separately.

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 52

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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