M1 June 2010 Q3

Figure 1: box on a horizontal floor pushed by a force of 100 N acting downwards at 30 degrees to the floor — Figure 1

A small box is pushed along a floor. The floor is modelled as a rough horizontal plane and the box is modelled as a particle. The coefficient of friction between the box and the floor is \(\dfrac{1}{2}\). The box is pushed by a force of magnitude 100 N which acts at an angle of 30\(^\circ\) with the floor, as shown in Figure 1.

Given that the box moves with constant speed, find the mass of the box. (7)

Scheme	Marks
\((\rightarrow)\ \ 100\cos 30 = F\)	M1 A1
\(F = 0.5R\) seen	A1 (B1)
\((\downarrow)\ \ mg + 100\cos 60 = R\)	M1 A1
\(m = 13\) kg or 12.6 kg	DM1 A1
	(7 marks)