AIR RESISTANCE AND TERMINAL VELOCITY
5 marks · HardThe diagram below shows the forces acting on a raindrop falling through air. The downward force is the weight of the raindrop and the upward force is air resistance.
Describe how the relative sizes of weight and air resistance change as the raindrop falls, and what effect this has on the motion of the raindrop. Refer to what happens at the start, as it speeds up, and at terminal velocity.
Explain why the raindrop does not accelerate at terminal velocity.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) At the start, weight is greater than air resistance, so the raindrop accelerates downwards. As it speeds up, air resistance increases and the difference between weight and air resistance decreases. Eventually, air resistance increases enough to equal the weight; when this occurs, the raindrop reaches terminal velocity and falls at a constant speed.
(b) Because the forces (weight and air resistance) are balanced so the resultant force is zero.
Common mistakes: Not mentioning that air resistance increases as speed increases; Not linking force balance to no acceleration
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Marking points
M1 (a) · 1 mark · States that at the start, weight is greater than air resistance.
M2 (a) · 1 mark · Mentions that as speed increases, air resistance increases.
M3 (a) · 1 mark · States that eventually air resistance equals weight (forces are balanced).
M4 (a) · 1 mark · States that when forces are balanced, the raindrop moves at constant speed (terminal velocity).
B1 (b) · 1 mark · Explains that with balanced forces, no resultant force, so no acceleration.
Worked solution
Part (a): At the start, the only significant force is weight (downwards); air resistance is very small, so the raindrop accelerates downwards. As speed increases, air resistance (upwards) increases. The difference between the downward weight and the upward air resistance reduces, causing less acceleration. Eventually, air resistance becomes equal to weight. When this happens, the forces are balanced and the raindrop continues falling at constant speed — this is terminal velocity.
Part (b): At terminal velocity, the upward air resistance exactly balances the downward weight, so there is no resultant force and the raindrop does not accelerate.