Physics 9702 · AS & A Level
Momentum and Newton's laws of motion
100 practice questions on Momentum and Newton's laws of motion, with worked solutions and instant marking.
Which statement gives the definition of force?
Feb/March 2016
On Pluto, the acceleration of free fall is $0.66\,\text{m s}^{-2}$. A certain object weighs $6.0\,\text{N}$ on Earth. What would its weight be on Pluto?
Feb/March 2017
Water emerges from a pipe and strikes a wall. As the jet impacts the wall, its horizontal velocity is $v$ and its cross-sectional area is $A$. The water has density $\rho$. The water does not bounce back from the wall. What force is exerted on the wall by the water?
Feb/March 2017
Steel pellets, each having a mass of $0.60$ g, drop straight down onto a horizontal plate at a rate of $100$ pellets per minute. They arrive at the plate with a velocity of $5.0\,\text{m s}^{-1}$ and then bounce back with a velocity of $4.0\,\text{m s}^{-1}$. What is the average force exerted on the plate by the pellets?
Feb/March 2018
Define displacement.
Feb/March 2019
A stone is projected horizontally from the top of a cliff and lands in the sea beneath. Air resistance may be ignored. The stone’s trajectory is illustrated. In what direction does the resultant force on the stone act while it is falling?
Feb/March 2020
A ball of momentum $p$ hits a horizontal surface at an angle $\theta$ to the surface, as illustrated. It leaves the surface again with the same momentum magnitude, making an angle $\theta$ to the surface. The duration of contact between the ball and the surface is time $t$. What is the magnitude of the average resultant force acting on the ball during the collision?
Feb/March 2021
Write your answers in the spaces provided for every question.
Feb/March 2021
A rigid sphere is kept stationary on the seabed. Once the sphere is let go, it moves up to the surface of the sea. The seawater has a constant density. Which statement about the sphere, from the moment it is released until it reaches the surface, is correct?
Feb/March 2022
One horizontal force $F$ acts on block X, which is touching a separate block Y, as illustrated. The blocks stay in contact while they accelerate over a horizontal frictionless surface. Air resistance is negligible. X has a larger mass than Y. Which statement is correct?
Feb/March 2022
A car of mass $750\ \text{kg}$ is acted on by a horizontal driving force of $2.0\ \text{kN}$. It undergoes a forward horizontal acceleration of $2.0\ \text{m s}^{-2}$. What is the resistive force acting horizontally?
Feb/March 2022
A sphere with radius $2.1\,\text{mm}$ descends through a liquid at terminal (constant) velocity, as illustrated in Fig. 1.1. Three forces act on the sphere while it is moving. Its weight is $7.2 \times 10^{-4}\,\text{N}$ and the upthrust on it is $4.8 \times 10^{-4}\,\text{N}$. The viscous force $F_v$ on the sphere obeys $F_v = krv$ where $r$ is the sphere’s radius, $v$ is its velocity and $k$ is a constant. The SI value of $k$ is $17$.
Feb/March 2022
A water jet strikes a vertical wall at right angles, as illustrated in Fig. 3.1. The water reaches the wall with a velocity of $5.0\,\text{m s}^{-1}$ in the horizontal direction. The jet has a cross-sectional area of $1.5 \times 10^{-4}\,\text{m}^2$. The density of the water is $1.0 \times 10^{3}\,\text{kg m}^{-3}$. After impact, the water flows down the wall.
Feb/March 2022
How is force defined?
Feb/March 2024
A car with mass $850\text{ kg}$ is moving along a straight horizontal path. The diagram shows two horizontal forces acting on the car in opposite directions. One force has magnitude $1200\text{ N}$, while the other has magnitude $1600\text{ N}$. What is the magnitude of the car’s acceleration?
Feb/March 2024
A body with constant mass starts from rest at point $P$. It then travels away from point $P$ with constant acceleration. Which statement describes the resultant force acting on the body while it is moving?
Feb/March 2024
A car experiences a constant resultant force of $300\,\text{N}$ and accelerates for $5.0\,\text{s}$. The way in which the car’s velocity, in $\text{cm s}^{-1}$, changes with time is shown. Find the mass of the car.
Feb/March 2025
An astronaut with mass $m$ inside a spacecraft experiences a gravitational force $F = mg$ while the spacecraft is at rest on the launchpad. What gravitational force acts on the astronaut when the spacecraft is launched vertically upwards with an acceleration of $0.2g$?
Feb/March 2025
A truck R of mass $9400\,\text{kg}$ travels down a slope in a straight line with constant acceleration, as shown in Fig. 3.1. At point A the truck has speed $13\,\text{m s}^{-1}$ and at point B its speed is $22\,\text{m s}^{-1}$. The distance from A to B is $180\,\text{m}$.
Feb/March 2025
A brick with a weight of $20\,\text{N}$ is placed on an inclined plane. The component of the brick’s weight acting parallel to the plane is $10\,\text{N}$. In addition, a frictional force of $4\,\text{N}$ acts on the brick. Calculate the acceleration of the brick down the plane. Take the acceleration of free fall $g$ to be equal to $10\,\text{m s}^{-2}$.
May/June 2010
A brick with weight $20\ \text{N}$ is at rest on a sloping plane. Its weight has a $10\ \text{N}$ component acting parallel to the plane. The brick also has a frictional force of $4\ \text{N}$ acting on it. What is the acceleration of the brick down the plane? Assume that the acceleration of free fall $g$ is equal to $10\ \text{m s}^{-2}$.
May/June 2010
A brick with weight $20\,\text{N}$ is stationary on an inclined plane. Its weight has a $10\,\text{N}$ component acting parallel to the plane. The brick is also acted on by a frictional force of $4\,\text{N}$. What is the acceleration of the brick down the plane? Take the acceleration of free fall $g$ to be equal to $10\,\text{m s}^{-2}$.
May/June 2010
A molecule of mass $m$ moving horizontally at velocity $u$ strikes a vertical wall perpendicular to its motion. It then bounces back horizontally with the same speed. What is the change in momentum?
May/June 2011
A force $F$ acts on an object that is moving freely. At a particular moment, the object’s velocity is $v$ and its acceleration is $a$. Which of these quantities must point in the same direction?
May/June 2011
An object's momentum increases from $160\,\text{kg m s}^{-1}$ to $240\,\text{kg m s}^{-1}$ over $2\,\text{s}$. What is the mean resultant force acting on the object during this interval?
May/June 2011
A car moves with acceleration along a straight line. A graph showing the car’s momentum against time is drawn. What is evaluated by calculating the gradient of the graph at a specific time?
May/June 2011
A stone is launched horizontally in a vacuum and follows the path illustrated. X is located on this path. Through X, XV and XH are the vertical and horizontal lines respectively. XT is the tangent to the path at X. In which directions do forces act on the stone at X?
May/June 2011
The diagram depicts two fixed pins, Y and Z. A length of elastic is stretched from Y to Z and passes around pin X, which is attached to a trolley. X is positioned at the midpoint of the elastic, and the trolley is to be driven in direction P at right angles to YZ. The tension in the elastic is $4\,\text{N}$. What force accelerates the trolley in direction P when the trolley is released?
May/June 2011
A molecule of mass $m$ moving horizontally at speed $u$ strikes a vertical wall perpendicular to its direction of motion. It then bounces back horizontally with the same speed. What is its change in momentum?
May/June 2011
State any two assumptions that belong to the simple kinetic model of a gas.
May/June 2011
A helicopter is shown in Fig. 3.1 with a cable hanging down from it towards the sea below. A man with mass $80\,\text{kg}$ rescues a child with mass $50.5\,\text{kg}$. Both are fastened to the cable and are raised from the sea to the helicopter. The lifting takes place in three stages: first a period of uniform acceleration, then a period of constant velocity, and finally it ends with a period of uniform deceleration.
May/June 2011
Each option shows a correct word equation that includes force. Which option states the definition of force?
May/June 2012
The resistive force acting against a car’s motion is assumed to vary in proportion to the square of the car’s speed. When the speed is $20\,\text{m s}^{-1}$, the force has a magnitude of $800\,\text{N}$. What effective power must the car’s engine provide in order to keep the car moving at a constant speed of $40\,\text{m s}^{-1}$?
May/June 2012
A box with mass $8.0\,\text{kg}$ is at rest on a rough horizontal surface. A string is fixed to the box, runs over a smooth pulley, and holds a $2.0\,\text{kg}$ mass on the opposite side. Once the box is let go, a frictional force of $6.0\,\text{N}$ acts on it. What is the acceleration of the box?
May/June 2012
Each option presents a correct word equation that includes force. Which option states the definition of force?
May/June 2012
A ball is launched straight downward toward the ground with an initial speed of $4.23\,\text{m s}^{-1}$. It travels for $1.51\,\text{s}$ before reaching the ground. Ignore air resistance.
May/June 2012
A motor pulls a log with mass $452\,\text{kg}$ up a slope using a cable, as illustrated in Fig. 2.1. The slope makes an angle of $14.0^\circ$ to the horizontal.
May/June 2012
A car with mass $750\,\text{kg}$ experiences a horizontal driving force of $2.0\,\text{kN}$. It moves with a forward horizontal acceleration of $2.0\,\text{m s}^{-2}$. What is the horizontal resistive force?
May/June 2013
A lift (elevator) has a passenger car that is held up by a cable passing over a light, frictionless pulley and attached to a balancing weight. As the passenger car moves upward, the balancing weight descends. The table lists some masses: Passenger car: $520\,\text{kg}$ Balancing weight: $640\,\text{kg}$ Passenger: $80\,\text{kg}$ When the car is carrying only one passenger and the pulley is free to rotate, what is the magnitude of the car’s acceleration?
May/June 2013
Define force in physics.
May/June 2013
The graph illustrates how the momentum of a motorcycle varies with time. What resultant force acts on the motorcycle?
May/June 2014
When a resultant force acts on a body, it accelerates. What is the resultant force equal to?
May/June 2014
A ship with mass $8.4 \times 10^7\,\text{kg}$ is moving towards a harbour at a speed of $16.4\,\text{m s}^{-1}$. If reverse thrust provides a steady total stopping force of $920\,000\,\text{N}$, Calculate the time taken to bring it to rest.
May/June 2014
For a time interval of $2.0\,\text{s}$, a body is acted on by a resultant force of $10\,\text{N}$. Which graph might represent how the momentum $p$ of the body changes with time $t$?
May/June 2014
State Newton’s first law of motion in your own words.
May/June 2014
What would be a reasonable estimate for the average gravitational force acting on a fully grown woman standing on Earth?
May/June 2015
A child riding on a sledge moves down a hill with acceleration $a$. The hill is inclined at an angle $\theta$ to the horizontal. The combined mass of the child and the sledge is $m$. The acceleration due to free fall is $g$. What is the friction force $F$?
May/June 2015
A box with mass $8.0\,\text{kg}$ is at rest on a horizontal rough surface. A string attached to the box runs over a smooth pulley and carries a $2.0\,\text{kg}$ mass at the other end. Once the box is released, a frictional force of $6.0\,\text{N}$ acts on it. What is the acceleration of the box?
May/June 2015
What is meant by the force acting on a body?
May/June 2015
A motor drives a conveyor belt so that it moves with velocity $v$. Sand falls straight down onto the belt at a rate of $m\,\text{kg s}^{-1}$. What extra power is required to keep the conveyor belt moving at constant speed when the sand begins to land on it?
May/June 2015
A firework rocket is launched straight upwards. Its fuel burns and gives the rocket a steady upward force. Once $5\,\text{s}$ have passed, all the fuel has been used up. Air resistance is negligible. What is the acceleration before and after $5\,\text{s}$?
May/June 2015
An astronaut launches a stone with a horizontal velocity close to the Moon’s surface. Which row describes the horizontal and vertical forces acting on the stone after it is released?
May/June 2015
Newton’s third law of motion is commonly expressed as ‘Every action (force) has an equal and opposite reaction.’ A book is at rest on a table. If the book’s weight is the ‘action’ force, what force is the corresponding ‘reaction’?
May/June 2015
Define power in words.
May/June 2015
A sphere is released from rest and falls through the air. The graph shows how the sphere’s velocity changes with time. Which diagram represents the forces acting on the sphere when its velocity is the one at point $P$ on the graph?
May/June 2016
A parachutist is descending at a constant (terminal) velocity. Which statement is incorrect?
May/June 2016
A ball drops straight down onto a horizontal surface and bounces back, as illustrated. Just before it strikes the ground, the ball has momentum $p_1$ downwards. Once it has rebounded, it moves away from the ground with momentum $p_2$ upwards. The ball remains in contact with the ground for $0.020\,\text{s}$. Over this time interval, an average resultant force of $25\,\text{N}$ acts on the ball. What is a possible combination of values for $p_1$ and $p_2$?
May/June 2016
The IKAROS satellite has a mass of $320\,\text{kg}$ and travels through space by means of a solar sail with area $20\,\text{m}^2$. The mean solar wind pressure is $1.0 \times 10^{-5}\,\text{N m}^{-2}$. What acceleration does the solar wind produce on the satellite?
May/June 2016
An electron is placed in an electric field of strength $5 \times 10^4\,\text{V m}^{-1}$. No other force acts on the electron. The mass and charge of an electron are known. Which quantity can be worked out without any additional information?
May/June 2016
A ball with mass $150\,\text{g}$ is stationary on a horizontal floor, as shown in Fig. 3.1.
May/June 2016
The graph illustrates the way the momentum of a motorcycle varies with time. What is the resultant force on the motorcycle?
May/June 2017
A rocket-propelled truck has a mass that is roughly the same as the mass of the fuel stored in its tank. The fuel is set alight, and a constant force drives the truck along horizontal tracks. Air resistance can be ignored. In a test run, the fuel is used up at a steady rate. Which statement describes how the acceleration of the truck changes during the test run?
May/June 2017
A rubber ball is released so that it falls onto a table and then rebounds upward. The table applies a force $F$ to the ball. Which graph most accurately represents how the force $F$ changes with time $t$ during the brief interval when the ball is touching the table?
May/June 2017
A golf ball with mass $m$ is released from rest and falls onto a hard surface from height $h_1$, then bounces up to height $h_2$. The momentum of the golf ball immediately before it hits the surface is not the same as its momentum immediately after it leaves the surface. What is the total change in momentum of the golf ball during the interval between these two moments? (Ignore air resistance.)
May/June 2017
A book of weight $W$ is resting on a table. A student tries to describe Newton’s third law of motion by saying that ‘action equals reaction’. If the book’s weight is treated as the ‘action’ force, what is the ‘reaction’ force?
May/June 2017
A ball with mass $2.0\,\text{kg}$ is moving horizontally at a speed of $4.0\,\text{m s}^{-1}$. It hits a wall and then rebounds in the opposite direction at a speed of $2.8\,\text{m s}^{-1}$. The collision lasts for $150\,\text{ms}$. What is the average force exerted on the wall?
May/June 2017
The graph illustrates how the weight of objects changes with mass on a certain planet. What is the value of the acceleration of free fall on the planet?
May/June 2018
The momentum of a car with mass $m$ rises from $p_1$ to $p_2$. What is the rise in the kinetic energy of the car?
May/June 2018
An astronaut launches a stone horizontally close to the Moon’s surface, where there is no atmosphere. Which row describes the horizontal and vertical forces acting on the stone after it has been released?
May/June 2018
A tennis ball with mass $55\,\text{g}$ moves horizontally at a speed of $30\,\text{m s}^{-1}$. It then strikes a wall and rebounds horizontally with a speed of $20\,\text{m s}^{-1}$. The ball remains in contact with the wall for $5.0 \times 10^{-3}\,\text{s}$. What is the average force exerted on the wall by the ball?
May/June 2018
Two masses, $M$ and $m$, are joined by an inextensible string that runs over a frictionless pulley. Mass $M$ is placed on a frictionless slope, as illustrated. The slope makes an angle $\theta$ with the horizontal. At first, the two masses are held at rest, and they are then released. Mass $M$ travels down the slope. Which expression is necessarily true?
May/June 2018
State Newton’s first law of motion in words.
May/June 2018
Each diagram shows two forces with the same magnitude. Which diagram is an example of a pair of forces that Newton’s third law of motion describes?
May/June 2019
A car of mass $m$ is considered. A person must apply a force $F$ to the car so that it accelerates at $a$. To make the car accelerate at $3a$, the person must apply a force $2F$. Which expression represents the constant resistive force acting against the car's motion?
May/June 2019
Two parallel vertical plates produce a uniform electric field. A positively charged particle is located in the vacuum region between the plates, as shown. Which statement is correct?
May/June 2019
State Newton’s second law of motion in words.
May/June 2019
For a raindrop of mass $m$ descending with speed $v$, the resultant force $F$ is described by the equation $F = mg - kv^2$, where $k$ is a constant and $g$ is the acceleration of free fall. What is the raindrop’s velocity when it has reached a constant (terminal) velocity?
May/June 2020
The resultant force acting on an object is gradually increased. Which graph could represent how the momentum $p$ of the object changes with time $t$?
May/June 2020
An astronaut weighs $660\,\text{N}$ while standing on the Earth’s surface. The acceleration of free fall on the surface of Mars is $3.71\,\text{m s}^{-2}$. What would the astronaut’s weight be if she were standing on the surface of Mars?
May/June 2020
A ball of mass $m$ moves vertically downward and then strikes a horizontal floor with speed $u$. It bounces vertically upward with speed $v$. The impact lasts for a time $\Delta t$. What is the average resultant force exerted on the ball during the collision?
May/June 2020
For a raindrop of mass $m$ descending vertically at speed $v$, the resultant force $F$ is described by $F = mg - kv^2$ in which $k$ is a constant and $g$ represents the acceleration of free fall. As the raindrop falls, it finally attains a constant (terminal) velocity. Which graph shows how the terminal velocity of the raindrop varies with mass $m$?
May/June 2020
A skier is dragged in a straight line across level ground by a wire attached to a kite. The skier has mass $89\,\text{kg}$. The wire makes an angle of $28^\circ$ with the horizontal. Fig. 2.2 shows how the skier’s velocity $v$ varies with time $t$.
May/June 2020
A rocket is launched from the Earth into space. Newton’s third law of motion explains that forces occur in pairs. One force in this pair is the weight of the rocket. What is the other force in this pair?
May/June 2021
A book with weight $W$ is resting on a table. A student tries to describe Newton’s third law of motion by stating that ‘action equals reaction’. If the book’s weight is the ‘action’ force, what force is the ‘reaction’ force?
May/June 2021
What does the term unit of momentum mean?
May/June 2021
Two masses, $M$ and $m$, are joined by an inextensible string that runs over a frictionless pulley. Mass $M$ is on a frictionless slope inclined at an angle $\theta$ to the horizontal. Initially, both masses are held at rest and are then released. Mass $M$ moves with acceleration down the slope. Which expression must be correct?
May/June 2021
The masses and weights of four distinct objects on the surfaces of four different planets are shown. On which planet is the acceleration of free fall at the surface the lowest?
May/June 2021
At an airport, a person is moving suitcases with a trolley. The combined mass of the trolley and suitcases is $72\,\text{kg}$.
May/June 2021
A ball is projected vertically downward to the ground from a height of $1.5\,\text{m}$, and it arrives at the ground with speed $8.7\,\text{m s}^{-1}$. Take air resistance to be negligible.
May/June 2021
An object travels in a straight line across the ground at a constant speed. Which statement about the resultant force acting on the object is correct?
May/June 2022
Water emerges from a pipe and strikes a wall. As the water jet reaches the wall, its horizontal speed is $v$ and its cross-sectional area is $A$. The density of the water is $\rho$. The water does not rebound from the wall. What force does the water exert on the wall?
May/June 2022
A projectile is fired at an angle to horizontal ground and moves through the air. It is at its greatest height at position $X$. Assume that no upthrust acts on the projectile. Which diagram shows the direction or directions of the force or forces acting on the projectile at position $X$?
May/June 2022
Which statement is not one of the conditions for a pair of forces to obey Newton’s third law of motion?
May/June 2022
A child with mass $20\,\text{kg}$ is standing on the rough top surface of a sledge whose mass is $40\,\text{kg}$. The sledge is able to move along a horizontal surface with no friction. One end of a rope is fixed to the sledge. The rope goes round a stationary frictionless pole, and the child holds the free end of the rope, as illustrated. The rope remains horizontal. The child exerts a horizontal pull of $12\,\text{N}$ on the rope. As a result, the child and the sledge accelerate together with the same acceleration towards the pole. What is the frictional force acting between the child and the sledge?
May/June 2022
A car speeds up from rest. The graph shows how the momentum of the car changes with time. What does the gradient of the graph at a specific time represent?
May/June 2022
A ball is released onto a horizontal surface and rebounds straight upwards. While the ball is touching the ground, the following forces are acting: • the weight $W$ of the ball • the contact force $P$ applied to the ground by the ball • the contact force $N$ applied to the ball by the ground. At the moment the ball is in contact with the ground, it is instantaneously at rest. At this instant, which relationship is correct?
May/June 2022
A camera drone with mass $1.20\,\text{kg}$ remains stationary in the air at a particular point above the ground. The drone is fitted with four propellers. During a period of $1.00\,\text{s}$, each propeller drives $0.400\,\text{kg}$ of air straight downwards. Take the air above the propellers to be at rest. What is the speed of the air as it leaves each propeller?
May/June 2023
A box is at rest on the Earth, as shown. Newton’s third law explains that forces of the same kind occur in pairs. One force in the pair is the box’s weight $W$. Which arrow shows the other force in this pair?
May/June 2023
A submarine with a total mass of $3200\,\text{kg}$ is stationary beneath the water. Its total mass is then reduced by $200\,\text{kg}$, as water is pumped out horizontally from the submarine in a negligible time. The upthrust on the submarine remains the same. Because the total weight of the submarine changes, it accelerates vertically upwards. What is the submarine's initial upwards acceleration?
May/June 2023
Each diagram shows two forces with the same magnitude. Which diagram shows a pair of forces that Newton’s third law of motion describes?
May/June 2023