Linear momentum and its conservation

A particle of mass $m$, moving at speed $u$, strikes a particle of mass $M$ that is at rest. The velocities of the two particles before and after the collision are illustrated. Which vector diagram shows the momenta correctly before and after the collision?

Feb/March 2016

A firework at rest bursts into three fragments. The masses and velocities of the three fragments immediately after the explosion are shown. What are speed $v_1$ and speed $v_2$?

Feb/March 2017

State what the principle of conservation of momentum says.

Feb/March 2017

Two balls, with masses $m$ and $2m$, are moving in a vacuum with initial velocities $2v$ and $v$ respectively, and they collide head-on, as illustrated. Following the collision, the ball of mass $m$ rebounds leftwards with velocity $v$. What is the loss of kinetic energy in the collision?

Feb/March 2019

Two balls $X$ and $Y$ are travelling towards one another at speeds of $5\,\text{m s}^{-1}$ and $15\,\text{m s}^{-1}$ respectively. They undergo a perfectly elastic head-on collision, after which ball $Y$ moves to the right at a speed of $7\,\text{m s}^{-1}$. What is the speed and direction of ball $X$ after the collision?

Feb/March 2019

As shown in Fig. 3.1, balls X and Y travel over a horizontal frictionless surface. Ball X begins with velocity $3.0\,\text{m s}^{-1}$ along line AB. Ball Y has mass $2.5\,\text{kg}$ and starts with velocity $9.6\,\text{m s}^{-1}$ at an angle of $60^{\circ}$ to line AB. They collide at point B. After the collision, the two balls remain stuck together and move across the horizontal surface in a direction at right-angles to line AB, as shown in Fig. 3.2.

Feb/March 2019

The diagram depicts a particle $P$, moving with speed $v$, just before it collides with a particle $Q$ at rest and of the same mass. The collision is perfectly elastic. Which statement describes the motion of $P$ and of $Q$ immediately after the collision?

Feb/March 2020

A firework initially at rest bursts into four fragments, each moving in a different direction within a horizontal plane. The diagram gives the velocity and mass of each fragment. What is the speed $v$ of fragment X?

Feb/March 2021

Two blocks $X$ and $Y$ rest on a horizontal frictionless surface. Block $Y$ has a greater mass than block $X$. A spring is attached to one end of block $Y$. The blocks are pressed together so that the spring is compressed between them, and they are kept stationary as illustrated. When they are released, the blocks travel in opposite directions. Which of the following statements is correct?

Feb/March 2021

An object of mass $2m$, moving through deep space with velocity $v$, breaks apart into two fragments of equal mass, with one fragment coming to rest. What is the kinetic energy of the fragment that is moving after the break-up?

Feb/March 2022

A firework that is initially at rest detonates and breaks into two fragments, which then travel horizontally in opposite directions. The explosion transfers a total kinetic energy of $E$ to the fragments. One fragment has mass $m$ and the other has mass $2m$. What is the speed of the fragment of mass $m$ immediately after the explosion?

Feb/March 2024

Two balls P and Q, with equal mass, are travelling in a straight line towards each other, as illustrated. Ball P has a velocity of $1.30\,\text{m s}^{-1}$ to the right. Ball Q has a velocity of $0.50\,\text{m s}^{-1}$ to the left. P and Q collide. The collision is perfectly elastic, so the total momentum is conserved. Which diagram shows the correct motion of P and Q after the collision?

Feb/March 2024

A nucleus that is at rest has nucleon number $A$. It decays by releasing a proton with speed $v$, producing a new nucleus with speed $u$. The proton and the new nucleus travel in opposite directions, moving away from each other. Which equation expresses $v$ in terms of $A$ and $u$?

Feb/March 2025

What does a statement of the principle of conservation of momentum for a system say?

Feb/March 2025

Objects P and Q make up an isolated system. Object P has mass $6.0\,\text{kg}$ and is travelling at a speed of $3.0\,\text{m s}^{-1}$. Object Q has mass $2.0\,\text{kg}$ and is travelling at a speed of $4.2\,\text{m s}^{-1}$ at an angle of $35^{\circ}$ to the path of P. Objects P and Q collide and remain stuck together. What is the magnitude of the component of the final momentum of the combined objects in the original direction of P?

Feb/March 2025

Two equal masses move towards one another on a frictionless air track with speeds of $60\,\text{cm s}^{-1}$ and $40\,\text{cm s}^{-1}$. On collision, they remain stuck together. What is the speed of the combined masses after the collision?

May/June 2010

The diagram depicts two identical spheres $X$ and $Y$. At the start, $X$ is moving at speed $v$ straight towards $Y$. $Y$ is at rest. The spheres undergo an elastic collision. What happens?

May/June 2010

In the diagram, there are two identical spheres X and Y. At first, X travels at speed $v$ straight towards Y, while Y is at rest. The spheres then undergo an elastic collision. What occurs?

May/June 2010

Two equal masses move towards one another on a frictionless air track with speeds of $60\ \text{cm s}^{-1}$ and $40\ \text{cm s}^{-1}$. On collision, they remain stuck together. What speed do the masses have after the collision?

May/June 2010

Two masses of equal mass move towards one another on a frictionless air track at speeds of $60\,\text{cm s}^{-1}$ and $40\,\text{cm s}^{-1}$. They become joined when they collide. What is the speed of the masses immediately after the collision?

May/June 2010

The diagram depicts two identical spheres X and Y. At the start, X is travelling at speed $v$ straight towards Y, while Y is at rest. The spheres undergo an elastic collision. What happens?

May/June 2010

The way the tension $F$ in a spring changes with extension $x$ is shown in Fig. 3.1. Use Fig. 3.1 to calculate the energy stored in the spring when the extension is $4.0\,\text{cm}$. Show your working.

May/June 2010

Define force

May/June 2010

A body with mass $m$, travelling at velocity $v$, collides with an identical body that is at rest and remains attached to it. Which row gives the momentum and kinetic energy of the two bodies after the collision?

May/June 2011

The diagram depicts particle P moving at speed $v$ and just about to strike a stationary particle Q with the same mass. The collision is perfectly elastic. Which statement gives the motion of P and of Q immediately after the collision?

May/June 2011

A body of mass $m$, travelling with velocity $v$, collides with another body of the same mass that is at rest and then remains attached to it. Which row shows the momentum and kinetic energy of the two bodies after the collision?

May/June 2011

Two identical spheres, each of mass $m$ and speed $v$, are moving directly towards one another. They undergo a head-on elastic collision. Which statement is correct?

May/June 2012

Which row correctly indicates whether momentum and kinetic energy are conserved in an inelastic collision when no external forces act?

May/June 2012

Two spheres travel towards one another along a single straight line. Before the collision, their speeds are $u_1$ and $u_2$. After the collision, the spheres separate with speeds $v_1$ and $v_2$ in the directions shown below. Which equation has to be true if the collision is perfectly elastic?

May/June 2012

Two identical spheres, each of mass $m$ and moving at speed $v$, travel towards one another. They undergo a head-on elastic collision. Which statement is correct?

May/June 2012

Which one of the following correctly states the principle of conservation of momentum?

May/June 2013

A $2.0\,\text{kg}$ mass, moving at $3.0\,\text{m s}^{-1}$ across a frictionless surface, collides head-on with a $1.0\,\text{kg}$ mass that is initially at rest. The two masses join together after the impact. What kinetic energy is lost in the collision?

May/June 2013

Two bodies moving along a straight line undergo a perfectly elastic collision. Which of the following statements must be true?

May/June 2013

A wall is struck by a strong wind travelling at $33\,\text{m s}^{-1}$. The air density is $1.2\,\text{kg m}^{-3}$. The wall presents an area of $12\,\text{m}^2$ perpendicular to the wind velocity. When the air reaches the wall, its speed is reduced to zero. What is the approximate force exerted by the air on the wall?

May/June 2013

A nucleus that is initially at rest has nucleon number $A$. It undergoes decay and emits a proton with speed $v$, producing a new nucleus with speed $u$. The proton and the new nucleus travel in opposite directions, moving apart from each other. Which equation gives $v$ in terms of $A$ and $u$?

May/June 2013

Two spheres have velocities $u_1$ and $u_2$ while moving along the same straight line. They then collide, and their velocities afterwards are $v_1$ and $v_2$. Which collision is inelastic?

May/June 2013

State the law of conservation of momentum.

May/June 2013

A body with mass $4.0\,\text{kg}$ and speed $3.0\,\text{m s}^{-1}$ collides with a stationary object in an inelastic collision. Which statement is correct?

May/June 2014

Two train carriages, each with a mass of $5000\,\text{kg}$, move towards one another on a level track. One is moving at $2.00\,\text{m s}^{-1}$ and the other at $1.00\,\text{m s}^{-1}$, as shown. They collide and stick together. What is the kinetic energy lost during the collision?

May/June 2014

A tennis ball is released above a table and rebounds after striking it. The table applies a force $F$ to the ball. Which graph most accurately shows how the force $F$ varies with time $t$ during the period when the ball is touching the table?

May/June 2014

A body at rest breaks apart into two fragments with masses $m$ and $2m$. The fragments acquire kinetic energies $X$ and $Y$, in that order. What is the value of the ratio $\frac{X}{Y}$?

May/June 2014

A molecule with mass $m$ and speed $v$ collides with a wall while moving at right angles to the wall. The collision is elastic. What changes are produced in the molecule’s momentum and kinetic energy by the collision?

May/June 2015

Trolley X, travelling on a horizontal frictionless track, collides with stationary trolley Y. The two trolleys stick together and then continue moving as one. Which statement concerning this interaction is correct?

May/June 2015

Which one of the following gives the statement of the principle of conservation of momentum?

May/June 2015

A moving object collides with an object at rest. The collision is inelastic, and the objects then travel away together. Which row gives the possible values of the system’s total momentum and total kinetic energy before and after the collision?

May/June 2015

Two balls $X$ and $Y$ are travelling towards one another with speeds of $5\,\text{m s}^{-1}$ and $15\,\text{m s}^{-1}$ respectively. They undergo a perfectly elastic head-on collision, and after the collision ball $Y$ moves to the right at a speed of $7\,\text{m s}^{-1}$. What are the speed and direction of ball $X$ after the collision?

May/June 2015

A timber block is resting freely on brackets $4.0\,\text{m}$ above the ground, as illustrated. A bullet with mass $5.0\,\text{g}$ is fired straight upwards into the timber block of mass $95\,\text{g}$. It becomes embedded in the block. As a result of the impact, the block moves up beyond its supporting brackets. The bullet strikes the block at a speed of $200\,\text{m s}^{-1}$. What height above the ground does the block reach at the top of its motion?

May/June 2015

As shown in Fig. 3.1, two balls X and Y are held by long strings. Each ball is drawn back and then released so that they move towards one another. When they collide at the position shown in Fig. 3.1, the strings are vertical. The balls then rebound in opposite directions. Fig. 3.2 gives the data for X and Y during this collision. Take the positive direction to be horizontal and to the right.

May/June 2015

A gas molecule’s mass is $6.64 \times 10^{-27}\,\text{kg}$ and its speed is $1250\,\text{m s}^{-1}$. It strikes a flat surface at right angles and then rebounds at the same speed, as shown in Fig. 4.1.

May/June 2015

Two spheres move towards one another along the same straight line. Before they collide, their speeds are $u_1$ and $u_2$. Once the collision is over, the spheres move apart with speeds $v_1$ and $v_2$ in the directions shown below. The collision is perfectly elastic. Which equation must be correct?

May/June 2016

The diagram depicts a man on a platform connected to a flexible pipe. Water is forced through the pipe so that the man and platform stay at the same height. The net vertical force acting on the platform is zero. The total mass of the man and platform is $96\,\text{kg}$. Each second, $40\,\text{kg}$ of water is expelled vertically downward from the platform. What is the speed of the water as it leaves the platform?

May/June 2016

Which statement about a perfectly elastic collision between two bodies in an isolated system is correct?

May/June 2016

A ball of mass $m$ moving with velocity $u$ collides with a second ball of mass $M$ that is initially at rest. After the collision, the two balls move with velocities $v$ and $V$ respectively, in the directions shown. A student then writes three equations for the collision. Which row in the table shows which equations are correct and which are incorrect? Equations: 1. $mu = M V + m v$ 2. $m v \sin 30^{\circ} = M V \sin 40^{\circ}$ 3. $mu = m v \cos 30^{\circ} + M V \cos 40^{\circ}$

May/June 2016

Two equal masses move towards one another along a frictionless track with speeds of $60\,\text{cm s}^{-1}$ and $30\,\text{cm s}^{-1}$. On collision, they remain stuck together. What is the speed of the masses after impact?

May/June 2016

Which line in the table shows the quantities that remain conserved in a perfectly elastic collision between two gas molecules?

May/June 2016

State the principle of conservation of momentum.

May/June 2016

In an inelastic collision, which quantities remain conserved?

May/June 2017

State Newton’s first law of motion by describing what happens when no resultant force acts on an object.

May/June 2017

State Newton’s second law of motion in words.

May/June 2017

Two identical spheres, each with mass $m$ and moving at speed $v$, are travelling directly towards one another. They undergo a head-on elastic collision. Which statement is correct?

May/June 2018

An elastic collision takes place between two bodies $X$ and $Y$. The mass of body $X$ is $m$ and the mass of body $Y$ is $4m$. Before the collision, body $X$ moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Body $Y$ is at rest before the collision. What is the kinetic energy of body $Y$ after the collision?

May/June 2018

A ball with mass $0.20\,\text{kg}$, moving in the $x$-direction at speed $0.50\,\text{m s}^{-1}$, strikes a ball of mass $0.30\,\text{kg}$ that is moving in the $y$-direction at speed $0.40\,\text{m s}^{-1}$. After the collision, the two balls remain stuck together and move at an angle $\theta$ to the $x$-direction. What is the value of $\theta$?

May/June 2018

State the meaning of the mass of a body.

May/June 2018

State the principle that momentum is conserved.

May/June 2018

A helium atom of mass $m$ strikes a wall head-on. It reaches the wall with speed $v$ and then returns along the same line of motion. Assume that the collision is perfectly elastic. What is the change in the momentum of the atom during the collision?

May/June 2019

Bar magnets P and Q are fixed on floats that can move along an air track with no friction. The two magnets move towards one another along the air track and interact, but do not touch. The relative speed at which the magnets approach is the same as their relative speed at which they move apart. Which statement about P and Q must be correct?

May/June 2019

A lead pellet is fired straight upwards into a clay block. At the instant of collision, the block is at rest, although it can move upwards freely afterwards. The pellet has mass $5.0\,\text{g}$ and the clay block has mass $95\,\text{g}$. Just before impact, the pellet is travelling vertically at an initial speed of $200\,\text{m s}^{-1}$. It becomes lodged in the block and does not come out. To what height, measured from its starting position, does the block rise?

May/June 2019

A nucleus strikes another nucleus that is initially at rest in a vacuum. The diagrams illustrate the motion of the nuclei before and after the collision. No other particles take part in the collision. Which diagram cannot be correct?

May/June 2019

A block $X$ moves along a horizontal frictionless surface towards a block $Y$ that is initially at rest, as shown in Fig. 2.1. No resistive forces act on block $X$ while it travels towards block $Y$. At time $t = 0$, block $X$ has momentum $0.40\,\text{kg m s}^{-1}$. A short time later, the blocks collide and then move apart. Fig. 2.2 shows how the momentum of block $Y$ varies with time $t$.

May/June 2019

A toy gun at rest fires a bullet. Immediately after it is fired, which statement about the bullet and the gun is not correct?

May/June 2020

A mass $m_1$ moving at speed $u_1$ collides with a mass $m_2$ moving at speed $u_2$ in the same direction. Following the collision, mass $m_1$ has speed $v_1$ and mass $m_2$ has speed $v_2$ in the same direction. The collision is perfectly elastic. Which equation is not correct?

May/June 2020

A ball of mass $m$, travelling with velocity $v$, strikes a second ball of mass $2m$ that is stationary. The two balls remain joined together. What fraction of the original kinetic energy is lost during the collision?

May/June 2020

Which quantities remain conserved during an inelastic collision?

May/June 2021

One nitrogen molecule $P$, moving at a speed of $320\,\text{m s}^{-1}$ in a vacuum, collides with a nitrogen molecule $Q$ that is at rest. Following the collision, $P$ moves with a velocity of $180\,\text{m s}^{-1}$ at an angle of $55^{\circ}$ to its original direction. $Q$ moves in a direction making an angle of $34^{\circ}$ with the initial direction of $P$. Assume that no external forces act on the molecules. What is the magnitude $v$ of the velocity of $Q$ after the collision?

May/June 2021

A rock in deep space heads towards a distant star and collides with a spacecraft that is at rest. Which result of the collision cannot happen?

May/June 2021

A beam of $\alpha$-particles is directed at a thin gold foil. One $\alpha$-particle has a head-on collision with a gold nucleus and is sent back along its original path. Which statement could account for the gold nucleus having a recoil speed that is small compared with the recoil speed of the $\alpha$-particle?

May/June 2021

What does the principle of conservation of momentum state?

May/June 2022

Ball X and ball Y travel towards one another at speeds of $5\,\text{m s}^{-1}$ and $15\,\text{m s}^{-1}$ respectively. They undergo a perfectly elastic head-on collision, and ball Y then moves to the right at a speed of $7\,\text{m s}^{-1}$. What is the speed and direction of ball X following the collision?

May/June 2022

Skaters with masses $80\,\text{kg}$ and $40\,\text{kg}$ travel straight towards one another and then collide. Before the collision, the heavier skater is travelling to the right with a speed of $2.0\,\text{m s}^{-1}$, while the lighter skater is travelling to the left with a speed of $1.0\,\text{m s}^{-1}$. Following the collision, the heavier skater travels to the right with a speed of $0.80\,\text{m s}^{-1}$. What is the relative speed of separation of the two skaters?

May/June 2022

State what the principle of conservation of momentum says.

May/June 2022

A body of mass $m$, travelling with speed $u$ on a smooth horizontal surface, undergoes a head-on collision with a body of mass $4m$ that is initially at rest. Following the collision, the mass-$m$ body moves back along the line of approach with $\frac{1}{4}$ of the kinetic energy it had before the impact. What is the speed of the mass-$4m$ body after the collision?

May/June 2023

Balls X and Y move towards one another along the same straight line and then collide. The collision is perfectly elastic. Their initial speeds are $u_x$ and $u_y$ respectively. After the collision, they separate with speeds $v_x$ and $v_y$ respectively. Their directions are shown. Which equation is right?

May/June 2023

A perfectly elastic collision takes place between two objects X and Y. The mass of X is $m$ and the mass of Y is $4m$. Before the collision, object X moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Object Y is at rest before the collision. Determine the kinetic energy of Y after the collision?

May/June 2023

A paint-spraying device is made from a box whose faces are arranged horizontally and vertically. Small openings are present in one of the vertical faces. Paint is supplied into the box at pressure through a vertical tube, then leaves the openings as narrow jets travelling horizontally. The paint leaves at a speed of $2.5\,\text{m s}^{-1}$ through $400$ holes, each with area $0.4\,\text{mm}^2$. The density of the paint is $900\,\text{kg m}^{-3}$. Calculate the horizontal force needed to keep the device at rest while the paint is being sprayed.

May/June 2023

State the momentum conservation principle.

May/June 2023

Spheres $X$ and $Y$ make up an isolated system. Sphere $Y$ has a greater mass than sphere $X$. At the start, sphere $Y$ is at rest. Sphere $X$ undergoes an elastic collision with sphere $Y$. Before the collision, the speed of sphere $X$ is $u$. Which statement must be correct?

May/June 2024

A lead pellet is fired vertically upwards into a clay block, which is at rest at the instant of impact but can move upwards freely after the impact. The pellet has a mass of $5.0\ \text{g}$ and the clay block has a mass of $95\ \text{g}$. The pellet strikes the block with an initial vertical velocity of $200\ \text{m s}^{-1}$. It becomes embedded in the block and does not come out. How high above its starting position does the block rise?

May/June 2024

In deep space, two satellites undergo an inelastic collision. What happens to the total kinetic energy and the total momentum?

May/June 2024

Which statement correctly describes a perfectly elastic collision between two objects?

May/June 2024

State what the principle of conservation of momentum means.

May/June 2024

A car with mass $m$ has its momentum rise from $p_1$ to $p_2$. What is the change in the car’s kinetic energy?

May/June 2025

What quantity is always conserved in elastic collisions?

May/June 2025

Which statement is not used to describe an elastic collision between two objects?

May/June 2025

A cart with no load is travelling along a level track at a steady velocity. The resistive forces on the cart are negligible. A heavy rock is dropped straight down into the cart. The cart then keeps moving horizontally with the rock inside it. How do the momentum and kinetic energy of the cart with the rock inside compare with the momentum and kinetic energy of the empty cart?

May/June 2025

A rocket engine expels $90\,\text{kg}$ of exhaust gas each second at a speed of $190\,\text{m s}^{-1}$ relative to the rocket. What force acts on the rocket as a result of the ejected gas?

May/June 2025

A nucleus strikes a nucleus that is at rest in a vacuum. The diagrams display the nuclei’s trajectories before the collision and after it. There are no other particles taking part in the collision. Which diagram cannot occur?

May/June 2025

Two gliders are moving towards one another on a horizontal air track. Glider P has a mass of $0.30\,\text{kg}$ and is travelling at a constant speed of $1.2\,\text{m s}^{-1}$. Glider Q has a mass of $0.60\,\text{kg}$ and is travelling at a constant speed of $1.8\,\text{m s}^{-1}$. The gliders undergo a perfectly elastic collision. What are the speeds of the two gliders after the collision?

May/June 2025

State the law of conservation of momentum.

May/June 2025

A body that is initially at rest explodes into two masses $M_1$ and $M_2$. They move away from each other with speeds $v_1$ and $v_2$, respectively. What is the ratio $\frac{v_1}{v_2}$?

Oct/Nov 2010

Two experiments are performed using two trolleys with equal masses. Every moving part of each trolley is frictionless, and the surface over which they travel is also frictionless. In both experiments, trolley X travels towards trolley Y, which is initially at rest. Following the collision in experiment 1, X comes to rest and Y moves away to the right. Following the collision in experiment 2, the trolleys stick together and move away as one. What kinds of collision occur in these experiments?

Oct/Nov 2010