A-LevelMathematicsMechanics9709/51 · Oct/Nov 2019 · Q710 Marks

ABC is the cross-section through the centre of mass of a uniform prism which rests with AB on a rough horizontal surface. AB = 0.4 m and C is 0.9 m above the surface (see diagram). The prism is on the point of toppling about its edge through B.

(i)Show that angle BAC = 48.4°, correct to 3 significant figures.[3]
(ii)A force of magnitude 18 N acting in the plane of the cross-section and perpendicular to AC is now applied to the prism at C. The prism is on the point of rotating about its edge through A. Calculate the weight of the prism.[3]
(iii)Given also that the prism is on the point of slipping, calculate the coefficient of friction between the prism and the surface.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] G is the CoM vertically above B. M is the mid-point of AB and E is v the point vertically below C on AB extended.
[M1] Use of similar triangles and trigonometry of a right angled triangle
[A1] A = 48.4° AG
[B1] Use trigonometry of a right angled triangle
[M1] Moments about A
[A1] W = 54.2 N
[B1] Resolve horizontally
[B1ft] Resolve vertically
[M1] Use F = μR
[A1] Accept 0.32

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.