Impulse and momentum in two dimensions

A camera records a collision between two marbles at 240 frames per second. Video-analysis software shows that one marble moves 18 mm between frame 12 and frame 18.
What is the speed of the marble?

A football of mass 0.43 kg is at rest. A player kicks it and it leaves her foot at 24 m s⁻¹. Her foot is in contact with the ball for 9.0 ms.
What is the average force on the ball?

An airbag reduces the risk of injury to a driver in a crash. Compared with the driver hitting the steering wheel, the airbag

An electron (mass 9.11 × 10⁻³¹ kg) in a beam has momentum 2.0 × 10⁻²⁴ kg m s⁻¹.
What is its kinetic energy?

A hammer head of mass 0.45 kg moves at 6.0 m s⁻¹ when it hits a nail. It comes to rest in 2.5 ms without bouncing.

Neutrons released in a nuclear reactor move at speeds much less than the speed of light. The mass of a neutron is 1.67 × 10⁻²⁷ kg.

A cyclist accelerates along a straight, level road. The graph shows how the momentum of the cyclist and bicycle varies with time.
What is the average resultant force on the cyclist and bicycle between t = 2 s and t = 6 s?

A firework shell is momentarily at rest at the top of its flight when it bursts into three fragments that all move off horizontally. The figure is a top view showing the velocities of fragments 1 and 2 just after the burst. Fragment 3 has a mass of 0.25 kg. Ignore gravity and air resistance during the burst.
What is the speed of fragment 3 just after the burst?

The figure shows two gliders on a level air track just before and just after they collide.
How much kinetic energy is transferred to other forms in the collision?

A student measures the impulse of the force on a trolley with a force sensor and data logger, and the change of momentum of the trolley using a light gate, for five different collisions. The graph shows her results.
Which conclusion is supported by the graph?

In a sports laboratory a robot leg kicks a stationary ball of mass 0.45 kg. The graph shows how the force of the foot on the ball varies with time.

Disc A slides across a horizontal air table and strikes disc B, which is at rest. The figure is a momentum vector diagram drawn to scale. It shows the momentum of A just before and just after the collision.

A 1.5 kg block is at rest on a smooth horizontal surface. A horizontal force acts on it. The force–time graph is a triangle: the force rises steadily from zero to 240 N and falls steadily back to zero, the whole pulse lasting 0.050 s.
What is the speed of the block after the force has acted?

Two toy cars move on a smooth horizontal floor. Car X (2.0 kg) moves east at 3.0 m s⁻¹. Car Y (1.5 kg) moves north at 4.0 m s⁻¹. They collide and lock together.
What is the speed of the cars just after the collision?

A ball of mass 0.060 kg hits a smooth wall at 12 m s⁻¹, travelling at 30° to the normal (the line perpendicular to the wall). It rebounds at the same speed and at 30° to the normal on the other side.
What is the magnitude of the impulse on the ball?

A proton (mass 1.67 × 10⁻²⁷ kg) and an alpha particle (mass 6.64 × 10⁻²⁷ kg) have momenta of the same magnitude.
What is the value of (kinetic energy of the proton) ÷ (kinetic energy of the alpha particle)?

A horizontal jet of water from a hose hits a vertical wall at right angles. Water leaves the hose at a rate of 0.80 kg each second and reaches the wall at 12 m s⁻¹. On hitting the wall the water spreads out along the wall surface and does not bounce back.

A model hovercraft of mass 0.75 kg rests on a smooth level floor. Its fan is switched on briefly. A force sensor records the horizontal thrust: it rises steadily from zero to 1.5 N in the first 0.20 s, stays at 1.5 N until t = 1.40 s, then falls steadily to zero at t = 1.60 s. Resistive forces are negligible.

A student wants to show that the impulse of a force on a trolley is equal to the change of momentum of the trolley. She has a runway, a trolley carrying a card, a light gate, a force sensor, a data logger and a top-pan balance.

A student uses a video camera and analysis software to study a glancing collision between a moving steel sphere and a stationary glass sphere on a smooth bench. The camera records 60 frames per second.

A model railway wagon of mass 1.5 kg rolls at 0.60 m s⁻¹ along a level track and couples with a stationary wagon of mass 0.50 kg. They move off together. Friction is negligible.

A trolley of mass 2.0 kg is at rest on a smooth horizontal track. The graph shows how the resultant force on the trolley varies with time.
What is the speed of the trolley at t = 5.0 s?

Ball X moves at 3.0 m s⁻¹ towards ball Y, which is at rest on a smooth horizontal surface. After the collision X moves at 2.0 m s⁻¹ at 35° to its original direction, as shown in the figure.
Which arrow could show the direction of the velocity of Y after the collision?

A sphere rolls across a horizontal table during a collision experiment. A camera above the table records 50 frames per second. The figure combines the images of the sphere from six consecutive frames on a grid of 1.0 cm squares.
What is the average speed of the sphere?

The graph shows how the kinetic energy E_k of a ball varies with the square of its momentum, p².
What is the mass of the ball?

A hockey ball of mass 0.16 kg moves east across the pitch. A player's stick strikes it and it moves off north. The figure shows the velocities just before and just after the hit. The stick is in contact with the ball for 4.0 ms.

A student investigates the impulse of a force and the change of momentum it produces. A trolley of mass 0.620 kg carries a card of length 0.0500 m. It passes through a light gate, collides with a buffer fixed to a force sensor, and rebounds back through the same light gate. The card blocks the gate for 0.0400 s before the collision and for 0.0625 s after it. The graph shows the force recorded by the sensor during the collision.

The graph shows how the kinetic energy E_k of each of two trolleys, X and Y, varies with the square of its momentum, p².

A gymnast of mass 60 kg jumps down from a platform and reaches the floor at 5.0 m s⁻¹. The graph shows the resultant force on her as she is brought to rest, for two landings: A, with her legs kept straight, and B, bending her knees as she lands.

Sphere A, of mass 0.064 kg, rolls along a straight horizontal groove and hits sphere B, of mass 0.032 kg, which is at rest. A video camera records 120 frames per second, and tracking software gives the position x of the centre of each sphere in every frame. The graph shows the results. Ignore friction and rotation.

A stationary object in deep space breaks into exactly three fragments. Which statement must be true?

A 2.0 kg trolley moving at 3.0 m s⁻¹ collides head-on with a stationary 1.0 kg trolley. Friction is negligible. Which pair of velocities after the collision, both in the original direction, describes an elastic collision?

In an investigation of impulse, a trolley of mass (0.850 ± 0.005) kg carries a card of length (0.0400 ± 0.0005) m. It runs through a light gate into a spring buffer attached to a force sensor and rebounds through the same gate. The card takes (0.0500 ± 0.0010) s to pass through the gate before the impact and 0.0750 s afterwards. The data logger gives the area under the force–time graph as 1.10 N s.

On a smooth ice surface, an ice-hockey puck A moving at 2.2 m s⁻¹ strikes an identical stationary puck B (same mass). After the collision A moves at 1.1 m s⁻¹ at 60.0° to its original direction.

A space probe of total mass 600 kg moves at 200 m s⁻¹ in the +x direction, relative to a distant star. Springs push a 150 kg module away from it. Just afterwards the module moves at 250 m s⁻¹ at 20.0° to the +x direction. Ignore external forces.

A tennis ball of mass 0.060 kg travels horizontally at 15 m s⁻¹ towards a racket. The graph shows how the force of the racket on the ball varies with time during the impact. The ball leaves the racket horizontally in the opposite direction. Ignore the weight of the ball.
What is the speed of the ball as it leaves the racket?

Trolley P, of mass 0.60 kg, moves along a straight, level track towards trolley Q, which is at rest. They collide at t = 2.0 s. The graph shows the displacement of each trolley from its own starting position. Friction is negligible.
Which row gives the mass of Q and the type of collision?

A puck glides east across a horizontal air table. A compressed spring inside it is released and the puck separates into two parts, A and B. The figure shows the motion before the separation and the velocity of A just after it. Friction is negligible.

A student uses video analysis to study a glancing collision. Sphere A, of mass 0.30 kg, rolls towards sphere B, of mass 0.20 kg, which is at rest on a horizontal surface. Tracking software marks the centre of each sphere every 0.10 s; the figure shows the positions on a grid of 2.0 cm squares. A collides with B when A's centre is at (24, 0) cm. Assume friction is negligible and ignore any rotation of the spheres.

On a smooth, level rink, bumper car X (total mass 200 kg) moves at 3.0 m s⁻¹ and strikes bumper car Y (total mass 300 kg), which is at rest. The figure shows the directions in which the cars move just after the collision. Ignore friction during the collision.