M1 June 2008 Q7

EdexcelOld spec11 marksForces & Newton's Laws Resolving Forces

Figure 3: package on a plane inclined at 30 degrees, pushed by a 45 N force at 50 degrees to the plane — Figure 3

A package of mass 4 kg lies on a rough plane inclined at 30\(^\circ\) to the horizontal. The package is held in equilibrium by a force of magnitude 45 N acting at an angle of 50\(^\circ\) to the plane, as shown in Figure 3. The force is acting in a vertical plane through a line of greatest slope of the plane. The package is in equilibrium on the point of moving up the plane. The package is modelled as a particle. Find

(a) the magnitude of the normal reaction of the plane on the package, (5)

(b) the coefficient of friction between the plane and the package. (6)

Scheme	Marks
\(R = 45\cos 40^\circ + 4g\cos 30^\circ\)	M1 A2 (1, 0)
\(R \approx 68\) accept 68.4	DM1 A1
	(5)

Scheme	Marks
Use of \(F = \mu R\)	M1
\(F + 4g\sin 30 = 45\cos 50^\circ\)	M1 A2 (1, 0)
Leading to \(\mu \approx 0.14\) accept 0.136	DM1 A1
	(6)
	(11 marks)