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IGCSE CIE Physics Recap | Adrian (2026)

Forces, Momentum and Energy

Subject: IGCSE CIE Physics

Adrian (2026)

For use on Monday, 28 September 2026

01

Forces, Momentum and Energy

Multiple-Choice Questions

Choose the best answer for each question. Use a gravitational field strength of 10 N/kg unless otherwise stated.

  1. A sealed metal block has an external volume of 250 cm3 and a mass of 1.60 kg. The density of the metal is 8.0 g/cm3. What is the volume of the hollow space inside the block?
    1. 20 cm3
    2. 50 cm3
    3. 200 cm3
    4. 450 cm3
  2. An astronaut has a mass of 72 kg and a volume of 0.080 m3. The astronaut travels to a planet where the gravitational field strength is 4.0 N/kg. Which row gives the astronaut’s weight and density on the planet?
    Option Weight/N Density/(kg/m3)
    A288360
    B288900
    C720360
    D720900
    1. Row A
    2. Row B
    3. Row C
    4. Row D
  3. A horizontal beam is pivoted at its centre. Downward forces of 18 N and 10 N act 0.40 m and 0.15 m to the right of the pivot. A third downward force acts 0.30 m to the left of the pivot. What must the third force be for the beam to remain in equilibrium?
    1. 19 N
    2. 24 N
    3. 29 N
    4. 34 N
  4. A car of mass 1200 kg travels forwards at 20 m/s. Its speed decreases uniformly to 8.0 m/s in 4.0 s. During this time, the total resistive force is 4200 N backwards. What is the forward driving force supplied by the engine?
    1. 600 N
    2. 3600 N
    3. 4200 N
    4. 7800 N
  5. A 2.0 kg trolley moves to the right at 6.0 m/s and collides with a 3.0 kg trolley moving to the left at 2.0 m/s. The trolleys join together. What is their velocity immediately after the collision?
    1. 1.2 m/s to the right
    2. 1.2 m/s to the left
    3. 3.6 m/s to the right
    4. 3.6 m/s to the left
  6. A ball of mass 0.15 kg travels towards a wall at 20 m/s. It rebounds directly away from the wall at 30 m/s. What is the magnitude of the impulse given to the ball?
    1. 1.5 N s
    2. 3.0 N s
    3. 4.5 N s
    4. 7.5 N s
  7. A 4.0 kg object moves to the right at 3.0 m/s and explodes into two parts. A 1.5 kg part moves to the left at 2.0 m/s. What is the velocity of the 2.5 kg part immediately after the explosion?
    1. 3.6 m/s to the right
    2. 4.8 m/s to the right
    3. 6.0 m/s to the right
    4. 7.2 m/s to the right
  8. An object of mass 0.40 kg initially moves east at 5.0 m/s. A resultant force of 10 N acts west for 0.30 s. What is the object’s final velocity?
    1. 2.5 m/s east
    2. 2.5 m/s west
    3. 5.0 m/s west
    4. 7.5 m/s west
  9. A roller-coaster car starts from rest at a height of 25 m above the bottom of a track. During its descent, 20% of its initial gravitational potential energy is transferred to the surroundings. What is its speed at the bottom?
    1. 10 m/s
    2. 18 m/s
    3. 20 m/s
    4. 22 m/s
  10. A motor lifts a 500 kg load vertically through 12 m in 20 s. The input power is 4.0 kW. What is the efficiency of the motor?
    1. 60%
    2. 70%
    3. 75%
    4. 80%
  11. The force moving an object increases uniformly from 0 N to 600 N during the first 4.0 m of motion. The force then remains at 600 N for a further 6.0 m. The complete motion takes 8.0 s. What is the average power developed?
    1. 450 W
    2. 525 W
    3. 600 W
    4. 750 W
  12. An object’s gravitational potential energy decreases by 1200 J as it falls. Its kinetic energy increases by 750 J. How much work is done against air resistance?
    1. 375 J
    2. 450 J
    3. 750 J
    4. 1950 J
  13. Machine X lifts a load of mass m through a height h in a time t. Machine Y lifts a load of mass 2m through a height 3h in a time 2t. What is the ratio of the power of Y to the power of X?
    1. 2/3
    2. 3/2
    3. 3
    4. 6
  14. Which energy resource does not ultimately obtain its energy from radiation from the Sun?
    1. Biofuel
    2. Hydroelectric power
    3. Tidal power
    4. Wind power
  15. A country requires a large-scale electricity source that can operate continuously, releases very little carbon dioxide during operation, uses a non-renewable fuel and produces hazardous waste requiring secure long-term storage. Which resource best matches this description?
    1. Biofuel
    2. Hydroelectric power
    3. Nuclear fission
    4. Solar power
15 marks
02

Density, Weight and Moments

Beam in Equilibrium

A uniform horizontal beam is 4.0 m long and has a mass of 10 kg. It is supported at a pivot 2.5 m from its left-hand end. A solid metal counterweight is attached to the left-hand end. The counterweight has a volume of 2.5 × 10−3 m3 and a density of 8.0 × 103 kg/m3. A student of mass 50 kg stands to the right of the pivot. The beam remains horizontal and in equilibrium.

  1. Calculate the mass of the counterweight. [2]
  2. Calculate the weight of the counterweight, the beam and the student. [2]
  3. State the position at which the weight of the uniform beam may be considered to act. [1]
  4. Calculate the total anticlockwise moment about the pivot due to the beam and counterweight. [3]
  5. Calculate the distance of the student from the pivot. [2]
  6. Calculate the upward force exerted on the beam by the pivot. [2]
  7. The student moves farther away from the pivot. Explain what happens to the beam. [2]
14 marks
03

Momentum and Energy

Two-Car Collision

Car A has a mass of 1200 kg and travels east at 18 m/s. It collides with stationary car B, which has a mass of 800 kg. The cars become locked together.

  1. Calculate the momentum of car A before the collision. [2]
  2. State the total momentum immediately before the collision. [1]
  3. Calculate the common velocity immediately after the collision. [3]
  4. Calculate the total kinetic energy immediately before and immediately after the collision. [4]
  5. Calculate the energy transferred from the kinetic energy store during the collision. [2]
  6. State two forms or stores to which this energy may have been transferred. [2]
  7. A resultant braking force brings the joined cars uniformly to rest in 5.0 s. Calculate:
    1. the change in momentum of the cars;
    2. the magnitude of the average braking force.
    [4]
  8. Explain why increasing the time taken to bring a passenger to rest reduces the average force on the passenger. [2]
20 marks
04

Work, Power and Efficiency

Electric Winch

An electric winch raises a 600 kg load vertically through 18 m at constant speed in 30 s. A constant resistive force of 1.2 kN acts against the upward motion. The electrical input power to the winch is 45 kW.

  1. Calculate the weight of the load. [1]
  2. Explain why the cable tension is greater than the weight even though the load moves at constant speed. [2]
  3. Calculate the tension in the cable. [2]
  4. Calculate:
    1. the work done against gravity;
    2. the work done against the resistive force;
    3. the total mechanical work done by the cable.
    [5]
  5. Calculate the mechanical output power delivered through the cable. [2]
  6. Calculate the electrical energy supplied during the lift. [2]
  7. The useful output is the increase in gravitational potential energy. Calculate the overall efficiency. [2]
  8. Explain why the overall efficiency is lower than the ratio of mechanical cable power to electrical input power. [2]
18 marks
05

Energy Sources and Power

Hydroelectric Power Station

Water flows through a hydroelectric power station at a rate of 120 m3 each second and falls through a vertical height of 45 m. The density of water is 1000 kg/m3. The overall efficiency of the station is 82%.

  1. Calculate the mass of water passing through the station each second. [2]
  2. Calculate the gravitational potential energy lost by this water each second. [3]
  3. Hence calculate the input power supplied by the falling water. [2]
  4. Calculate the electrical power generated. [2]
  5. Describe the principal energy transfers between the reservoir and the electrical output. [4]
  6. Explain the function of the turbine and the generator. [2]
  7. State two advantages of hydroelectric power compared with a fossil-fuel power station. [2]
  8. State two disadvantages or environmental effects associated with a large hydroelectric dam. [2]
  9. Explain why hydroelectric energy can be considered to originate mainly from the Sun. [2]
21 marks
06

Evaluating Energy Resources

Island Electricity Supply

An island has an approximately constant average electrical power demand of 2.0 MW. It is considering the following renewable installations.

Resource Maximum output Operating information
Solar cells 4.0 MW Equivalent to full output for 5 hours per day
Wind turbines 3.0 MW Average output is 40% of maximum
Tidal generators 1.5 MW Full output for 8 hours per day
Biofuel station 2.5 MW Can operate when required if fuel is available
  1. Calculate the total electrical energy required in one day, in MWh. [2]
  2. Calculate the daily energy generated by the solar cells, wind turbines and tidal generators. [6]
  3. Determine whether their combined daily energy is theoretically sufficient. Support your answer with a calculation. [3]
  4. Explain why sufficient total daily energy does not mean that demand can be met at every moment. [3]
  5. Explain why tidal power is more predictable than wind power but cannot provide a continuous supply. [2]
  6. State two advantages and two disadvantages of biofuel compared with fossil fuel. [4]
  7. Evaluate using solar, wind and tidal power whenever possible while keeping biofuel generation available. [5]
  8. Identify the resource whose energy does not originate mainly from the Sun and explain your answer. [2]
27 marks

Question 1 — Multiple-Choice Answers

  1. B — 50 cm3.
    Volume of metal = 1600/8.0 = 200 cm3
    Hollow volume = 250 − 200 = 50 cm3
  2. B — 288 N and 900 kg/m3.
    W = mg = 72 × 4.0 = 288 N
    ρ = m/V = 72/0.080 = 900 kg/m3
  3. C — 29 N.
    Clockwise moment = (18 × 0.40) + (10 × 0.15) = 8.7 N m
    F × 0.30 = 8.7
    F = 29 N
  4. A — 600 N.
    a = (8.0 − 20)/4.0 = −3.0 m/s2
    Resultant force = 1200 × 3.0 = 3600 N backwards
    Driving force = 4200 − 3600 = 600 N
  5. A — 1.2 m/s to the right.
    Initial momentum = (2.0 × 6.0) − (3.0 × 2.0) = 6.0 kg m/s
    v = 6.0/(2.0 + 3.0) = 1.2 m/s to the right
  6. D — 7.5 N s.
    Magnitude of change in velocity = 20 + 30 = 50 m/s
    Impulse = 0.15 × 50 = 7.5 N s
  7. C — 6.0 m/s to the right.
    Initial momentum = 4.0 × 3.0 = 12 kg m/s
    12 = (1.5 × −2.0) + 2.5v
    v = 6.0 m/s
  8. B — 2.5 m/s west.
    Initial momentum = 0.40 × 5.0 = 2.0 kg m/s east
    Impulse = 10 × 0.30 = 3.0 N s west
    Final momentum = 1.0 kg m/s west
    v = 1.0/0.40 = 2.5 m/s west
  9. C — 20 m/s.
    0.80mgh = ½mv2
    v = √(2 × 0.80 × 10 × 25) = 20 m/s
  10. C — 75%.
    Useful power = mgh/t
    = (500 × 10 × 12)/20 = 3000 W
    Efficiency = 3000/4000 × 100% = 75%
  11. C — 600 W.
    Work = ½(4.0)(600) + (6.0)(600)
    = 1200 + 3600 = 4800 J
    Average power = 4800/8.0 = 600 W
  12. B — 450 J.
    Energy transferred against resistance = 1200 − 750 = 450 J
  13. C — 3.
    PY/PX = [(2m)(g)(3h)/(2t)] ÷ [mgh/t] = 3
  14. C — Tidal power.

    Tidal energy is mainly caused by the gravitational effects of the Moon and, to a lesser extent, the Sun.

  15. C — Nuclear fission.

    Nuclear power provides a controllable output with low carbon dioxide emissions during operation, but it uses non-renewable fuel and produces radioactive waste.

Question 2 — Beam in Equilibrium

  1. Mass of counterweight = 20 kg.
    m = ρV
    m = (8.0 × 103)(2.5 × 10−3) = 20 kg
  2. Counterweight = 200 N; beam = 100 N; student = 500 N.
    W = mg
    Counterweight: 20 × 10 = 200 N
    Beam: 10 × 10 = 100 N
    Student: 50 × 10 = 500 N
  3. At the centre of the beam, 2.0 m from its left-hand end.
  4. Total anticlockwise moment = 550 N m.
    Counterweight moment = 200 × 2.5 = 500 N m
    Beam moment = 100 × 0.5 = 50 N m
    Total = 550 N m
  5. Distance from pivot = 1.1 m.
    Clockwise moment = anticlockwise moment
    500d = 550
    d = 1.1 m
  6. Upward pivot force = 800 N.
    Upward force = total downward force
    = 200 + 100 + 500 = 800 N
  7. The beam rotates clockwise, with the right-hand side moving down.

    Moving the student farther from the pivot increases the student’s clockwise moment. It then becomes greater than the anticlockwise moment.

Question 3 — Two-Car Collision

  1. Momentum of car A = 21 600 kg m/s east.
    p = mv = 1200 × 18 = 21 600 kg m/s
  2. Total momentum = 21 600 kg m/s east.
  3. Common velocity = 10.8 m/s east.
    21 600 = (1200 + 800)v
    v = 21 600/2000 = 10.8 m/s
  4. Before: 194 400 J. After: 116 640 J.
    KE before = ½(1200)(182) = 194 400 J
    KE after = ½(2000)(10.82) = 116 640 J
  5. Energy transferred = 77 760 J.
    194 400 − 116 640 = 77 760 J
  6. Any two: internal energy, sound, deformation of the cars.
  7. Change in momentum = 21 600 kg m/s west; average braking force = 4320 N west.
    Δp = 0 − 21 600 = −21 600 kg m/s
    F = Δp/Δt = −21 600/5.0 = −4320 N
  8. The same momentum change occurring over a longer time produces a smaller average force.
    F = Δp/Δt

Question 4 — Electric Winch

  1. Weight = 6000 N.
    W = mg = 600 × 10 = 6000 N
  2. The tension must balance both the weight and the downward resistive force.

    Constant speed means zero acceleration and zero resultant force. The upward tension must therefore equal the total downward force.

  3. Tension = 7200 N.
    T = 6000 + 1200 = 7200 N
  4. Against gravity: 1.08 × 106 J; against resistance: 2.16 × 104 J; total: 1.1016 × 106 J.
    Wgravity = mgh = 600 × 10 × 18 = 1 080 000 J
    Wresistance = Fd = 1200 × 18 = 21 600 J
    Total = 1 101 600 J
  5. Mechanical output power = 36.72 kW.
    P = W/t = 1 101 600/30 = 36 720 W
  6. Electrical energy supplied = 1.35 × 106 J.
    E = Pt = 45 000 × 30 = 1 350 000 J
  7. Overall efficiency = 80%.
    Efficiency = 1 080 000/1 350 000 × 100% = 80%
  8. Some cable output is used to overcome resistance and does not increase the load’s gravitational potential energy.

    The cable-power ratio includes work done against resistance as mechanical output, but the stated useful output includes only the increase in gravitational potential energy.

Question 5 — Hydroelectric Power Station

  1. Mass passing each second = 120 000 kg.
    m = ρV = 1000 × 120 = 120 000 kg
  2. GPE lost each second = 5.4 × 107 J.
    ΔE = mgh
    = 120 000 × 10 × 45
    = 54 000 000 J
  3. Input power = 54 MW.
    P = E/t = 54 000 000 J/s = 54 MW
  4. Electrical power = 44.28 MW, or approximately 44 MW.
    Output power = 0.82 × 54 MW = 44.28 MW
  5. Gravitational potential energy → kinetic energy of water → kinetic energy of turbine → electrical energy.

    Some energy is also transferred to the surroundings by heating and sound.

  6. The turbine is rotated by moving water. The generator converts the turbine’s kinetic energy into electrical energy.
  7. Any two: renewable; no fuel cost; little atmospheric pollution during operation; rapid start-up; reliable when water is available.
  8. Any two: habitats and farmland may be flooded; communities may be displaced; construction is expensive; river ecosystems and fish migration may be disrupted.
  9. Solar radiation supplies the energy that evaporates water and drives the water cycle.

    Rainfall returns water to high-altitude reservoirs, giving it gravitational potential energy.

Question 6 — Island Electricity Supply

  1. Daily energy demand = 48 MWh.
    E = Pt = 2.0 × 24 = 48 MWh
  2. Solar = 20 MWh; wind = 28.8 MWh; tidal = 12 MWh.
    Solar: 4.0 × 5 = 20 MWh
    Wind average power = 0.40 × 3.0 = 1.2 MW
    Wind energy = 1.2 × 24 = 28.8 MWh
    Tidal: 1.5 × 8 = 12 MWh
  3. Yes, theoretically.
    Total = 20 + 28.8 + 12 = 60.8 MWh
    Surplus = 60.8 − 48 = 12.8 MWh
  4. Generation and demand may occur at different times.

    Solar power is unavailable at night, wind output varies, and tidal output occurs only during suitable tidal flows. Without storage or backup, a daily surplus cannot supply electricity during every shortfall.

  5. Tides follow predictable gravitational cycles, but tidal flow becomes too small around high and low tide.
  6. Advantages: renewable when crops are replanted; potentially close to carbon neutral; fuel can be stored; output is controllable.

    Disadvantages: combustion produces carbon dioxide and pollutants; land is required; food production or habitats may be affected; transport and processing require energy.
  7. The proposal is reasonable as part of a mixed energy system.

    Solar, wind and tidal resources are renewable and reduce fossil-fuel use, but their output is intermittent. Biofuel can be stored and used when renewable output is insufficient, improving reliability. However, the island must maintain fuel supplies and generating equipment, and biofuel combustion still produces emissions. Storage and demand management could further reduce the need for backup generation.

  8. Tidal power.

    Tidal energy comes mainly from the gravitational attraction of the Moon. Solar, wind and biofuel energy originate mainly from solar radiation.

Formula Reference

Density: ρ = m/V
Weight: W = mg
Moment = force × perpendicular distance from pivot
Momentum: p = mv
Resultant force: F = Δp/Δt
Kinetic energy: Ek = ½mv2
Gravitational potential energy: ΔEp = mgΔh
Work done: W = Fd
Power: P = E/t = W/t
Efficiency = useful energy output / total energy input
Direction reminder: Momentum, velocity, force and impulse are vector quantities. Opposite directions must be represented using opposite signs.
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