June 2024 Paper 1 Q7

OCR MEICurrent spec7 marksMoments

7 A rectangular book ABCD rests on a smooth horizontal table. The length of AB is 28 cm and the length of AD is 18 cm. The following five forces act on the book, as shown in the diagram.

4 N at A in the direction AD
5 N at B in the direction BC
3 N at B in the direction BA
9 N at D in the direction DA
3 N at D in the direction DC

Rectangle ABCD with A top left, B top right, C bottom right, D bottom left; 4 N down at A, 5 N down at B, 3 N leftwards at B, 3 N rightwards at D and 9 N up at D

(a) Show that the resultant of the forces acting on the book has zero magnitude. [2]

(b) Find the total moment of the forces about the centre of the book. Give your answer in N m. [3]

Mark scheme (a)

Scheme	Marks	AO
Total in the AB direction is \(3 - 3 = 0\) Total in the direction AD is \(4 + 5 - 9 = 0\)	M1	2.1
So zero resultant force	A1	2.1
	[2]

Notes

M1: Considers forces in each direction

A1: AG Allow if clear statement of zero force in two perpendicular directions, Do not allow for “equilibrium” on its own eg 3=3 and 4+5=9 is not sufficient without a comment

Mark scheme (b)

Scheme	Marks	AO
Take moments anticlockwise (N cm)	B1	1.1
\(4 \times 14 - 5 \times 14 + 3 \times 9 - 9 \times 14 + 3 \times 9\)	M1	1.1
\(= -86\) N cm
\(= -0.86\) [N m]	A1	1.1
	[3]

Notes

B1: At least one moment about the centre or any corner

M1: Combines moments of 5 forces about the centre. Allow only sign errors

\(-86\) N cm: Do not allow as final answer

A1: Allow for 0.86 N m clockwise but not \(-0.86\) N m clockwise
Allow B1 SC1 for \(-0.86\) Nm as the total moment about a different point.

Mark scheme (c)

Scheme	Marks	AO
The book will rotate	B1	2.2a
clockwise [about the centre of mass]	B1	1.2
	[2]

Notes

B1: Allow turn or spin but not move, tilt or flip

B1: Allow “there is a clockwise moment” for the second mark