Exercises: Third law: action and reaction

When walking, your foot pushes the ground backwards, yet you move forwards. Identify the action and reaction forces: explain who exerts each one and which body it acts upon.

A swimmer moves forward because her arms push the water backwards. Explain, using Newton's third law, why pushing the water backwards propels her forwards.

You inflate a balloon and release it without tying it: it shoots off while deflating. What force propels it? Identify the action and reaction in this case, indicating which body each force acts upon.

Complete the statement of Newton's third law: "If a body A exerts a force on a body B, then B exerts on A another force with the same $\dots$, the same $\dots$, and $\dots$ direction". Then give an everyday example.

For a rowing boat to move forward, the rower pushes the water backwards with the blades of the oars. Explain what force the water exerts on the oars and why the boat moves forward.

To jump upwards, you bend your legs and push the ground downwards. Explain using the third law why you are propelled upwards. Who is actually pushing you?

If you punch a wall, you hurt your hand, even though the wall did not move. Explain, using Newton's third law, where the force that causes the pain comes from.

A rocket ascends because it expels gases downwards at high speed, as shown in the figure.

Identify the action-reaction pair and explain why the rocket accelerates upwards.

A student claims: "If every action has an equal and opposite reaction, the two forces cancel each other out and nothing could ever move." Explain where their mistake lies, reasoning about which body each force acts upon. Think about the case of a person walking.

Two ice skaters, stationary and facing each other, push off each other with their hands, as shown in the figure. Both slide away in opposite directions.

1. a) Identify the action and the reaction.
2. b) If one has a mass of $40\ \text{kg}$ and the other $80\ \text{kg}$, which one moves faster? Justify your answer by combining the third and second laws.

When fired, a cannon pushes the cannonball forwards while the cannon itself recoils backwards, as shown in the figure.

1. a) Explain the recoil using Newton's third law.
2. b) If the force acting on the cannonball and on the cannon is the same, why does the cannon recoil much more slowly than the cannonball shoots out? Consider their masses.

Walking on smooth ice is almost impossible: your feet slip backwards when trying to move forwards. Relate this problem to the reaction force from the ground used for walking, and explain why we can walk normally with rough-soled shoes on a dry pavement.

A helicopter stays in the air because its blades push the air downwards. Explain the action-reaction pair and why the helicopter does not need to 'push off' the ground to climb.

A squid propels itself by squirting a jet of water through a siphon. Explain how it uses Newton's third law to escape predators and name another animal, or a means of transport, that moves using the same principle.

A boy jumps from the bow of a small boat towards the pier, as shown in the diagram. As he jumps, the boat moves backwards and the boy almost falls into the water.

1. a) Explain why the boat moves.
2. b) Predict what would happen if he jumped from a large ferry instead of a small boat. Justify your answer by considering their masses.

When hitting a ball with a racket, a tennis player feels a sharp impact on their arm.

1. a) Identify the action and reaction forces in the collision between the racket and the ball.
2. b) Explain why the much lighter ball shoots off, while the arm barely slows down.

In a fable, a horse refuses to pull a cart, arguing: 'If I pull the cart forward with a force, the third law says the cart pulls back on me with an equal force; so we can never move.' Gently explain to the horse where its reasoning is wrong, indicating which body each force acts upon and what other forces (those of the ground on its hooves) make the movement possible.

When you jump, you push the Earth downwards with a force of $600\ \text{N}$ and the Earth pushes you upwards with another $600\ \text{N}$, as shown in the diagram.

1. a) Calculate your initial acceleration if your mass is $60\ \text{kg}$ (do a simplified calculation, without subtracting your weight).
2. b) The mass of the Earth is about $6\times10^{24}\ \text{kg}$: calculate the acceleration you produce on the Earth.
3. c) Explain why no one notices the Earth moving when we jump.

A boy is inside a train carriage and pushes the back wall with all his strength: the carriage does not move. He steps outside onto the platform, pushes the same wall from there, and the carriage begins to roll slowly.

1. a) Explain using Newton's third law why he cannot move it from inside: think about the forces exerted between the boy and the carriage (including at his feet).
2. b) Why can he move it from the outside? Which body receives the reaction force now?
3. c) Relate this to the impossibility of 'lifting oneself up by pulling one's own hair'.

On a drifting raft, with no current or wind, a castaway sets up a battery-powered fan blowing against the sail of the boat to try to move forward, as shown in the diagram.

1. a) Will the raft move forward? Analyse the forces between the fan, the air, and the sail using the third law.
2. b) What if he removed the sail and pointed the fan backwards, blowing the air out of the boat? Compare the two cases.

A $100\ \text{g}$ frog jumps horizontally from a $200\ \text{g}$ lily pad floating still in the water, as shown in the diagram.

1. a) If the frog pushes the leaf with a force of $2\ \text{N}$, with what force does the leaf push the frog? Justify your answer using Newton's third law.
2. b) Convert the masses to $\text{kg}$ and calculate the initial acceleration of the frog and that of the leaf.
3. c) Explain why the leaf moves backwards less than the distance the frog jumps.

Identify, in each scene, the action force, the reaction force, and the body upon which each force acts:

1. a) A basketball player bounces the ball against the ground.
2. b) A swimmer pushes off against the pool wall to turn around.
3. c) A standing fan on castors tends to move backwards when turned on.

Álex ($50\ \text{kg}$) and Martina ($40\ \text{kg}$), both on scooters and at rest, push off against each other. During the push, each exerts an average force of $100\ \text{N}$ on the other for $0.5\ \text{s}$.

1. a) With what force does Martina push Álex? And Álex push Martina?
2. b) Calculate the acceleration of each while the push lasts.
3. c) Calculate the velocity of each upon separating and comment on why the lighter one moves away faster.

At the science fair you want to launch a bottle rocket: a plastic bottle with water and pressurised air that ejects the water downwards.

1. a) Explain using Newton's third law what propels the bottle upwards.
2. b) Predict the advantage of ejecting the water at a higher speed and justify your answer using Newton's laws.
3. c) When the water runs out, the rocket continues to climb for a distance and then falls: explain these two stages using Newton's first law and the weight of the rocket.