M1 June 2015 Q1

EdexcelOld spec6 marksImpulse & Momentum

1. Particle \(P\) of mass \(m\) and particle \(Q\) of mass \(km\) are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the speed of \(P\) is \(5u\) and the speed of \(Q\) is \(u\). Immediately after the collision the speed of each particle is halved and the direction of motion of each particle is reversed.

Find

(a) the value of \(k\), (3)

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

Mark scheme (a)

Scheme	Marks
\(m.5u - kmu = -\dfrac{m.5u}{2} + \dfrac{km.u}{2}\)	M1 A1
\(k = 5\)	A1
	(3)

Notes

M1 for attempt at CLM equation, with correct no. of terms, dimensionally correct. Allow consistent extra g’s and cancelled \(m\)’s and \(u\)’s and sign errors.

First A1 for a correct equation with or without \(m\)’s and \(u\)’s

Second A1 for \(k = 5\)

N.B. They may find the impulse on each particle and then equate the impulses to produce an equation. Apply the scheme to this equation.

Mark scheme (b)

Scheme	Marks
For \(P: I = m\left(\dfrac{5u}{2} - -5u\right)\) OR For \(Q: I = km\left(\dfrac{u}{2} - -u\right)\)	M1 A1
\(= \dfrac{15mu}{2}\) \(= \dfrac{15mu}{2}\)	A1
	(3)
	(6 marks)

Notes

M1 for attempt at impulse = difference in momenta, for either particle, (must be considering one particle) (M0 if g’s are included or if \(m\) or \(u\) omitted) Allow \(\pm m(\tfrac{5}{2}u - 5u)\) or \(\pm km(\tfrac{1}{2}u - u)\).

First A1 for \(\pm m(\tfrac{5}{2}u - -5u)\) or \(\pm km(\tfrac{1}{2}u - -u)\)

A1 for \(7.5mu\) oe cao (\(-7.5mu\) is A0) Allow change of sign at end to obtain magnitude