M1 January 2013 Q1

EdexcelOld spec7 marksImpulse & Momentum

1. Two particles \(P\) and \(Q\) have masses \(4m\) and \(m\) respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of \(P\) and \(Q\) immediately before the collision are \(2u\) and \(5u\) respectively. Immediately after the collision, the speed of \(P\) is \(\dfrac{1}{2}u\) and its direction of motion is reversed.

(a) Find the speed and direction of motion of \(Q\) after the collision. (4)

(b) Find the magnitude of the impulse exerted on \(P\) by \(Q\) in the collision. (3)

Scheme	Marks
\(4m.2u - m.5u = -4m.\tfrac{1}{2}u + mv\)	M1 A1
\(3mu = -2mu + mv\)
\(v = 5u\), opposite direction	A1, A1 cso
	(4)

Scheme	Marks
\(I = 4m\left(\tfrac{1}{2}u - {-2u}\right)\) OR \(I = m(5u - {-5u})\)	M1 A1
\(= 10mu\) \(= 10mu\)	A1
	(3)
	(7 marks)