Turning effects of forces

The diagram represents a uniform beam PQ. Its length is $3.0\,\text{m}$ and its weight is $50\,\text{N}$. The beam rests on a pivot that is $1.0\,\text{m}$ from end P. A load with weight $W$ is suspended from end P, and the beam is balanced. What is the value of $W$?

Feb/March 2016

At points V and W on an object, two forces of magnitude $F$ each are applied. Together, these forces make a couple. As shown, the object has the form of a right-angled triangle with side lengths $x$ and $y$. Which expression represents the torque produced by the couple?

Feb/March 2016

A uniform metre rule with weight $2.0\,\text{N}$ is supported on a pivot at the $60\,\text{cm}$ mark. A $4.0\,\text{N}$ load is hung from one end, so that the rule turns around the pivot. When the rule is horizontal, what is the resultant moment about the pivot?

Feb/March 2017

The upward forces from the ground acting on a van that is stationary are shown. The van is $2.50\,\text{m}$ long, with the wheels $0.600\,\text{m}$ from the front of the van and $0.400\,\text{m}$ from the rear of the van. How far horizontally is the van’s centre of gravity from the front of the van?

Feb/March 2017

The diagram illustrates four forces acting on a circular object. Which row states the resultant force and resultant torque on the object?

Feb/March 2018

A fairground ride has four carriages attached to a central vertical pole, as the plan view below shows. A motor turns the central pole about its axis, causing each of the four carriages to travel along a circular path. The distance from the centre of each carriage to the axis of the pole is $3.20\,\text{m}$. While moving, each carriage is acted on by an air resistance force of $85.0\,\text{N}$. Assume that no other significant resistive forces act. Which torque must the motor exert on the pole to maintain the system at constant maximum speed?

Feb/March 2019

A horizontal beam OX is uniform, is $4.0\,\text{m}$ in length and has a weight of $100\,\text{N}$. It is hinged to a wall at point O and held up by a cord XY that is fixed to the wall at Y. What is the tension in the cord?

Feb/March 2019

A uniform rod with a weight of $20\,\text{N}$ and a length of $2.0\,\text{m}$ is subjected to two vertical forces, as illustrated. The forces indicated are $15\,\text{N}$ and $5.0\,\text{N}$. What are the resultant force acting on the rod and the resultant moment about the centre of gravity of the rod?

Feb/March 2020

A rod of length $5d$ is acted on by two parallel forces, each having magnitude $F$. Which diagram gives the locations of the two forces that produce the greatest torque on the rod?

Feb/March 2021

A metal bar PQ lies horizontally and has a length of $50.0\,\text{cm}$; it is hinged at the end P. The diagram presents the bar as seen from above. At end Q, two forces, one of $16.0\,\text{N}$ and the other of $5.0\,\text{N}$, act in the horizontal plane, as indicated. What is the resultant moment about P caused by these two forces?

Feb/March 2022

A cube WXYZ with edge length $2.0\,\text{cm}$ and mass $24.0\,\text{g}$ is placed on a metre rule of negligible mass. The cube’s geometrical centre is directly above the $70.0\,\text{cm}$ mark on the scale of the rule. Because the cube is not of uniform density, its centre of gravity does not coincide with its geometrical centre. The cube’s centre of gravity lies in the plane of the diagram. The rule is supported by a pivot at the $50.0\,\text{cm}$ mark. A mass of $23.4\,\text{g}$ is positioned vertically above the $30.0\,\text{cm}$ mark. The rule remains horizontal and is in equilibrium. What can be inferred about the location of the cube’s centre of gravity?

Feb/March 2022

A rod is mounted so that it can turn about one end. At the start, the angle $\theta$ between the rod and the horizontal is $0^{\circ}$. The rod’s weight produces a moment $M$ about the pivot. The rod is then turned in a vertical plane so that the angle $\theta$ of the rod rises from $0^{\circ}$ to $180^{\circ}$. Which graph represents the way $M$ varies with $\theta$?

Feb/March 2024

The diagram depicts four forces acting on a circular disc. Each force has magnitude $F$. Two of the forces act vertically, while the other two forces act horizontally. All four forces lie in the same plane as the disc. No additional forces act on the disc. The disc has diameter $d$. Which statement is correct?

Feb/March 2024

A shop sign with weight $75\,\text{N}$ 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 $30^\circ$ to the horizontal. Rod XY is hinged to the wall at X and its length is $0.50\,\text{m}$. Take the weights of the rods to be negligible. What horizontal force does the wall exert on rod XY?

Feb/March 2025

The diagram represents a child X with mass $20\,\text{kg}$ and a child Y with mass $15\,\text{kg}$ sitting on a uniform plank. The plank has a mass of $7.0\,\text{kg}$ and a pivot located at its midpoint. The plank is horizontal and is in equilibrium. Which statement about the weight of the plank is correct?

Feb/March 2025

State the principle of moments in words.

Feb/March 2025

The diagram illustrates four forces acting on a circular object. Which row states the resultant force and the resultant torque on the object?

May/June 2011

A metre rule that is uniform and has a mass of $100\,\text{g}$ is held up by a pivot at the $40\,\text{cm}$ mark and by a string attached at the $100\,\text{cm}$ mark. The string goes over a frictionless pulley and supports a mass of $20\,\text{g}$, as shown in the diagram. At which mark on the rule should a $50\,\text{g}$ mass be hung so that the rule is in balance?

May/June 2011

The diagrams each depict a pair of equal forces acting on a metre rule. Which diagram shows forces that produce a couple and zero resultant force?

May/June 2011

A uniform rod XY, with weight $10.0\,\text{N}$, is attached by a free hinge to a wall at X. As shown, it remains horizontal because of a force $F$ applied at Y at an angle of $30^\circ$ to the horizontal. What is the value of $F$?

May/June 2011

The diagram illustrates four forces acting on a circular object. Which row gives the resultant force and resultant torque on the object?

May/June 2011

A uniform metre rule with mass $100\,\text{ g}$ is held up by a pivot at the $40\,\text{ cm}$ mark and by a string attached at the $100\,\text{ cm}$ mark. The string goes over a frictionless pulley and supports a mass of $20\,\text{ g}$, as shown in the diagram. At what mark on the rule should a $50\,\text{ g}$ mass be hung so that the rule is in balance?

May/June 2011

The diagram illustrates a crane holding up a load $L$. A mass is used to supply a balancing load $W$. The load is positioned so that the system is in exact equilibrium, with $Wx = Ly$. The ground exerts a reaction force $R$. The distance $x$ remains unchanged. If the load is shifted further outward so that the distance $y$ increases, and the crane still does not topple, which statement is correct?

May/June 2012

The diagram depicts a solid cube of weight $W$ and side length $L$. It is held on a frictionless spindle that goes through the centres of two opposite vertical faces, one of which is shaded. The spindle is then taken away and fitted again at a position $\frac{L}{4}$ to the right of where it was originally. If the shaded face is being viewed, what torque of the couple must now be applied to prevent the cube from toppling?

May/June 2012

The diagram illustrates a crane carrying a load $L$. A mass acts as a balancing load $W$. The load is positioned so that the system is exactly in equilibrium, with $Wx = Ly$. The ground exerts a reaction force $R$. The distance $x$ stays unchanged. If the load is moved further away so that the distance $y$ becomes larger and the crane does not topple, which statement is correct?

May/June 2012

A horizontal bar rests on a pivot placed at its centre of gravity. A fixed load is fastened to one end of the bar. To maintain equilibrium, a force $F$ is exerted at a distance $x$ from the pivot. How does $F$ depend on $x$?

May/June 2013

A uniform beam of mass $1.4\,\text{kg}$ is supported at the pivot $P$ as shown. The beam is $0.60\,\text{m}$ long, and $P$ lies $0.20\,\text{m}$ from one end. Masses of $3.0\,\text{kg}$ and $6.0\,\text{kg}$ hang from the beam at distances of $0.35\,\text{m}$ and $0.15\,\text{m}$ from the pivot, as shown. What torque is needed to be applied to keep the beam in equilibrium?

May/June 2013

As illustrated, two forces act on a circular disc. A force of $3\,\text{N}$ acts straight upwards at the top of the disc, and a force of $4\,\text{N}$ acts horizontally towards the right through the centre. Which diagram indicates the line of action of the resultant force?

May/June 2013

Define the centre of gravity.

May/June 2013

A man is supporting a $100\,\text{N}$ load motionless in his hand. The total weight of the forearm and hand is $20\,\text{N}$. The forearm remains horizontal, as shown. What vertical force $F$ is required in the biceps?

May/June 2014

A spindle is fixed at one end to the midpoint of a lever with length $1.20\,\text{m}$ and at the other end to the midpoint of a disc with radius $0.20\,\text{m}$. A string is wound around the disc, goes over a pulley and is connected to a $900\,\text{N}$ weight. What is the smallest force $F$, applied at each end of the lever, that could raise the weight?

May/June 2014

The diagram illustrates four forces acting on a circular object. Which of the following states the resultant force and resultant torque on the object?

May/June 2014

A uniform beam is pivoted at $P$ as illustrated. Weights of $10\,\text{N}$ and $20\,\text{N}$ are fixed to its two ends. The beam is labelled at $0.1\,\text{m}$ intervals. The beam itself weighs $100\,\text{N}$. At what point must an additional weight of $20\,\text{N}$ be attached so that the beam is in equilibrium?

May/June 2014

A uniform metre rule is supported at the $34.0\,\text{cm}$ mark, as illustrated. The rule is in equilibrium when a $64\,\text{g}$ mass is suspended from the $4.0\,\text{cm}$ mark. Calculate the mass of the metre rule.

May/June 2015

A molecule can be modelled as an electric dipole made up of two equal point charges with opposite sign, separated by a fixed distance. As shown, the molecule enters a vertical uniform electric field while travelling with constant horizontal velocity. The positive and negative charges of the molecule enter the field simultaneously. Which row gives the velocity of the molecule in the field?

May/June 2015

As shown in Fig. 3.1, a rod $PQ$ is fastened at $P$ to a vertical wall. The rod has a length of $1.60\,\text{m}$. Its weight $W$ acts $0.64\,\text{m}$ from $P$. A wire attached to $Q$ and to the wall at $R$ keeps the rod horizontal and in equilibrium. The wire exerts a force $F$ on the rod of $44\,\text{N}$ at $30^\circ$ to the horizontal.

May/June 2015

Two coplanar forces act at the edge of a wheel. The forces have equal magnitudes. Which arrangement of forces produces only a couple?

May/June 2016

What is meant by the centre of gravity of an object?

May/June 2016

As shown, a bicycle pedal is joined to a pivot by a metal bar. A downward force of $60\,\text{N}$ acts on the pedal. What moment does this force produce about the pivot?

May/June 2016

The diagram illustrates a beam resting on two pivots. Which statement describes the condition of the upper surface X and the lower surface Y?

May/June 2016

A sphere is acted on by several forces, each with the same magnitude. Which arrangement of forces produces a resultant torque but no resultant force on the sphere?

May/June 2017

In a machine, several couples act on a rotating object, as shown. What is the net torque acting on the rotating object?

May/June 2017

A uniform beam is pivoted at $P$ as shown. A $10\,\text{N}$ weight and a $20\,\text{N}$ weight are fixed to the two ends. The beam is graduated in $0.1\,\text{m}$ intervals. The beam itself has a weight of $100\,\text{N}$. At which point should an additional $20\,\text{N}$ weight be placed so that the beam is in equilibrium?

May/June 2017

Two forces are acting on a circular disc, as illustrated. Which diagram shows the line of action of the resultant force?

May/June 2017

A uniform beam with mass $1.4\,\text{kg}$ is mounted on a pivot at $P$, as illustrated. The beam is $0.60\,\text{m}$ long, and $P$ lies $0.20\,\text{m}$ from one end. Masses of $3.0\,\text{kg}$ and $6.0\,\text{kg}$ are hung $0.35\,\text{m}$ and $0.15\,\text{m}$ from the pivot, as shown. What torque must be applied to the beam so that it stays in equilibrium?

May/June 2017

A horizontal metal bar PQ with a length of $50.0\,\text{cm}$ is hinged at P. The diagram shows the metal bar as seen from above. At end Q, two forces of $16.0\,\text{N}$ and $5.0\,\text{N}$ act in the horizontal plane, as shown in the diagram. What is the combined moment about P caused by the two forces?

May/June 2018

Two forces of equal magnitude $F$ act in parallel on a rod of length $5d$. Which diagram shows where the two forces should be applied to give the greatest torque on the rod?

May/June 2018

A diving-board with uniform mass distribution is supported by two fixed rods at points P and Q. A person is standing at the end R of the diving-board, as illustrated. The forces produced by the rods on the board are vertical. The board stays in equilibrium while the person gradually moves from R towards point Q. Which row shows how the forces produced by the rods on the board change?

May/June 2018

Two forces, each with magnitude $F$, are applied to a rod in opposite directions. The point of application of each force is a distance $d$ from pivot $P$. What is the torque of this couple about $P$?

May/June 2018

Which diagram illustrates a couple produced by two forces, each with magnitude $F$, acting on a rod?

May/June 2018

As illustrated, a couple acts on a tap. What is the torque of the couple?

May/June 2019

A crane is fitted with a counterweight so that it does not topple while raising a load, as illustrated. The counterweight has a mass of $5000\ \text{kg}$. The crane is designed to lift a load of $12.0\ \text{kN}$, and the horizontal distance from the pivot to the load is $17.0\ \text{m}$. At what distance from the pivot must the centre of gravity of the counterweight be placed to maintain equilibrium of the crane?

May/June 2019

What is the torque produced by the couple shown?

May/June 2019

Which statement gives the best description of a couple?

May/June 2020

A uniform rod XY, with weight $10.0\,\text{N}$, is freely hinged at X to a wall. As shown, it is kept level by a force $F$ applied at Y at an angle of $30^\circ$ to the horizontal. What is the value of $F$?

May/June 2020

A bicycle pedal is linked to a pivot by a metal bar, as illustrated. The force acting on the pedal is $60\,\text{N}$ vertically downward. What is the moment of this force about the pivot?

May/June 2020

Two forces, each having magnitude $F$, are applied along the sides of a rectangular metal plate, as illustrated. The plate measures length $a$ and width $b$. What is the torque about point $P$?

May/June 2020

A rod that is not uniform has a mass of $100\,\text{g}$ and a length of $50\,\text{cm}$. A chain supports it at its midpoint. Equilibrium is maintained by suspending a mass of $60\,\text{g}$ from the right-hand end, as shown. The centre of gravity of the rod is at a distance $d$ from its left-hand end. What is the value of $d$?

May/June 2020

State what the principle of moments is.

May/June 2020

Which pair of forces produces a couple with a torque of $30\,\text{N m}$?

May/June 2021

A rigid uniform bar XZ with negligible mass has a length of 1.20 m. The bar is mounted on a pivot at point P. As shown, three coplanar forces act on the bar. Forces of $16\,\text{N}$ and $20\,\text{N}$ are applied perpendicularly to the bar at points X and Y respectively. Force $F$ is applied at point Z at an angle of $30^\circ$ to the axis of the bar. The positions of the pivot and the forces along the bar are shown. The bar has a resultant moment about P of $6.0\,\text{N m}$ clockwise. What is the magnitude of $F$?

May/June 2021

A disc with radius $r$ is subjected to two equal forces of magnitude $F$ that act in opposite directions. These forces create a couple, as illustrated. What is the torque of this couple?

May/June 2021

A square sign of uniform weight $40\,\text{N}$ is hung vertically from its top edge by a horizontal hinge, as illustrated. The hinge is not frictionless. If an external force moves the sign away from the vertical and it is then let go, it does not return to the vertical position. The greatest torque exerted by the hinge on the sign is $6.0\,\text{N m}$. The sign is turned through $90^{\circ}$ so that it is horizontal and is then slowly released. At what angle to the vertical does the sign remain after release?

May/June 2021

What does the term couple mean?

May/June 2021

As shown, four coplanar forces act on a rigid rod. The rod is hinged at point $P$. Which force creates the largest moment about point $P$?

May/June 2021

A rectangular book of weight $W$ and uniform thickness is held in a vertical plane with its longer sides arranged vertically. Which expression gives the approximate torque produced by the hand on the book?

May/June 2021

Define the moment of a force around a point in terms of its turning effect.

May/June 2021

A wooden plank is arranged horizontally and pivots at one end, as illustrated. Its mass is $100\,\text{kg}$ and its length is $10\,\text{m}$. The plank’s centre of gravity lies $4\,\text{m}$ from the pivot. What is the moment of the plank’s weight about the pivot?

May/June 2022

A couple is produced by two forces. Which statement describes these two forces?

May/June 2022

A diving board has length $5.0\,\text{m}$ and is hinged at one end. It is held up $2.0\,\text{m}$ from that end by a spring with spring constant $10\,\text{kN m}^{-1}$. A child with mass $40\,\text{kg}$ stands at the outer end of the board. What additional compression does the spring experience because of the child standing on the end of the board?

May/June 2022

Which statement describes the two forces that make up a couple?

May/June 2022

An unknown mass and a $1.00\,\text{kg}$ mass are attached to the two opposite ends of a bar. The bar has negligible mass and a total length of $30.0\,\text{cm}$. The bar is in equilibrium when it is supported by a pivot located $20.0\,\text{cm}$ from the unknown mass, as shown. Determine the unknown mass.

May/June 2022

State the meaning of the centre of gravity of an object.

May/June 2022

A car driver exerts two parallel forces on a steering wheel, as illustrated. Each force has a magnitude of $15\,\text{N}$ and acts in the direction shown. The steering wheel has a diameter of $0.40\,\text{m}$. What is the torque exerted on the steering wheel?

May/June 2023

A farmer is attempting to raise the corner of a large water tank. She uses a metal rod as a lever. The farmer’s vertical force is constant and is always exerted at the end of the rod. Which change must make the upward force on the water tank larger?

May/June 2023

The rod is pivoted at point O, and a force $F$ is applied to it at point W, as shown. What moment does the force $F$ produce about O?

May/June 2023

A uniform rod XY, with weight $10.0\,\text{N}$, is hinged freely to a wall at X. As shown, it is kept horizontal by a force $F$ applied at Y at an angle of $30^{\circ}$ to the horizontal. What is the value of $F$?

May/June 2023

Which of the following is not needed for two forces to form a couple?

May/June 2023

A metre rule of uniform density is supported on a pivot at the $34.0\,\text{cm}$ mark, as shown. The rule is in equilibrium when a mass of $64\,\text{g}$ is suspended from the $4.0\,\text{cm}$ mark. What is the mass of the metre rule?

May/June 2023

A beam $PQ$ of uniform density lies horizontally on a support at point $S$. A rope is fixed to one end of the beam. The rope makes an angle of $60^{\circ}$ with the vertical and applies a force $F$, measured in newtons, to the beam. What is the moment, in $\text{N m}$, of the force $F$ about point $S$?

May/June 2024

An object is acted on by two forces. Which diagram shows a couple?

May/June 2024

The diagram represents a uniform rod, XY, which is freely hinged to a vertical wall at end Y. The rod makes an angle of $60^{\circ}$ with the wall. At end X, a force $F$ acts at an angle of $30^{\circ}$ to the rod. The rod weighs $3.0\ \text{N}$ and is in equilibrium. Determine the magnitude of force $F$?

May/June 2024

The diagram gives a view from above of a sprinkler system used to water a garden. The sprinkler is made from a tube of length $0.15\,\text{m}$. The tube is pivoted at its midpoint and rotates in a horizontal plane while releasing jets of water from both ends. The two water jets act in opposite directions to each other. Each water jet applies a horizontal force of $3.0\,\text{N}$ on the tube at right angles to the tube. What is the magnitude of the torque on the tube due to the water jets?

May/June 2024

Which row identifies a pair of forces that makes a couple?

May/June 2025

A student supports a $30\,\text{cm}$ ruler on a fulcrum positioned at the $15\,\text{cm}$ mark. She then puts a $50\,\text{g}$ mass at the $23\,\text{cm}$ mark and a $20\,\text{g}$ mass at the $11\,\text{cm}$ mark, as illustrated. Which mass should she put on the $7\,\text{cm}$ mark to make the ruler balance again?

May/June 2025

A square shop sign with uniform density has a mass of $2.4\,\text{kg}$ and side length $0.86\,\text{m}$. It is held up by a hinge fixed along its top edge. Because there is friction in the hinge, the sign hangs in equilibrium at an angle of $15^{\circ}$ to the vertical, as shown. Calculate the moment about the hinge due to the sign’s weight.

May/June 2025

The diagram depicts a couple. How is the torque of the couple found?

May/June 2025

A non-uniform bar PQ is 50\,\text{cm} long and has weight 200\,\text{N}. A block of weight 400\,\text{N} is fixed at the centre of the bar. The bar is supported on horizontal ground. An upward vertical force of 360\,\text{N} is then applied at end Q and is just enough to raise end Q clear of the ground. What is the distance from the centre of gravity of the bar to end P?

May/June 2025

Which statement about a couple is true?

May/June 2025

State the principle of moments for equilibrium.

May/June 2025

Define the moment of a force about a point by describing its turning effect.

May/June 2025

Define what is meant by the moment of a force about a pivot.

May/June 2025

Define the moment of a force in terms of turning effect.

May/June 2025

A rigid L-shaped lever arm is pivoted at point $P$. Three forces act on the lever arm, as shown in the diagram. What is the magnitude of the resultant moment produced by these forces about point $P$?

Oct/Nov 2010

As illustrated, two parallel forces of magnitude $F$ each act on a body. What is the size of the torque produced on the body by these forces?

Oct/Nov 2010

The diagram shows a spanner being used to tighten a nut. A force $F$ acts at right-angles to the spanner at a point $0.25\,\text{m}$ from the centre of the nut. Once the nut has been tightened completely, the applied force is $200\,\text{N}$. What is the resistive torque, in an anticlockwise direction, that stops any further tightening?

Oct/Nov 2010

A rigid lever arm shaped like an L is mounted so that it pivots about point P. As shown in the diagram, three forces are applied to the lever arm. What is the magnitude of the resultant moment of these forces about point P?

Oct/Nov 2010

As illustrated, two parallel forces, each with magnitude $F$, act on a body. What is the size of the torque on the body due to these forces?

Oct/Nov 2010

State what the centre of gravity of a body means.

Oct/Nov 2010

A ruler of length $0.30\,\text{m}$ is supported at its midpoint. Forces of equal size, $2.0\,\text{N}$, act in opposite directions at the two ends of the ruler, producing a couple as shown. What is the magnitude of the torque of the couple on the ruler in the position shown?

Oct/Nov 2011