🌎 Weight (downwards)
The pull of the Earth on the object. It acts straight down and it stays the same all the way through the fall, however fast the object moves.
Forces, Movement, Shape and Momentum » Falling Objects and Terminal Velocity
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.21
- Which forces act on an object as it falls through the air
- Why a falling object stops speeding up and reaches a terminal velocity
- What happens to a skydiver before and after the parachute opens
- Why a feather and a hammer land together when there is no air
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Unlock This CourseThe forces on a falling object
Drop a marble and a flat sheet of paper from the same height. The marble hits the floor first. Both are pulled down by gravity, so why does the paper lose? The answer is in the two forces that act on anything falling through the air.
💨 Air resistance (upwards)
Also called drag. It acts upwards, against the motion. It changes during the fall: the faster the object moves, the bigger the drag.
Why does drag grow with speed? A faster object hits more air particles every second, and hits them harder, so the air pushes back with a bigger force.
Drag also depends on shape and size. A wide, flat object has to push much more air out of the way than a small, smooth one. That is why the sheet of paper falls slowly. Screw the same paper into a tight ball and it falls almost as fast as the marble, even though its weight has not changed.
In the exam, draw the forces as two arrows from the object: one straight down labelled weight, and one straight up labelled air resistance (or drag).
Why falling objects reach a terminal velocity
The key idea is that weight stays fixed while drag grows. Follow the story of an object dropped from a great height, one stage at a time.
- At the start the object is not moving, so there is no drag. The only force is its weight. The resultant force is large and downwards, so the object accelerates at about 10 m/s2.
- As it speeds up, the drag increases. The weight is still bigger than the drag, so the object keeps accelerating. But the resultant force (weight − drag) is now smaller, so the acceleration is smaller too.
- The speed keeps rising, so the drag keeps rising. The resultant force and the acceleration keep shrinking. The object is still getting faster, just more and more slowly.
- In the end the drag equals the weight. The forces are balanced, so the resultant force is zero and the acceleration is zero. The object now falls at a constant velocity. This is its terminal velocity.
Key terms:
- Terminal velocity: the constant velocity a falling object reaches when the drag acting upwards is equal to its weight acting downwards, so the resultant force is zero.
Worked example: a skydiver's acceleration
A skydiver has a mass of 70 kg. Calculate her acceleration (a) at the moment she jumps, (b) when the drag is 280 N, (c) when the drag is 700 N.
First find her weight: W = m × g = 70 × 10 = 700 N.
(a) Drag = 0 N, so resultant force = 700 N downwards.
a = F / m = 700 / 70 = 10 m/s2
(b) Resultant force = 700 − 280 = 420 N downwards.
a = F / m = 420 / 70 = 6 m/s2
(c) Resultant force = 700 − 700 = 0 N.
a = 0 / 70 = 0 m/s2. She has reached terminal velocity.
The velocity-time graph for a falling object
You may be asked to sketch or describe this graph. Put velocity on the vertical axis and time on the horizontal axis, then build it in three parts.
- Start at the origin. The line begins steep, because the acceleration is at its biggest.
- The line curves over. It gets less and less steep, because the acceleration is getting smaller as the drag grows.
- The line becomes horizontal. The gradient, which is the acceleration, is now zero and the velocity is constant. The height of this flat part is the terminal velocity.
A skydiver and a parachute
A skydiver reaches two different terminal velocities in one jump. Her weight is the same the whole time. Only the drag changes. The open parachute has a very large area, so it gives a much bigger drag at the same speed.
| Stage | Forces | Motion |
|---|---|---|
| Just after jumping | Weight is much bigger than drag | Accelerates downwards |
| Falling faster | Drag is growing, but weight is still bigger | Still speeding up, with a smaller acceleration |
| First terminal velocity | Drag = weight | Constant velocity, about 50 m/s |
| Parachute opens | Drag is suddenly much bigger than weight | Decelerates (still moving downwards) |
| Slowing down | Drag is shrinking as the speed falls, but is still bigger than weight | Still slowing, with a smaller deceleration |
| Second terminal velocity | Drag = weight again | Constant velocity, about 5 m/s |
On the velocity-time graph, the first flat line is followed by a steep drop when the parachute opens. The line then curves and levels off again at a much lower flat line.
Falling with no air
Take the air away and there is no drag at all. The only force on a falling object is its weight, so it never reaches a terminal velocity. It keeps accelerating until it hits the ground.
With no air, every object falls with the same acceleration, whatever its mass. In 1971 the astronaut David Scott tested this on the Moon, which has no air. He dropped a hammer and a feather at the same moment. They fell side by side and landed together.
On Earth the feather loses the race. It has a tiny weight and a large surface area for that weight, so the drag equals its weight almost at once and it drifts down at a very low terminal velocity. The hammer needs a far bigger drag to balance its weight, so it is still speeding up when it lands.
Investigating falling objects
The specification suggests an optional investigation into the motion of falling.
🧪 Ball in a thick liquid
Fill a tall, clear tube with a thick liquid such as oil. Put marks at equal distances down the tube. Drop in a small steel ball and time it between each pair of marks. Near the top the times get shorter, because the ball is still speeding up. Lower down the times are equal, which shows the ball has reached terminal velocity. A liquid gives much more drag than air, so this happens in a short distance.
🧁 Paper cake cases
Drop a paper cake case from a fixed height and time its fall. It is light and wide, so it reaches terminal velocity very quickly. Then stack two, three and four cases together and repeat. The shape is the same but the weight is bigger, so a bigger drag is needed to balance it. The stack has to fall faster to get that drag, so its terminal velocity is higher.
Common mistakes
- Saying the object stops at terminal velocity. It is still falling, at a constant velocity.
- Saying the drag becomes bigger than the weight during a normal fall. It grows until it is equal to the weight, then stops growing.
- Saying the weight gets smaller. Weight never changes during the fall. Only the drag changes.
- Saying a skydiver moves upwards when the parachute opens. She keeps moving downwards and slows down.
Exam-style question
A hailstone of mass 0.002 kg falls from a cloud. It reaches terminal velocity before it hits the ground.
(a) State the names of the two forces acting on the hailstone as it falls, and the direction of each. [2 marks]
(b) At one moment the air resistance on the hailstone is 0.005 N. Calculate the acceleration of the hailstone at this moment. Use g = 10 N/kg. [3 marks]
(c) Explain why the hailstone reaches a terminal velocity. [4 marks]
Model answer
(a) Weight, acting downwards (1). Air resistance (drag), acting upwards (1).
(b) W = m × g = 0.002 × 10 = 0.02 N (1)
Resultant force = 0.02 − 0.005 = 0.015 N (1)
a = F / m = 0.015 / 0.002 = 7.5 m/s2 (1)
(c) At first the weight is bigger than the air resistance, so there is a resultant force downwards and the hailstone accelerates (1). As its speed increases, the air resistance increases (1). This makes the resultant force, and so the acceleration, smaller (1). When the air resistance is equal to the weight, the resultant force is zero, so the hailstone falls at a constant (terminal) velocity (1).
Exam tip
For an 'explain why it reaches terminal velocity' question, tell the story in order and name the forces at every step: weight bigger than drag, drag increases with speed, resultant force gets smaller, drag equals weight, resultant force zero, constant velocity. Do not leave out 'resultant force is zero'. It is an easy mark to lose.