Turning effect of forces

A beam of uniform density is supported on a pivot at its midpoint. Two weights are then positioned on the beam as illustrated, and an upward force $F$ keeps the beam in equilibrium. What is the magnitude of $F$?

May/June 2015

Fig. 2.1 shows a student carrying out a press-up. An upward total force $F$ acts on his hands, and an upward force also acts on his toes. The student’s weight is 600 N, and this force acts downward through his centre of mass.

May/June 2015

A beam of uniform density is horizontal and pivoted at its right-hand end, and it is in equilibrium. As shown, a force of 60 N acts vertically upwards on the beam. The beam has distances marked as 20 cm and 30 cm. What is the weight of the beam?

May/June 2016

A uniform plank is supported on a pivot at its mid-point. Two weights are placed on the plank, with one weight on each side of the pivot in the positions shown. A vertical force is then applied at point X so that the plank is in equilibrium. What are the magnitude and direction of this force?

May/June 2016

A beam of uniform density is mounted so that it can turn about its midpoint. Three weights, placed as shown, keep the beam in equilibrium. What is the value of $d$?

May/June 2017

Fig. 3.1 shows a car brake pedal linked to a brake cylinder. A force $F$ is applied to the brake, and this creates a moment around the pivot. When the brake is pressed, a force of 80 N acts on the piston.

May/June 2017

The diagram represents a muscle and the bones in a person’s arm. The hand is supporting a load with weight $40\,\text{N}$. The elbow serves as the pivot, and the muscle tension keeps the forearm horizontal. What is the tension in the muscle caused by the load?

May/June 2018

Two objects X and Y hang from a uniform rod that is pivoted at its centre. The rod is balanced. Which statement about X and Y is correct?

May/June 2018

A uniform rod with weight $5.0\,\text{N}$ is first kept at rest. The diagram indicates the forces acting on the rod at the moment it is let go. What occurs to the rod when it is released?

May/June 2018

The metre rule shown is in equilibrium when a $4.0\text{ N}$ weight is used. Determine the weight $W$ of the metre rule.

May/June 2019

A metre rule of uniform composition is in equilibrium under a $4.0\,\text{N}$ weight, as illustrated. What is the weight $W$ of the metre rule?

May/June 2019

Some forces act at varying distances from a pivot. Which diagram shows the force that creates the greatest moment about the pivot?

May/June 2021

Fig. 3.1 shows a small brick suspended from a newton meter. The newton meter reading is $3.0\,\text{N}$.

May/June 2021

In the diagram, a uniform solid rectangular block has weight $50\,\text{N}$ and is pivoted at point $P$. Its height is $40\,\text{cm}$, while its base measures $8.0\,\text{cm}$ across. Which horizontal force $F$ is just sufficient to cause the block to begin turning about $P$?

May/June 2022

Fig. 1.1 presents a model of the human arm. In this model, the rubber band stands for the muscle that lifts part XY of the arm upward. A mass is hung from XY, as shown in Fig. 1.2. The weight of section XY is negligible, and the model is in equilibrium.

May/June 2022

A horizontal beam of uniform density is balanced in equilibrium and is pivoted at its right-hand end. A $60\,\text{N}$ force acts vertically upward on the beam, as shown. What is the beam’s weight?

May/June 2023

A uniform beam is supported at its centre by a pivot. An object with weight $40\,\text{N}$ is positioned on the beam $20\,\text{cm}$ to the left of the pivot, as illustrated. Which force and location will keep the system in balance?

May/June 2023

Which of the following statements about the moment of a force about a pivot are correct?

May/June 2024

A crane carries a $5800\,\text{N}$ counterweight, placed $2.3\,\text{m}$ from the tower on a horizontal jib. The centre of gravity $P$ of the crane jib is shown. What horizontal distance must separate the $2300\,\text{N}$ load from $P$ for the moment about $P$ to be zero?

May/June 2024

A student studies how a metre rule balances when a load of mass $M$ is attached to it at the 5.0 cm mark.

May/June 2024

An airline passenger wants to check the weight of a suitcase he is carrying as hand luggage on to an aeroplane. He balances a uniform wooden plank, pivoted at its centre, as shown in Fig. 2.1. The plank is in equilibrium with the suitcase on one side of the pivot and three bags of sugar, each with mass $2.0\,\text{kg}$, on the opposite side. The distances are shown in Fig. 2.1.

May/June 2025

The combined weight of the load and the wheelbarrow shown is $600\,\text{N}$. What magnitude of force $F$ is needed just to raise the loaded wheelbarrow?

Oct/Nov 2015

The combined weight of the load and the wheelbarrow illustrated is $600\,\text{N}$. What magnitude of force $F$ is required to lift the loaded wheelbarrow just off the ground?

Oct/Nov 2015

Fig. 2.1 illustrates a bed that folds up against a wall in the daytime. In the horizontal position, it is held up on one side by a hinge and on the other side by two legs. The weight $W$ of the bed acts through its centre of mass, which is $0.35\,\text{m}$ horizontally from the hinge.

Oct/Nov 2016

When a freezer lid is lifted, it turns about the hinge at the back of the freezer, while the handle is located at the front. Fig. 3.1 shows a side view of the freezer. The handle is $0.70\,\text{m}$ from the hinge. The lid has a mass of $2.0\,\text{kg}$. The gravitational field strength $g$ is $10\,\text{N kg}^{-1}$.

Oct/Nov 2016

A diver weighing $500\,\text{N}$ is standing at the far end of a springboard that is $2.0\,\text{m}$ long and fixed at point $P$. The springboard itself weighs $500\,\text{N}$. Its centre of mass is located at the midpoint of the board. What is the total moment about point $P$ due to the diver and the board?

Oct/Nov 2017

Fig. 1.1 illustrates a painter standing on a wooden plank, positioned directly above the support on the right. The plank measures 3.6 m in length, 0.35 m in width and 0.025 m in thickness. The gravitational field strength $g$ is $10\,\text{N kg}^{-1}$ and the plank has a mass of 23 kg.

Oct/Nov 2017

A rope is used to haul a bucket of water up from a well. Fig. 8.1 shows the rope coiling onto a cylinder as the handle is rotated. The empty bucket has a mass of $1.0\,\text{kg}$.

Oct/Nov 2018

What expression gives the moment of a force about a pivot?

Oct/Nov 2019

One force acts on a body. Which result is impossible?

Oct/Nov 2019

A student performs an experiment to determine the mass of a metre rule. She makes use of several identical metal rings and a pivot. Each ring has a mass of $3.3\,\text{g}$. The apparatus is arranged as shown in Fig. 2.1. The student positions the pivot beneath the $45.0\,\text{cm}$ mark on the metre rule. She then adds rings, one after another, at point A, $5.0\,\text{cm}$ from the end of the rule. She changes the number of rings until the rule is as nearly balanced as possible. She notes the number $N$ of rings needed to balance the rule.

Oct/Nov 2019

A length of thread is joined to a lamina at point P, as shown in the diagram. The lamina is able to rotate freely around point Q. The tension in the thread is $F$. What is the moment of $F$ about Q?

Oct/Nov 2020

Fig. 3.1 presents, from above, a door together with an automatic door-closer. When the door swings open and shut, the hinge functions as the pivot. A girl opens the door by applying a force $P$ at point X. Force $P$ acts perpendicular to the surface of the door.

Oct/Nov 2020

A student looks into how bridge strength changes with width. Fig. 1.1 shows the apparatus the student uses.

Oct/Nov 2020

A student carries out an investigation into balancing a metre rule. She uses a metre rule with a small hole drilled through it at the 5.0 cm mark. • She places the pivot at the 5.0 cm mark. • She supports the far end of the rule with a newton meter attached to a loop of string at the 95.0 cm mark. • She hangs a 200 g mass from the rule by means of a loop of thread. • The student shifts the loop of thread holding the 200 g mass until it is positioned at the 25.0 cm mark on the metre rule. Fig. 1.1 shows the apparatus arranged by the student. • She works out the distance $d$ of the mass from the pivot and enters her value in the first row of Table 1.1. • She changes the height of the clamp supporting the newton meter until the rule is horizontal. • She notes the reading $F$ on the newton meter in the first row of Table 1.1. • The student then repeats the procedure with the loop of thread supporting the mass placed at the 40.0 cm, 55.0 cm, 65.0 cm and 80.0 cm marks on the metre rule.

Oct/Nov 2020

Fig. 1.1 depicts a wooden bench with a weight of 2000 N.

Oct/Nov 2021

The moment of a force is the quantity used to describe its turning effect.

Oct/Nov 2021

A beam of uniform mass is hinged at its midpoint. Two weights are positioned on the beam as shown, and an upward force $F$ keeps the beam in equilibrium. What is the magnitude of $F$?

Oct/Nov 2022

A uniform beam is supported on a pivot at its midpoint. Two weights are fixed to the beam at the positions shown, and an upward force $F$ keeps the beam balanced. What is the size of $F$?

Oct/Nov 2022

A force $F$ produces a moment about point $O$ on an L-shaped bar. The force $F$ is applied at point $P$. What is the moment of $F$ about $O$?

Oct/Nov 2023

A metre rule of uniform mass distribution, with weight $W$, is balanced horizontally by pivoting it at the $25\,\text{cm}$ mark and applying an upward force $F$ at the $100\,\text{cm}$ mark. A vertical force $P$ acts at the pivot to support the rule. What is the magnitude of $P$?

Oct/Nov 2023

An irregular lamina lying in a plane has a mass of $50\,\text{g}$. It is suspended from a nail passing through a small hole H close to the edge of the lamina. The nail serves as a pivot and the lamina is able to swing around it. The lamina is kept in the position shown in Fig. 3.1, a short distance above a horizontal bench. The centre of gravity of the lamina is at G.

Oct/Nov 2023

A beam of uniform mass is supported at its midpoint and kept in balance by three weights, as illustrated. What is the value of distance $x$?

Oct/Nov 2024

A force $F$ acts on a lever at a distance $l$ from the pivot, as illustrated. The length $d$ is the perpendicular separation between the force and the pivot. Which expression gives the moment of force $F$ about the pivot?

Oct/Nov 2024

A student carries out an experiment to determine the mass of a metre rule.

Oct/Nov 2024

A long plank is balanced on a pivot at its centre of gravity. Two objects, X and Y, are then positioned on the plank. X has a weight of $140\text{ N}$ and is $1.2\text{ m}$ to the left of the pivot. Y has a weight of $220\text{ N}$ and is $0.55\text{ m}$ to the right of the pivot. A third object with weight $110\text{ N}$ is placed on the plank so that the plank remains in equilibrium. On which section of the plank is the object placed?

Oct/Nov 2025

A student uses a balancing technique to find the mass of a metre rule.

Oct/Nov 2025