Cars X and Y are the same in every way except mass, and X is the heavier.
Compare the greatest acceleration car X can reach with that of car Y.
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Show model answer for 06.1Hide model answer for 06.1
Car X can accelerate less than car Y.. The cars can apply the same greatest force.. acceleration = force over mass. So more mass gives less acceleration.
How the marks are earned
- Car X has the smaller greatest acceleration.
A crash stops a car almost at once. Explain how an inflating air bag lowers the chance of the driver being injured.
See how you would score on Force & CollisionsShow model answer for 06.2Hide model answer for 06.2
The air bag cushions the driver, so the driver slows to a stop over a longer time. Their momentum falls by the same amount, but it happens more gradually.
The slower change of momentum means gentler deceleration. Since force is the rate at which momentum changes, the driver feels less force and injury is less likely.
How the marks are earned
- One mark: the bag makes the driver take longer to stop. Saying the momentum change is the same but takes place over a longer time earns this mark and the next one too.
- One mark: either the momentum changes more slowly, or the driver decelerates less sharply.
- One mark: the driver therefore feels less force.
Why it scores
A longer stopping time is the starting idea, and it is worth the first mark.
Rate of change of momentum links the time to the force. Each step earns its own mark.
Revise Force & CollisionsA 1400 kg car slows evenly from 18 m/s to rest over 24 m of braking. Find the resultant force acting on it.
See how you would score on Newton's Laws of MotionShow model answer for 06.3Hide model answer for 06.3
Use this equation, with final speed 0 and initial speed 18 m/s:. v2 − u2 = 2 × a × s. Put in the values:. 0 − 182 = 2 × a × 24
Rearrange for a:. a = fraction: −324 over 48, end of fraction. = −6.75 m/s2. The minus sign shows the car is slowing: the deceleration is 6.75 m/s2.
Use this equation, with the size of the deceleration:. F = m × a. Put in the values:. F = 1400 × 6.75. = 9450 N
How the marks are earned
- One mark: put the values into v2 − u2 = 2 × a × s, giving 0 − 182 = 2 × a × 24.
- One mark: rearrange to find a, a = −324 ÷ 48.
- One mark: the deceleration, 6.75 m/s2 (the acceleration is −6.75).
- One mark: put the mass and acceleration into F = m × a, so F = 1400 × 6.75.
- One mark: the final force, 9450 N. An energy route also earns full marks: kinetic energy 226 800 J = F × 24 gives 9450 N.
- A route through time also earns full marks, five in all: the car averages 9 m/s, half of 18 (1); 24 = 9 × t (1); so the stop lasts 24 ÷ 9 s, about 2.67 s; keep the unrounded value (1); force is momentum lost per second, 1400 × 18 = 25 200 kg m/s ÷ (24 ÷ 9) s (1); so the force is 9450 N (1).
Why it scores
This equation has the distance, not the time, so it suits the data. Both real values in place earn the first mark.
The rearranged form and the evaluated acceleration earn two marks.
The substitution and the final value earn the last two marks. Check by energy: half × 1400 × 182 = 226 800 J, and 226 800 ÷ 24 = 9450 N.
Revise Newton's Laws of MotionThe brakes get hotter as the car slows. Explain why.
See how you would score on Work Done & Energy TransferShow model answer for 06.4Hide model answer for 06.4
Friction between the brake pads and the wheel does work as the car slows. This transfers kinetic energy from the car to the thermal store of the brakes, so their temperature rises.
How the marks are earned
- One mark: friction in the brakes does work. Friction on its own earns nothing.
- One mark: some of the car's kinetic energy is transferred to the thermal store of the brakes.
Why it scores
Work done by friction is the mechanism, and the energy transfer is the result. Both parts are needed.
Revise Work Done & Energy TransferA driver brakes so hard that the deceleration is very large. Give two risks this creates.
See how you would score on Stopping DistancesShow model answer for 06.5Hide model answer for 06.5
The brakes could overheat, and the driver could lose control of the car, for example by skidding.
How the marks are earned
- One mark: the brakes may overheat.
- One mark: the driver may lose control of the car.
Why it scores
A large deceleration needs a large braking force. That brings much more heating in the brakes and a risk of the tyres losing grip.
Revise Stopping Distances