M1 June 2006 Q4

EdexcelOld spec11 marksForces & Newton's Laws Resolving Forces

Figure 2: particle P on a plane inclined at alpha, force 4 N up the plane — Figure 2

A particle \(P\) of mass 0.5 kg is on a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\tan\alpha = \tfrac{3}{4}\). The particle is held at rest on the plane by the action of a force of magnitude 4 N acting up the plane in a direction parallel to a line of greatest slope of the plane, as shown in Figure 2. The particle is on the point of slipping up the plane.

(a) Find the coefficient of friction between \(P\) and the plane. (7)

The force of magnitude 4 N is removed.

(b) Find the acceleration of \(P\) down the plane. (4)

Diagram: forces R, F down the plane, 4 up the plane and 0.5g — Mark scheme (a)

Diagram: forces R, F up the plane and 0.5g, acceleration a down the plane — Mark scheme (b)

Scheme	Marks
\(R = 0.5g\cos\alpha = 0.4g\)	M1 A1
\(4 = F + 0.5g\sin\alpha\)	M1 A1
\(F = \mu R\) used	M1
\(4 = 0.4g.\mu + 0.3g\) \(\Rightarrow \mu \approx 0.27(0)\)	M1 A1
	(7)

Scheme	Marks
\(0.5a = 0.3g - 0.27 \times 0.4g\)	M1 A2,1,0ft
\(\Rightarrow a \approx (+)\ 3.76\) m s\(^{-2}\) (or 3.8)	A1
	(4)
	(11 marks)

M1 June 2006 Q4

M1 June 2006 Q4

Notes

Notes