Physics 9702 · AS & A Level
Equilibrium of forces
100 practice questions on Equilibrium of forces, with worked solutions and instant marking.
A crane has an arm with a frictionless pulley fixed to it. A cable runs over the pulley and carries a load of $10\,\text{kN}$ as shown. The crane arm applies a force $F$ to the pulley. What is the value of $F$?
Feb/March 2016
A spherical object travels through water at constant speed as it falls. Three forces act on the object. Which diagram, showing these three forces to scale, is correct?
Feb/March 2017
An object is suspended using two cords wrapped around two rods, as illustrated. The object is in equilibrium under the action of the forces $F_1$ and $F_2$. The object has a weight of $10\,\text{N}$. Friction between the rods and the cords is negligible. Angle $\theta$ is $90^{\circ}$. Which row in the table gives an angle $\theta$ of $90^{\circ}$?
Feb/March 2017
A horizontal force $H$ keeps a pendulum bob at rest. The diagram shows the three forces acting on the bob. The tension in the pendulum string is $T$. The weight of the pendulum bob is $W$. The string is inclined at an angle of $30^\circ$ to the vertical. Which statement is correct?
Feb/March 2017
A steady potential difference is maintained across two horizontal metal plates. An electrically charged oil droplet is kept stationary by the electric field between the plates. When part of the oil evaporates, the droplet’s mass decreases and it begins to accelerate. Its charge stays the same. In which direction will the droplet accelerate, and what change must be made to the separation of the plates to stop this acceleration?
Feb/March 2017
Complete Fig. 1.1 by placing a tick (✓) in the correct column to show whether each listed quantity is a scalar or a vector.
Feb/March 2017
State the meaning of velocity.
Feb/March 2017
A charged oil drop remains at rest between two charged parallel plates. Which forces are acting on the oil drop?
Feb/March 2018
For which example is the underlined body unable to be in equilibrium?
Feb/March 2018
Two forces of the same size are shown by two coplanar vectors. One points east and the other points north. In which direction should a single force act to balance these two forces?
Feb/March 2018
A stone with mass $m$ is released from a tall building. Air resistance is significant. The acceleration of free fall is $g$. While the stone is moving with constant (terminal) velocity, which statement is correct?
Feb/March 2018
A ball moves downward through a liquid at steady speed. Three forces act on it: upthrust, drag-force and weight. Which statement is correct?
Feb/March 2019
A block is acted on by three coplanar forces. Which diagram shows the directions of the forces so that the block could be in equilibrium?
Feb/March 2020
A mass of $30\,\text{kg}$ hangs from the lower end of a wire. A horizontal force $F$ acts on the mass so that it remains in equilibrium, while the wire makes an angle of $30^\circ$ to the vertical, as shown. What is the magnitude of $F$?
Feb/March 2021
An aircraft moves with a constant velocity of $90\,\text{m s}^{-1}$ while flying horizontally. The diagram shows the horizontal forces acting on the aircraft. The mass of the aircraft is $2000\,\text{kg}$. Calculate the power generated by the thrust force.
Feb/March 2021
A ball moves through a liquid at a steady speed. Three forces act on it: an upthrust, a drag force and its weight. The liquid has a uniform density. Which statement is correct?
Feb/March 2024
A trapdoor with a hinge is kept shut in the horizontal position by means of a cable. There are three forces acting on the trapdoor: its weight $W$, the tension $T$ in the cable, and the force $H$ at the hinge. Which list shows these three forces in order of increasing magnitude?
Feb/March 2024
The diagram represents a uniform plank XY with length $4.0\,\text{m}$ and weight $300\,\text{N}$. The plank is supported by fixed supports at both ends X and Y. A child whose weight is $600\,\text{N}$ is placed at different points on the plank. At end X, the support applies an upward force $F$ on the plank. What is the value of $F$ when the child is positioned at X and when the child is positioned at Y?
Feb/March 2025
Forces of $3\,\text{N}$, $4\,\text{N}$ and $5\,\text{N}$ are applied at a single point on an object. The directions of the forces may be changed. What is the magnitude of the smallest resultant force from these forces?
May/June 2010
Forces of $3\ \text{N}$, $4\ \text{N}$ and $5\ \text{N}$ act together at a single point on an object. The directions in which the forces act may change. What is the value of the minimum resultant force of these forces?
May/June 2010
At a single point on an object, forces of $3\,\text{N}$, $4\,\text{N}$ and $5\,\text{N}$ act. The directions of these forces may be adjusted. What is the minimum possible value of the resultant force from these forces?
May/June 2010
State the two conditions that must be satisfied if a body is to be in equilibrium.
May/June 2010
A cable car with weight $W$ is suspended in equilibrium from its cable at point P. As shown, the cable exerts tensions $T_1$ and $T_2$. Which diagram shows the forces acting at point P correctly?
May/June 2011
A cable car with weight $W$ is in equilibrium, suspended from its cable at point $P$. The cable exerts tensions $T_1$ and $T_2$ as shown. Which diagram correctly shows the forces acting at point $P$?
May/June 2011
Explain the meaning of centre of gravity.
May/June 2011
A climber is held against a vertical wall by a rope, as illustrated in Fig. 2.1. The climber’s weight $W$ is $520\,\text{N}$. The rope, with negligible weight, is fastened to the climber and to a fixed point $P$, where it is inclined at an angle of $18^\circ$ to the vertical. A reaction force $R$ acts at right-angles to the wall. The climber is in equilibrium.
May/June 2011
A car with mass $m$ moves uphill at steady speed on a slope inclined at an angle $\theta$ to the horizontal, as shown in the diagram. Air resistance and friction create a resistive force $F$. What force is required to drive the car at this steady speed?
May/June 2012
A ladder stands on icy (frictionless) ground and is leaning against a rough wall. The moment it is released, it starts to slip. Which diagram correctly indicates the directions of the forces $P$, $W$ and $R$ acting on the ladder as it starts to slide?
May/June 2012
A car with mass $m$ moves up a slope at a constant speed, where the slope makes an angle $\theta$ with the horizontal, as illustrated. Air resistance and friction exert a resistive force $F$. What force must be applied to keep the car moving at this constant speed?
May/June 2012
State Newton’s first law in words.
May/June 2012
Explain how distance and displacement differ.
May/June 2012
A cable keeps a hinged trapdoor closed while it is in the horizontal position. The trapdoor is acted on by three forces: the weight $W$ of the door, the tension $T$ in the cable, and the force $H$ at the hinge. Which list arranges these three forces in order of increasing magnitude?
May/June 2013
A vehicle is stationary on an incline. It is taken to have three forces acting on it so that it remains in equilibrium. These are its weight $W$, a normal reaction force $R$ and a frictional force $F$. Which triangle of forces is correct?
May/June 2013
All external forces acting on a body balance each other out. Which statement must be correct?
May/June 2013
A wooden block is placed on a rough board. The far end of the board is then lifted until the block moves down the surface of the board with constant velocity $v$. Which row shows the forces acting on the block while it is sliding at constant velocity?
May/June 2013
Distinguish between mass and weight by giving the difference.
May/June 2013
The diagrams illustrate two different ways of suspending the same picture. In each case, a string is fixed to the same points on the picture and arranged symmetrically over a nail in a wall. The forces shown are the ones acting on the nail. In diagram 1, the string loop is shorter than it is in diagram 2. Which statement about the magnitude of the forces is correct?
May/June 2014
A tractor with mass $1000\,\text{kg}$ is attached to a trailer of mass $1000\,\text{kg}$ by a tow-bar. The overall resistance to motion is constant and equal to $4000\,\text{N}$. A quarter of this resistance acts on the trailer. If the tractor and trailer are travelling over horizontal ground at a steady speed of $6\,\text{m s}^{-1}$, what force does the tow-bar exert on the tractor?
May/June 2014
What condition must an object satisfy to be in equilibrium?
May/June 2014
A uniform plank AB, with length $5.0\,\text{m}$ and weight $200\,\text{N}$, is laid across a stream, as illustrated in Fig. 3.1. A man whose weight is $880\,\text{N}$ stands at a distance $x$ from end A. The ground exerts a vertical force $F_A$ on the plank at end A and a vertical force $F_B$ on the plank at end B. While the man walks along the plank, the plank remains in equilibrium.
May/June 2014
A ladder rests on icy (frictionless) ground and is leaning against a rough wall. The moment it is let go, it starts to slip. Which diagram correctly shows the directions of the forces $P$, $W$ and $R$ acting on the ladder while it is sliding?
May/June 2015
An air bubble in a tank of water is moving upwards at constant velocity. The forces acting on the bubble are $X$, $Y$ and $Z$ as shown. Which statement describes these three forces?
May/June 2015
The diagrams show systems of coplanar forces acting at a point. The lengths of the force vectors indicate the sizes of the forces. Which system of forces is in equilibrium?
May/June 2015
A rigid body is acted on by forces. All of the forces lie in one plane. Which diagram shows the body in equilibrium?
May/June 2016
A trailer with weight $30\,\text{kN}$ is connected to a cab at $X$, as shown in the diagram. What upward force does the cab exert on the trailer at $X$?
May/June 2016
A light rigid rod $XY$ has an object of weight $W$ attached at one end. The rod is balanced, with support from a roller at $Z$ and a vertical wall at $X$. The roller provides a force $R$ on the rod, as shown. The diagram indicates the directions, but not the sizes, of the forces $R$ and $W$. What is the direction of the force acting on the rod at $X$?
May/June 2016
Just before a thunderstorm, the hairs on your head may occasionally stand up. A hair with mass $0.50\,\text{mg}$ and charge $1.0\,\text{pC}$ is held in equilibrium by a force produced by an electric field. Ignore all forces apart from the weight of the hair and the electric force. Find the electric field strength?
May/June 2016
An object is acted on by three coplanar forces in the directions shown. Which diagram shows a possible equilibrium situation for the object?
May/June 2016
A horizontal footbridge of uniform density has a length of $12\,\text{m}$ and a weight of $4000\,\text{N}$. It is supported at two points, X and Y, as illustrated. A man whose weight is $600\,\text{N}$ stands $4\,\text{m}$ from support X. What upward force does support X exert on the footbridge?
May/June 2017
A metal cylinder hangs vertically at rest, supported by a cord. The diagram shows the cylinder in four separate positions P, Q, R and S. Which statement accounts for the change in the tension $T$ in the cord?
May/June 2017
A bubble of air moves upwards through a liquid with a constant speed. The forces acting on it are the upthrust $U$, the viscous drag $D$ and its weight $W$. Which diagram shows the directions of these forces and their relative sizes?
May/June 2017
State the two conditions that must be satisfied for a system to be in equilibrium.
May/June 2017
Two forces of magnitude $5.0\,\text{N}$ and $12\,\text{N}$ act from the same point on an object. Calculate the magnitude of the resultant force $R$ when the forces are in opposite directions.
May/June 2017
An aircraft is moving in horizontal flight with a constant velocity of $90\ \text{m s}^{-1}$. The diagram indicates some of the forces acting on it. The aircraft has a mass of $2000\ \text{kg}$. What is the power developed by the thrust force?
May/June 2018
The vector diagram illustrates three coplanar forces acting on an object at $P$. The magnitude of the resultant of these three forces is $1\,\text{N}$. What is the direction of this resultant force?
May/June 2018
The diagram depicts a ball of weight $W$ suspended in equilibrium by a string. The string makes an angle $\theta$ with the vertical. The tension in the string is $T$. A horizontal force $P$ from a metal rod keeps the ball away from the wall. What is the relationship between the magnitudes of $T$, $P$ and $W$?
May/June 2018
Three forces act in parallel on an object. The object is in equilibrium because of these forces. What conditions must these forces satisfy?
May/June 2019
A submarine moves downward vertically at a steady velocity. The three forces acting on it are viscous drag, upthrust and weight. Which relationship between the sizes of these forces is correct?
May/June 2019
A car with mass $m$ moves up a slope inclined at an angle $\theta$ to the horizontal at constant speed, as shown in the diagram. Air resistance and friction exert a resistive force $F$. The acceleration of free fall is $g$. What force is required to drive the car at this constant speed?
May/June 2019
A parachutist is descending at constant (terminal) velocity. Which statement is incorrect?
May/June 2019
A picture is held up from a nail by one cord attached to two points $X$ and $Y$ on the picture. Friction between the cord and the nail is negligible, so the tension is the same on both sides of the cord. The picture is in a symmetrical position, as illustrated. The tension in the cord is $T$. On each side, the angle between the cord and the vertical is $\theta$. Which statement is correct?
May/June 2019
A shop sign with a weight of $75\,\text{N}$ is suspended from a frame fixed to a vertical wall. The frame is made up of a horizontal rod $XY$ and a rod $YZ$ which makes an angle of $30^\circ$ with the horizontal. Rod $XY$ is joined to the wall at $X$ by a hinge and has a length of $0.50\,\text{m}$. The weights of the rods may be ignored. What horizontal force does the wall exert on rod $XY$?
May/June 2019
State what the term centre of gravity of a body means.
May/June 2019
A wooden block is placed on the rough top surface of a board. The board is then lifted at one end until the block slides down it with constant velocity $v$. What describes the forces acting on the block while it is sliding at constant velocity?
May/June 2020
Four sets of vectors are illustrated, and each set shows every force acting on an object. All the forces lie in one plane. The object is in equilibrium. Which set of vectors could show the forces acting on the object?
May/June 2020
A slender horizontal beam XY is attached by a free hinge at point Y to a vertical wall. The beam is kept in equilibrium by a cable XZ fixed to the wall at point Z. A weight $W$ acts on the beam at point X. The force in the cable is $F_C$, and the force in the beam is $F_B$ respectively. Which vector triangle shows the forces on point X?
May/June 2020
A light rigid rod $XY$ carries an object of weight $W$ attached at one end. The rod is balanced in equilibrium, supported at $Z$ and against a vertical wall at $X$. As shown, the support applies a force $R$ to the rod. The diagram indicates the directions, but not the sizes, of the forces $R$ and $W$. What is the direction of the force acting on the rod at $X$?
May/June 2020
An oil drop carrying negative charge and having mass $m$ is located between two horizontal metal plates that are parallel and separated by a distance $d$. With a potential difference (p.d.) of $V_1$ across the plates, the drop moves upwards with constant speed. If the p.d. is reduced to $V_2$, the drop moves downwards with the same constant speed. Whenever the drop is in motion, air resistance acts on it. The upthrust on the drop is negligible. The acceleration of free fall is $g$. What is the charge on the oil drop?
May/June 2020
State two conditions that must be satisfied for an object to be in equilibrium.
May/June 2020
A charged oil drop remains at rest between two charged parallel plates. Which forces are exerted on the oil drop?
May/June 2021
A steel ball is falling through still air at constant (terminal) speed. The forces acting on the ball are upthrust, viscous drag and weight. In order of increasing magnitude, what are these three forces?
May/June 2021
At what time is an object in equilibrium?
May/June 2022
A diving board of uniform density is supported by two fixed rods at points $P$ and $Q$. A person stands at the end $R$ of the diving board, as shown. The forces from the rods acting on the board are vertical. The board stays in equilibrium while the person moves slowly from $R$ towards point $Q$. Which row shows how the magnitudes of the forces from the rods on the board change?
May/June 2022
A uniform rod is hinged to a wall at one end. Its other end is held up by a wire, keeping the rod horizontal and in equilibrium. Which arrow indicates the direction of the force exerted on the rod by the hinge?
May/June 2022
A wall-mounted street lamp is supported by a metal rod and a cable. Which vector triangle could show the forces acting on the end of the rod at point $P$?
May/June 2022
Forces with magnitudes $2\,\text{N}$, $4\,\text{N}$ and $7\,\text{N}$ are combined to give a resultant force. The three force magnitudes are fixed, although the forces can act in any direction within the same plane. Which magnitude is not a possible value for the resultant force?
May/June 2022
A metal wire connects a sphere to the horizontal bed at the bottom of a river, as illustrated in Fig. 2.1. The sphere is completely below the water surface and in equilibrium, with the wire making an angle of $68^\circ$ to the horizontal surface. The sphere’s weight is $32\,\text{N}$. The upthrust on the sphere is $280\,\text{N}$. The water has density $1.0 \times 10^3\,\text{kg m}^{-3}$. Assume that the force on the sphere caused by the water flow acts horizontally.
May/June 2022
An equilibrium diagram shows a ball of weight $W$ suspended from a string. The string makes an angle $\theta$ with the vertical. The tension in the string is $T$. A metal rod exerts a horizontal force $P$ on the ball, keeping it away from the wall. Which relation between the magnitudes of $T$, $P$ and $W$ is correct?
May/June 2023
A rigid, uniform beam of weight $W$ is joined to a fixed support by a hinge, as illustrated in Fig. 2.1. A compressed spring applies a total upward force of $8.2\,\text{N}$ to the horizontal beam. A block with weight $0.30\,\text{N}$ is resting on the beam. The beam’s right-hand end is tied to the ground by a string making an angle of $30^\circ$ to the horizontal. The tension in the string is $4.8\,\text{N}$. The distances measured along the beam are shown in Fig. 2.1. The beam is in equilibrium. Take the hinge to be frictionless.
May/June 2023
State what the centre of gravity of an object means.
May/June 2023
An isolated object with negligible weight is subject to two coplanar forces of equal magnitude. In which diagram is the object in equilibrium?
May/June 2024
The diagram illustrates the dimensions of an elastic cord that is used to launch a stone. When the cord is stretched into the arrangement shown, the tension in the cord is $T$. Which force is exerted on the stone by the elastic cord?
May/June 2024
An object is in equilibrium under three forces, all of which lie in the same plane. The diagram shows two of the forces acting on the object. The third force is not shown in the diagram. What is the missing third force?
May/June 2024
An object has two forces acting on it altogether. The object is in equilibrium. Which of the following statements about the forces are correct? 1. The two forces must be of equal magnitude. 2. The two forces must act in the same direction. 3. The two forces must pass through the same point.
May/June 2024
The drag force $F_D$ on an object falling through air is defined by $F_D = \frac{1}{2} C \rho A v^2$, where $A$ represents the cross-sectional area of the object, $v$ is the object's speed in the air, $\rho$ is the density of the air and $C$ is a constant known as the drag coefficient.
May/June 2024
For a sphere falling through a liquid, the drag force $F_{D}$ is $F_{D} = 6\pi\eta r v$, where $r$ represents the sphere’s radius, $v$ is the sphere’s speed in the liquid, and $\eta$ is the liquid property called viscosity.
May/June 2024
A parachutist is descending at constant (terminal) velocity. Which statement is incorrect?
May/June 2025
A wooden block is kept at rest in a container of water by means of a string fixed to both the wooden block and the base of the container. The wooden block has mass $m$ and volume $V$. The water has density $\rho$. The acceleration of free fall is $g$. What is the magnitude of the force exerted on the block by the tension in the string?
May/June 2025
A block is in equilibrium on an inclined plane. Which vector triangle corresponds to the three forces on the block?
May/June 2025
A picture frame is suspended by a string, and the string is held up by a pin. The frame is in equilibrium. Which diagram shows the vector triangle of forces acting on the picture frame?
May/June 2025
A street lamp is attached to a wall using a metal rod and a cable. Which vector triangle shows the forces acting at point $P$?
Oct/Nov 2010
The diagram illustrates a rope bridge constructed by a student on an adventure training course. The student has weight $W$. Which equation gives the tension $T$ in the rope?
Oct/Nov 2010
A street lamp is attached to a wall by means of a metal rod and a cable. Which vector triangle shows the forces acting at point P?
Oct/Nov 2010
A ladder is balanced in equilibrium, with its foot on rough ground and its top leaning against a rough wall. Its weight $W$ acts through the centre of gravity $G$. Additional forces act on the ladder at $P$ and at $Q$. These forces are $P$ and $Q$ respectively. Which vector triangle shows the forces acting on the ladder?
Oct/Nov 2011
A trailer with weight $30\,\text{kN}$ is attached to a cab at X, as shown in the diagram. What is the upward force applied by the cab on the trailer at X?
Oct/Nov 2011
A ladder is in equilibrium, with one end on rough ground and the other against a rough wall. Its weight $W$ acts through the centre of gravity $G$. In addition, forces act on the ladder at $P$ and at $Q$. These forces are $P$ and $Q$ respectively. Which vector triangle shows the forces acting on the ladder?
Oct/Nov 2011
An object is falling through a uniform gravitational field and experiences air resistance. The air resistance rises until terminal velocity is attained. Which factor has no effect on its terminal velocity?
Oct/Nov 2011
The diagram illustrates an experiment for determining the force acting on a ball due to a horizontal stream of air. The ball hangs from a light string and has a weight of $0.15\,\text{N}$. The string is deflected by $30^{\circ}$ from the vertical. What is the force on the ball caused by the air flow?
Oct/Nov 2012
A sledge moves down a slope with constant velocity. The three forces acting on the sledge are the normal contact force $C$, the weight $W$ and a frictional force $F$ of constant size. Which diagram shows these forces acting on the sledge?
Oct/Nov 2012
A picture hanging on a wall is held in place by a wire that passes over a nail. The mass of the picture is $4.2\text{ kg}$. What is the tension in the wire supporting it?
Oct/Nov 2012