October 2021 Paper 1 Q5

OCR MEICurrent spec5 marksMoments

5 ABCD is a rectangular lamina in which AB is 30 cm and AD is 10 cm.

Three forces of 20 N and one force of 30 N act along the sides of the lamina as shown in the diagram.

Rectangle ABCD with AB along the top: 20 N acts to the left at A along BA extended, 20 N acts upwards at B, 20 N acts to the right at C along DC extended, 30 N acts upwards at D; a force F N acts downwards on AB at a point x cm from A

An additional force \(F\) N is also applied at right angles to AB to a point on the edge AB \(x\) cm from A.

(a) Given that the lamina is in equilibrium, calculate the values of \(F\) and \(x\). [3]

The point of application of the force \(F\) N is now moved to B, but the magnitude and direction of the force remain the same.

(b) Explain the effect of the new system of forces on the lamina. [2]

Mark scheme (a)

Scheme	Marks	AO
\(F = 50\)	B1	1.1b
Take moments about A (or D) \(Fx = 20 \times 30 + 20 \times 10\) OR Take moments about B (or C) \(F(30 - x) + 20 \times 10 = 30 \times 30\)	M1	1.1a
\(x = \dfrac{800}{50} = 16\)	A1	1.1b
	[3]

Notes

B1: cao

M1: Forming an equation for moments about any point – allow their value of \(F\) used. Allow one incorrect distance or a missing term
Do not allow for moment = force

A1: Allow 0.16 m if unit given

Mark scheme (b)

Scheme	Marks	AO
Forces have a resultant moment	E1	2.4
which have a clockwise turning effect on the lamina	E1	2.4
	[2]

Notes

E1: Allow ‘resultant moment’ or ‘not in equilibrium’ soi
Do not allow for ‘a resultant force’ on its own

E1: Clockwise must be indicated