A-level · Moments

Moments of forcesExam-style questions

The moment (turning effect) of a force as force × perpendicular distance from the pivot, measured clockwise or anticlockwise, in newton-metres — including forces acting at an angle to a rod.

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23 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A non-uniform rod $AB$ of length $6$ m and mass $40$ kg hangs horizontally from a ceiling, supported by two light vertical wires attached at $C$ and $D$ , where $AC = 1$ m and $AD = 5$ m. The tension in the wire at $D$ is twice the tension in the wire at $C$ . Take $g = 9.8$ m s⁻².(a) Find the tension in each wire. (2 marks)
(b) Determine the distance of the centre of mass of the rod from $A$ . (2 marks)

A block of mass $30$ kg is now hung from the rod at $B$ .
(c) Find the new tension in each wire. (3 marks)
(d) Determine the greatest mass that could instead be hung at $B$ without the wire at $C$ becoming slack. (2 marks)
Level 4 · 9 marksTry it
2
Kofi and Jess carry a uniform pole $PQ$ , of length $4.8$ metres. The pole is horizontal and at rest.

Kofi holds the pole at the end $P$ , and Jess holds it at the point $X$ , where $QX = 1.2$ metres, as shown in the diagram below.Kofi and Jess each exert a vertical force on the pole.
(a) The force that Kofi exerts on the pole is $10g$ newtons.
(a) (i) Show that the mass of the pole is $30$ kilograms.

(ii) Find, in terms of $g$ , the force that Jess exerts on the pole.

(4 marks)
(b) A bucket of mass $6$ kilograms is hung from the midpoint of the pole. Kofi and Jess still hold the pole at $P$ and $X$ , and the pole is still horizontal and at rest.

Kofi says that, as the bucket hangs from the middle of the pole, he and Jess will each support half of its weight.

Explain, with a reason, whether Kofi is correct.

(2 marks)
Level 4 · 6 marksTry it
3
In a play area, a uniform log $AB$ , of length $6$ metres, rests horizontally on two tree stumps.

One stump supports the log at $C$ , $0.5$ metres from $A$ , and the other supports it at $D$ , $1.5$ metres from $B$ , as shown in the diagram below.A child of mass $24$ kilograms stands on the log at the end $B$ , and the log stays horizontal and in equilibrium. The child may be modelled as a particle.
(a) The stump at $C$ exerts an upward force of $15g$ newtons on the log.
(a) (i) Show that the mass of the log is $64$ kilograms.

(ii) Find, in terms of $g$ , the reaction force on the log at $D$

(4 marks)
(b) The child now gets off the log.

A parent says that, now the child is no longer on the log, the reaction force on the log at $C$ will be less than $15g$ newtons.

Explain, with a reason, whether the parent is correct.

(2 marks)
Level 4 · 6 marksTry it