M1 June 2009 Q5

EdexcelOld spec9 marksForces & Newton's Laws Resolving Forces

Figure 1: box of mass 15 kg on a horizontal plane, pulled by a force of P N at 50 degrees to the horizontal — Figure 1

A small box of mass 15 kg rests on a rough horizontal plane. The coefficient of friction between the box and the plane is 0.2. A force of magnitude \(P\) newtons is applied to the box at 50\(^\circ\) to the horizontal, as shown in Figure 1. The box is on the point of sliding along the plane.

Find the value of \(P\), giving your answer to 2 significant figures. (9)

Scheme	Marks
\(F = P\cos 50^\circ\)	M1 A1
\(F = 0.2R\) seen or implied.	B1
\(P\sin 50^\circ + R = 15g\)	M1 A1 A1
Eliminating \(R\); Solving for \(P\); \(P = 37\) (2 SF)	DM1; DM1; A1
	(9 marks)