Newton's laws of motion practice questions.

A curling stone travels down the sheet at almost constant velocity for several seconds after the sweeper releases it. Which statement applies Newton's first law to this observation?

• The forces acting on the stone are almost balanced, so its velocity changes only slowly
• The stone carries a store of force from the delivery that is gradually used up as it travels
• Friction from the ice acts forwards on the stone and keeps it moving down the sheet
• The inertia of the stone acts on it as an additional forward force

Answer: The forces acting on the stone are almost balanced, so its velocity changes only slowly

Newton's first law says that a body keeps its velocity unless a net external force acts, so the near-constant speed shows that friction and air resistance are small rather than that a force is stored in the stone. Force is an interaction between two bodies, never a quantity carried inside a moving object.

Two rugby players are each driven forwards by the same net force of 900 N in a scrum machine drill. Player X has a mass of 90 kg and player Y a mass of 120 kg. Which comparison of their initial accelerations is correct?

• X accelerates at 7.5 m s-2 and Y at 10 m s-2
• X accelerates at 10 m s-2 and Y at 7.5 m s-2
• Both accelerate at 10 m s-2 because the net force is the same
• Y accelerates faster because a greater mass gives it more momentum

Answer: X accelerates at 10 m s-2 and Y at 7.5 m s-2

Newton's second law gives a = F / m, so 900 / 90 = 10 m s-2 and 900 / 120 = 7.5 m s-2. For a fixed net force the acceleration is inversely proportional to mass, which is why the heavier forward is the slower starter even though he is the harder man to stop once moving.

A swimmer pushes backwards on the wall with a force of 600 N during a tumble turn. Which statement describes the paired force in this interaction?

• The wall pushes the swimmer forwards with less than 600 N because the wall does not move
• The water pushes the swimmer forwards with 600 N once the feet have left the wall
• The wall pushes the swimmer forwards with 600 N
• The swimmer's leg muscles supply a further forward force of 600 N in addition to the push

Answer: The wall pushes the swimmer forwards with 600 N

Newton's third law makes the two forces equal in magnitude and opposite in direction, and the fact that the wall does not move is irrelevant. The two forces never cancel because they act on different bodies: only the wall's push acts on the swimmer.

A sprinter drives out of the starting blocks. Which description of the ground reaction force acting on her at that moment is correct?

• It acts vertically upwards only, because a surface cannot push horizontally
• It acts backwards and downwards, in the same direction as the foot pushes on the blocks
• It stays equal in size to her body weight throughout the drive phase
• It acts forwards and upwards, opposite to the push of the foot on the blocks

Answer: It acts forwards and upwards, opposite to the push of the foot on the blocks

The ground reaction force is the third-law partner of the athlete's push, so it is equal in size and opposite in direction, and its horizontal component is what accelerates her down the track. It exceeds body weight during the drive, which is why the vertical force trace rises well above the standing value.

A goalkeeper catches a football and draws her hands back towards her chest as the ball arrives. What is the effect of the longer contact time on the catch?

• The change in momentum of the ball is smaller, so a smaller force is needed
• The impulse is unchanged, but the mean force on her hands is smaller
• Both the impulse and the mean force on her hands are increased
• The momentum of the ball is passed to the ground rather than to her hands

Answer: The impulse is unchanged, but the mean force on her hands is smaller

The ball has to lose the same momentum whatever the technique, so the impulse F t is fixed and increasing t can only lower the mean force. Reading a soft catch as 'less momentum to absorb' is the standard error in impulse questions.

A sprinter's spikes grip a dry synthetic track during the drive phase. Which change would increase the maximum friction force available at her shoe?

• A larger area of sole in contact with the track surface
• A sole material with a lower coefficient of friction
• A greater horizontal velocity along the track
• A greater normal force between the shoe and the track

Answer: A greater normal force between the shoe and the track

The limiting friction force is the coefficient of friction multiplied by the normal force, so pressing harder into the track raises the grip available. Neither the contact area nor the speed appears in that relationship, which is why a wider sole does not by itself give more grip.