Momentum

Curling is a sport played on ice. Players slide stones made of granite along the ice. The aim of the sport is to slide a stone into a circular area called the target.

The diagram below shows two stones, A and B. Each stone has a mass of 18 kg.

Stone A is moving with a velocity of 2.1 m s^–1, as shown. B is initially stationary.

Show that the momentum of A is about 40 N s.

Stone A collides with stone B.

The diagram below shows the velocity of stone B after the collision. The point

Deduce whether stone A moves in the direction shown after the collision.

Stone A comes to rest 1.9 m from X. The deceleration of the stone on the ice

Deduce whether the collision was elastic.

Over one hundred years ago, Rutherford supervised a series of experiments using a source of alpha particles and thin gold foil.

Describe the model of the atom that Rutherford proposed as a result of this series of experiments.

The initial kinetic energy of an alpha (⁴₂α) particle is 7.310⁻¹³J.

In a textbook, it states that an alpha particle with this energy would be brought to rest when it reached a distance of 5.010⁻¹⁴m from the centre of the

Deduce whether this statement is correct.

Determine the initial momentum of the alpha particle.

An alpha particle moves along a path directly towards a gold nucleus, as shown.

An elastic interaction occurs and the alpha particle recoils.

State what is meant by an elastic interaction.

State what happens to the atoms in the gold foil as a result of these interactions.

*(a) Describe how the principle of energy conservation and the principle of momentum conservation apply to this situation.

Consider the situation from the instant the spring gun is released to the instant the bob reaches its maximum height.

When the modelling clay hits the pendulum bob, the pendulum swings to one side.

Show that the time taken for the pendulum bob to move from its lowest position to its highest position is about 0.6 s.

effective length of pendulum = 1.25 m

The pendulum bob was then attached to a spring of stiffness 0.12 N m^–1. When the bob was displaced vertically and released, it oscillated with a time period equal to that of the pendulum.

Calculate the mass of the pendulum bob.

In cricket a fielder is often placed at the boundary edge as shown. If the fielder catches the ball, the batter is out.

The fielder is 55.0 m away from the batter. The fielder can catch the ball providing the ball is less than three metres above the height at which it was hit.

The ball is hit with a velocity of 23.8 m s^–1 and at an angle of 50.0 to the horizontal.

Deduce whether the fielder can catch the ball in this case.

The ball was bowled. Just after the bat hit the ball, the ball had a velocity of

Show that the magnitude of the momentum of the ball, after it was hit, was about 3.3 N s.

mass of cricket ball = 0.140 kg

A series of experiments was carried out in the 1970s to investigate the structure of protons using the linac at Stanford, USA.

*(a) Explain how an electron is accelerated in a linac.

The electron leaves the accelerator with a high energy.

Explain why electrons need high energies to investigate the structure of a proton.

An electron leaves the accelerator with a momentum of 20 GeV / c.

Explain, with reference to base units, why GeV / c can be used as a unit of momentum.

An electron with initial momentum 20 GeV / c collides with a stationary proton. After the collision the electron is deflected by an angle of 20° as shown and its momentum is 9.1 GeV / c. The momentum of the proton after the collision is 11.9 GeV / c.

Deduce whether the law of conservation of momentum is obeyed.

The collisions between electrons and the protons in these experiments are sometimes inelastic.

State what is meant by an inelastic collision.

A projectile of mass 65 g is fired vertically upwards into a stationary wooden block of mass 2.400 kg, as shown.

The projectile becomes embedded in the block. They both move vertically upwards through a vertical displacement of 55 cm before momentarily coming to rest.

Calculate the energy dissipated as the projectile hits the block.

Explain how the principle of conservation of energy applies to this collision.

Two gliders, X and Y, are placed on an air track. The gliders are pushed towards each other as shown.

The gliders collide and continue to move after the collision.

Which row of the table could show the velocities of X and Y, in m s⁻¹, after the collision?

A negatively charged pion decays into a muon and an antineutrino. The diagram shows tracks in a particle detector formed in such an event.

Deduce whether the antineutrino is charged, giving two reasons for your decision.

Write a particle equation to represent this decay.

According to the standard model, the pion and muon are classified within two different groups of particles.

State which group each particle belongs to and describe the two groups.

The momentum of the pion just before it decays is 9.1 × 10⁻²⁰N s.

Determine the magnetic flux density of the magnetic field which acts in the detector and state its direction.

Scale of diagram 1 cm represents 10 cm

Use a vector diagram to determine the momentum of the antineutrino.

The initial momentum of the muon is 1.59 × 10⁻¹⁹N s.

A negatively charged pion decays into a muon and an antineutrino. The diagram shows tracks in a particle detector formed in such an event.

Deduce whether the antineutrino is charged, giving two reasons for your decision.

Write a particle equation to represent this decay.

According to the standard model, the pion and muon are classified within two different groups of particles.

State which group each particle belongs to and describe the two groups.

The momentum of the pion just before it decays is 9.1 × 10⁻²⁰N s.

Determine the magnetic flux density of the magnetic field which acts in the detector and state its direction.

Scale of diagram 1 cm represents 10 cm

Use a vector diagram to determine the momentum of the antineutrino.

The initial momentum of the muon is 1.59 × 10⁻¹⁹N s.

initial final

The student read that the frictional force between an object and a surface is directly

In the sport of curling, two teams of ‘curlers’ take turns sliding polished granite stones across an ice surface towards a circular target marked on the ice.

A stone of mass 19.6 kg is accelerated uniformly for 1.25 s before being released by a curler. The stone then decelerates uniformly to rest, travelling 32.5 m in a time of 17.5 s.

Calculate the average useful power developed by the curler in accelerating the stone.

*(b) Stone B is stationary. Stone A travels towards the target and makes a direct hit on stone B as shown. Both stones have mass m.

The collision is elastic. Just before the collision stone A has a velocity v. After the collision stone B moves off with velocity v.

Discuss how the relevant conservation laws apply to this collision.

While a stone is moving towards the target, the curlers vigorously sweep the ice directly in front of the stone.

Explain why this may make the stone travel further.

A ‘Gauss gun’ can be made from five ball bearings of equal mass and two magnets, as shown.

Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.

Explain what happens to make the last ball bearing on the right subsequently move off with a large velocity.

A student set up the apparatus shown to measure the speed of the last ball bearing. The ‘Gauss gun’ was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.

As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.

Calculate the energy stored in the capacitor when it was fully charged.

The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.

Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.

The two foil strips were 0.50 m apart.

Calculate the horizontal velocity of the ball bearing.

The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.

Deduce whether the ball bearing broke the second foil strip at its centre.

Assume the ball bearing was travelling horizontally as it broke the first foil strip.