State what is meant by the acceleration of free fall and give its approximate value.
State whether the acceleration of free fall depends on the mass of the object, and justify your answer.
A stone is dropped from rest from a height of 20 m. Find (a) the time to reach the ground and (b) the speed on impact.
A ball is thrown straight up at 15 m s−1. Find (a) the maximum height reached and (b) the total time of flight back to the start.
Describe an experiment to determine the acceleration of free fall using a falling object. In your answer include:
Explain why a coin and a feather fall at the same rate in a vacuum but not in air.
Describe how the acceleration of a falling object changes when air resistance is significant, and what happens to its velocity in the long run.
Total: 23 marks. Original work by the TheLucidSTEM team. Written in the style of the papers; no past paper question is reproduced.
Answer key · full worked solutionsclick to reveal
it is the acceleration of an object falling under gravity alone, with no air resistance; near the Earth's surface it is about 9.81 m s−2, directed downward.
it does not depend on mass. With no air resistance all objects fall with the same acceleration g, so a heavy and a light object fall together.
(a) s = ½ g t² gives 20 = ½ × 9.81 × t², so t² = 4.077 and t = 2.0 s.
(b) v = g t = 9.81 × 2.0 = 20 m s−1 (to two significant figures). Or v² = 2 g s = 2 × 9.81 × 20 = 392, so v = 20 m s−1.
take up as positive, a = −9.81 m s−2.
(a) at the top v = 0: 0 = 15² + 2(−9.81)s, so s = 225 / 19.62 = 11.5 m.
(b) time to the top: 0 = 15 + (−9.81)t, so t = 1.53 s; total time of flight = 3.1 s.
marking points (any five): release a steel ball from an electromagnet above a trapdoor; the timer starts as the magnet switches off and stops when the ball opens the trapdoor; measure the drop height s with a metre rule and the time t with the timer; repeat for several heights and plot s against t squared; the gradient equals g / 2, so g = 2 × gradient; the timing is the main source of uncertainty, so keep the ball dense and the drop modest so air resistance is negligible.
in a vacuum there is no air resistance, so both the coin and the feather have the same acceleration g and fall together. In air the feather has a large area and small weight, so air resistance has a large effect on it and slows its fall, while the coin is much less affected.
as the object speeds up, the air resistance increases, so the resultant downward force and therefore the acceleration decrease. Eventually the air resistance equals the weight, the resultant force is zero, and the object falls at a constant terminal velocity.