M3 June 2005 Q1

EdexcelOld spec6 marksHooke's Law

Figure 1: particle on a plane inclined at alpha, attached by a spring to O up the slope, distance 1.6 m — Figure 1

A particle of mass 0.8 kg is attached to one end of a light elastic spring, of natural length 2 m and modulus of elasticity 20 N. The other end of the spring is attached to a fixed point \(O\) on a smooth plane which is inclined at an angle \(\alpha\) to the horizontal, where \(\tan\alpha = \tfrac{3}{4}\). The particle is held on the plane at a point which is 1.6 m down a line of greatest slope of the plane from \(O\), as shown in Figure 1. The particle is then released from rest.

Find the initial acceleration of the particle. (6)

Force diagram: thrust T down the slope, weight mg, plane at angle alpha — Mark scheme

Scheme	Marks
HL \(T = \dfrac{20 \times 0.4}{2}\ \ (= 4)\) accept \(-4\)	M1 A1
\(mg\sin\alpha + T = ma\)	M1 A1
\(0.8g \times 0.6 + 4 = 0.8a\)	M1
\(a = 10.88 \approx 10.9\ (\text{m s}^{-2})\) accept 11	A1
	(6 marks)

Notes