Energy, Forces & Motion

A 2 kg trolley moves at a speed of 3 m/s. Using the equation kinetic energy = ½ × mass × speed², what is its kinetic energy?

• A36 J
• B9 J✓
• C3 J
• D18 J

Answer: Kinetic energy is calculated as half the mass multiplied by the speed squared, so 0.5 × 2 kg × (3 m/s)² = 9 J. Forgetting to square the speed gives too small a value, and forgetting to halve the result gives too large a value.

A 5 kg box is lifted to a height of 4 m. Taking gravitational field strength as 10 N/kg, what is the gain in gravitational potential energy?

• A20 J
• B200 J✓
• C400 J
• D50 J

Answer: Gravitational potential energy equals mass × gravitational field strength × height, so 5 kg × 10 N/kg × 4 m = 200 J. Leaving out either the field strength or the height from the calculation gives a much smaller or larger incorrect value.

A spring with a spring constant of 40 N/m is stretched by 0.2 m within its limit of proportionality. Using elastic potential energy = ½ × spring constant × extension², what energy is stored?

• A0.8 J✓
• B1.6 J
• C4 J
• D16 J

Answer: Elastic potential energy is half the spring constant multiplied by the extension squared, so 0.5 × 40 N/m × (0.2 m)² = 0.8 J. Forgetting to square the extension, or forgetting to halve the result, both lead to a much larger answer than is actually stored.

2 kg of water with a specific heat capacity of 4,200 J/kg°C is heated so its temperature rises by 5°C. How much thermal energy was transferred?

• A42,000 J✓
• B8,400 J
• C21,000 J
• D84,000 J

Answer: Thermal energy transferred is found using mass × specific heat capacity × temperature change, giving 2 kg × 4,200 J/kg°C × 5°C = 42,000 J. Leaving the mass or the temperature change out of the calculation gives a far smaller figure.

An electric heater transfers 6,000 J of energy in 30 seconds. Using power = energy transferred ÷ time, what is its power output?

• A200 W✓
• B2,000 W
• C20 W
• D600 W

Answer: Power is the rate of energy transfer, calculated as energy divided by time, so 6,000 J ÷ 30 s = 200 W. Misplacing a decimal point or dividing by the wrong time interval both give an answer that is out by a factor of ten or more.

A ball is thrown straight upward and rises before falling back down. As it rises, what happens to its energy stores?

• AEnergy shifts from the kinetic store to the gravitational potential store✓
• BEnergy shifts from the gravitational potential store to the kinetic store
• CNo energy at all shifts between any of the stores while the ball travels through the air
• DEnergy is transferred entirely and permanently into the thermal store of the surrounding air

Answer: As the ball rises, it slows down, so energy shifts from the kinetic energy store to the gravitational potential energy store. The reverse happens as it falls back down, and some energy is also dissipated to the thermal store of the surroundings due to air resistance.

A car's brakes are applied and the car decelerates to a stop on a level road. Which energy store mainly increases as a result?

• AThe chemical energy store of the fuel tank
• BThe thermal energy store of the brakes✓
• CThe kinetic energy store of the car
• DThe gravitational energy store of the car

Answer: Friction between the brake pads and the wheels transfers energy from the car's kinetic store mainly into the thermal store of the brakes, which is why they get hot. On a level road the height does not change, so the gravitational store stays the same, and no chemical energy is involved once the engine is disengaged.

An electric kettle is switched on to boil water. Which energy transfer takes place?

• AElectrical energy is transferred to the gravitational store of the water
• BElectrical energy is transferred to the thermal energy store of the water✓
• CChemical energy stored in the fuel is transferred to the kinetic energy store of the water
• DThermal energy already in the room is transferred to the electrical store of the element

Answer: An electric kettle transfers electrical energy to the thermal energy store of the water, raising its temperature until it boils. The transfer is not to a kinetic or gravitational store, and energy does not flow backwards from thermal to electrical inside the heating element.

A 1,000 W toaster is used for 120 seconds. Using energy transferred = power × time, how much energy does it transfer?

• A8.33 J
• B1,200 J
• C120,000 J✓
• D12,000 J

Answer: Energy transferred is power multiplied by time, so 1,000 W × 120 s = 120,000 J. Dividing power by time instead of multiplying, or misplacing a decimal point, both give answers far smaller than the true energy transferred.

An electric motor is supplied with 500 J of energy and usefully transfers 350 J as kinetic energy, the rest being wasted as heat. What is its efficiency?

• A30%
• B35%
• C140%
• D70%✓

Answer: Efficiency is the useful energy output divided by the total energy input, multiplied by 100, so 350 J ÷ 500 J × 100 = 70%. Calculating the wasted energy's share instead of the useful share, or inverting the fraction, both give an incorrect percentage.

Which of these is classified as a renewable energy resource?

• AGas power
• BNuclear power
• CCoal power
• DWind power✓

Answer: Wind power is renewable because it is replenished naturally and will not run out on a human timescale. Coal and gas are fossil fuels formed over millions of years, and nuclear power relies on a finite supply of mined uranium, so all three are classed as non-renewable.

Which of these is a non-contact force?

• AGentle push force
• BRope tension force
• CFrictional force
• DMagnetic force✓

Answer: Magnetism is a non-contact force because a magnet can attract or repel another magnetic object without the two touching. Friction, tension and pushing all require two surfaces or objects to be in direct contact, so they are classed as contact forces.

A rock has a mass of 8 kg. Taking gravitational field strength as 10 N/kg, what is its weight?

• A18 N
• B800 N
• C80 N✓
• D8 N

Answer: Weight is calculated as mass × gravitational field strength, so 8 kg × 10 N/kg = 80 N. Adding the two values instead of multiplying, or misplacing a factor of ten, both give an incorrect weight.

Two forces act on a stationary object: 15 N to the right and 15 N to the left. What is the resultant force, and what does this mean for the object?

• A30 N to the right, so the object accelerates
• BZero, so the object remains at rest✓
• C15 N to the left, so the object moves left
• DZero, so the object accelerates steadily

Answer: The two forces are equal in size and opposite in direction, so they cancel out and the resultant force is zero, meaning the object stays at rest or continues at constant velocity. A non-zero resultant would be needed to accelerate the object, and simply adding the two force sizes ignores that they act in opposite directions.

A free body diagram is drawn for a book resting on a table. What should the diagram show?

• AEvery force acting anywhere in the surrounding room, drawn as arrows of equal length
• BOnly the forces that the book itself exerts down onto the table, drawn as arrows
• CAll the forces acting on the book, drawn as arrows showing size and direction✓
• DThe internal structure and material composition of the book, drawn without any arrows

Answer: A free body diagram shows all the forces acting on a single object, each drawn as an arrow whose length and direction represent the force's size and direction. It does not show forces the object exerts on other things, the object's internal structure, or unrelated forces acting elsewhere in the room.

A spring is stretched and then returns exactly to its original length when the force is removed. What type of distortion has occurred?

• AElastic distortion✓
• BInelastic distortion
• CPermanent distortion
• DPlastic distortion

Answer: Elastic distortion occurs when an object returns to its original shape and size once the deforming force is removed. Inelastic, plastic and permanent distortion all describe a change of shape that remains after the force has been taken away.

A spring has a spring constant of 25 N/m. Using force = spring constant × extension, what force is needed to extend it by 0.4 m?

• A1 N
• B25 N
• C16 N
• D10 N✓

Answer: Force is calculated as spring constant × extension, so 25 N/m × 0.4 m = 10 N. Misreading the spring constant, or copying the spring constant across without multiplying by the extension at all, both give an incorrect result.

A force-extension graph for a spring within its limit of proportionality is a straight line through the origin. What does the gradient of this line represent?

• AThe elastic potential energy stored
• BThe mass of the object attached
• CThe value of the spring constant✓
• DThe total extension of the spring

Answer: For a straight-line force-extension graph, the gradient equals force divided by extension, which is the definition of the spring constant. The elastic potential energy is instead found from the area under the graph, and the graph does not directly show the spring's mass.

A spring is stretched beyond its limit of proportionality. How does its force-extension graph change?

• AThe line curves and is no longer directly proportional✓
• BThe line completely reverses its direction and slopes steadily downward
• CThe line becomes a straight line passing through the origin point
• DThe line stays straight but its gradient decreases to zero

Answer: Beyond the limit of proportionality, force and extension are no longer directly proportional, so the graph curves away from the straight line seen at lower forces. It does not stay straight, and it does not reverse direction, since extension continues to increase as force increases.

A force of 50 N pushes a crate a distance of 6 m across a floor. Using work done = force × distance, how much work is done?

• A300 J✓
• B3,000 J
• C30 J
• D56 J

Answer: Work done is calculated as force × distance, so 50 N × 6 m = 300 J. Adding the two values instead of multiplying, or misplacing a decimal point, both give an incorrect answer.

Why are at least two forces needed to stretch, bend or compress an object?

• AA single force would only change the object's temperature
• BA single force would have no effect on the object at all
• CA single force would cause the object to rotate but not deform
• DA single force would simply move the whole object rather than change its shape✓

Answer: A single unbalanced force on an object just accelerates it in one direction, so a second force is needed to oppose it and cause the object to stretch, bend or compress. Claiming a single force has no effect, only changes temperature, or only causes rotation all misdescribe how forces actually act on materials.

How does an object's weight differ from its mass?

• AMass is actually a force that depends on gravitational field strength, while weight does not
• BWeight is a force that depends on gravitational field strength, while mass does not✓
• CWeight stays the same everywhere, while mass changes with gravitational field strength
• DWeight and mass are ultimately just two different units for exactly the same physical quantity

Answer: Weight is a force, measured in newtons, that depends on the strength of the gravitational field an object is in, whereas mass is a fixed amount of matter measured in kilograms. This is why an object's weight changes on the Moon while its mass stays the same, the opposite of what happens if the two quantities are swapped around.

A car travels around a bend at a constant reading on its speedometer. Why is its velocity changing even though its speed is not?

• AVelocity includes direction, and the car's direction is changing around the bend✓
• BSpeed includes direction, and the car's direction is changing around the bend
• CVelocity is unrelated to direction, so it cannot change on a bend
• DThe car's speed must also be changing whenever its direction changes

Answer: Velocity is a vector quantity that includes both speed and direction, so a change in direction alone means the velocity is changing even if the speed reading stays constant. Speed itself is a scalar quantity with no direction, so it is unaffected by the change in direction.

Which of these is closest to a typical walking speed for a person?

• A30 m/s
• B0.1 m/s
• C1.5 m/s✓
• D15 m/s

Answer: A typical walking speed is around 1.5 m/s, roughly the pace of an unhurried stroll. A speed of 0.1 m/s is far too slow even for walking, while 15 m/s and 30 m/s are closer to fast cycling or motorway traffic.

An object falls freely near the Earth's surface with no significant air resistance. Approximately what is its acceleration?

• A98.0 m/s²
• B0.98 m/s²
• C9.8 m/s²✓
• D4.90 m/s²

Answer: An object in free fall near the Earth's surface accelerates at approximately 9.8 m/s², often rounded to 10 m/s² for calculations. Values ten times too small, ten times too large, or exactly half this figure are common slips when recalling the constant.

A cyclist travels 60 m in 5 seconds. Using speed = distance ÷ time, what is her average speed?

• A1.2 m/s
• B300 m/s
• C12 m/s✓
• D55 m/s

Answer: Average speed is distance divided by time, so 60 m ÷ 5 s = 12 m/s. Misplacing a decimal point, subtracting instead of dividing, or multiplying instead of dividing all give a wildly incorrect speed.

A van's velocity increases from 4 m/s to 24 m/s in 4 seconds. Using acceleration = change in velocity ÷ time, what is its acceleration?

• A20 m/s²
• B6 m/s²
• C7 m/s²
• D5 m/s²✓

Answer: Acceleration is the change in velocity divided by time, so (24 m/s − 4 m/s) ÷ 4 s = 5 m/s². Dividing the final velocity alone by the time, or adding the two velocities instead of subtracting, both give an incorrect answer.

On a distance-time graph, a straight line has a steep, constant gradient. What does this indicate about the object's motion?

• AThe object is accelerating rapidly
• BThe object is stationary throughout
• CThe object is moving at a constant, high speed✓
• DThe object is moving at a constant, low speed

Answer: On a distance-time graph, the gradient represents speed, so a steep straight line shows a constant, high speed. A flat line would show the object is stationary, and a curving line, not a straight one, would indicate acceleration.

On a velocity-time graph, what does the area between the line and the time axis represent?

• AThe average velocity only
• BThe acceleration of the object
• CThe net force on the object
• DThe distance travelled✓

Answer: The area between a velocity-time graph's line and the time axis represents the distance travelled, since it sums velocity over each small interval of time. Acceleration is instead shown by the gradient of the line, not the area underneath it.

According to Newton's First Law, what happens to an object's motion if the resultant force acting on it is zero?

• AIt continues at the same velocity, whether that is stationary or moving in a straight line✓
• BIt always slows down on its own and quickly comes to a complete rest
• CIt accelerates steadily, continuously gaining speed, in the direction of its original motion
• DIt changes direction randomly and unpredictably, even though no force is acting on it at all

Answer: Newton's First Law states that an object continues at a constant velocity, including remaining stationary, unless a resultant force acts on it to change that motion. It does not automatically stop, accelerate, or change direction without an unbalanced force causing it to do so.

A resultant force of 60 N acts on an object of mass 12 kg. Using force = mass × acceleration, what is the object's acceleration?

• A72 m/s²
• B5 m/s²✓
• C0.2 m/s²
• D720 m/s²

Answer: Rearranging force = mass × acceleration gives acceleration = force ÷ mass, so 60 N ÷ 12 kg = 5 m/s². Multiplying the two values together, or dividing mass by force instead of force by mass, both give an incorrect result.

A swimmer pushes backward against the water to move forward. Which law explains this pair of forces?

• ANewton's Third Law of motion✓
• BNewton's Second Law of motion
• CThe law of conservation of momentum
• DNewton's First Law of motion

Answer: Newton's Third Law states that when one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first, which is why pushing water backward propels the swimmer forward. Newton's First and Second Laws instead describe motion under a resultant force, not force pairs between two objects.

A driver's reaction time increases because they are tired. Which part of the car's overall stopping distance does this directly increase?

• AThe car's thinking distance✓
• BThe car's braking distance
• CThe distance to the next junction
• DThe car's braking force

Answer: The thinking distance is the distance travelled while the driver reacts before applying the brakes, so a slower reaction time directly increases it. The braking distance instead depends on factors such as road conditions and vehicle mass, not on reaction time, and the distance to the next junction is unrelated to how the car itself behaves.

A 1,200 kg car travels at a velocity of 15 m/s. Using momentum = mass × velocity, what is its momentum?

• A1,215 kg m/s
• B18,000 kg m/s✓
• C80 kg m/s
• D180,000 kg m/s

Answer: Momentum is calculated as mass × velocity, so 1,200 kg × 15 m/s = 18,000 kg m/s. Adding the two values, or dividing instead of multiplying, both give a result far removed from the true momentum.

A car of mass 1200 kg travels at 15 m/s.

How much kinetic energy does it have?

• A270 000 J
• B9000 J
• C18 000 J
• D135 000 J✓

Answer: Kinetic energy = ½ × mass × speed² = 0.5 × 1200 × 15² = 0.5 × 1200 × 225 = 135 000 J. The tempting 270 000 J leaves out the ½, 9000 J forgets to square the speed (0.5 × 1200 × 15), and 18 000 J is mass × speed, which is momentum in kg m/s, not energy.

A ball of mass 0.20 kg is dropped from a height of 5.0 m. Ignore air resistance. (Gravitational field strength = 9.8 N/kg)

What is the ball's speed just before it hits the ground?

• A9.9 m/s✓
• B7.0 m/s
• C49 m/s
• D98 m/s

Answer: Gravitational potential energy lost = kinetic energy gained, so mgh = ½mv² and v² = 2gh = 2 × 9.8 × 5.0 = 98. v = √98 = 9.9 m/s; the mass cancels. The tempting 7.0 m/s is √49, from leaving out the 2; 49 and 98 are v²/2 and v² before the square root is taken.

A spring has a spring constant of 40 N/m. It is stretched by 0.15 m without going past its limit of proportionality.

How much energy is stored in the spring?

• A0.45 J✓
• B0.90 J
• C3.0 J
• D6.0 J

Answer: Elastic potential energy = ½ × spring constant × extension² = 0.5 × 40 × 0.15² = 0.5 × 40 × 0.0225 = 0.45 J. The tempting 0.90 J leaves out the ½, 3.0 J forgets to square the extension, and 6.0 J is k × e, the force in newtons needed to stretch the spring, not the energy stored.

An electric motor lifts a 50 kg load through a height of 12 m in 20 s. The input power to the motor is 500 W. (Gravitational field strength = 9.8 N/kg)

What is the efficiency of the motor?

• A41%
• B6.0%
• C170%
• D59%✓

Answer: Useful energy output = gain in gravitational potential energy = mgh = 50 × 9.8 × 12 = 5880 J. Total energy input = power × time = 500 × 20 = 10 000 J. Efficiency = 5880 ÷ 10 000 = 0.588, about 59%. The tempting 41% is the fraction wasted; 6.0% leaves out g, and 170% divides input by output: efficiency can never be more than 100%.

A 2.0 kW kettle heats 0.80 kg of water from 20 °C to 100 °C in 150 s. The specific heat capacity of water is 4200 J/kg °C.

What is the efficiency of the kettle?

• A112%
• B22%
• C10%
• D90%✓

Answer: Energy transferred to the water = m × c × Δθ = 0.80 × 4200 × 80 = 268 800 J. Electrical energy supplied = P × t = 2000 × 150 = 300 000 J. Efficiency = 268 800 ÷ 300 000 = 0.896, about 90%. The tempting 112% uses 100 °C as the temperature change instead of 80 °C, 22% uses 20 °C, and 10% is the energy wasted.

A cyclist speeds up uniformly from 2.0 m/s to 8.0 m/s in 4.0 s.

What is the cyclist's acceleration?

• A2.0 m/s²
• B0.67 m/s²
• C1.5 m/s²✓
• D2.5 m/s²

Answer: Acceleration = change in velocity ÷ time = (8.0 − 2.0) ÷ 4.0 = 1.5 m/s². The tempting 2.0 m/s² uses the final speed alone (8.0 ÷ 4.0), 0.67 m/s² divides the time by the change in velocity, and 2.5 m/s² adds the two speeds instead of subtracting.