M1 June 2006 Q2

EdexcelOld spec7 marksImpulse & Momentum

2. Two particles \(A\) and \(B\) have mass 0.4 kg and 0.3 kg respectively. They are moving in opposite directions on a smooth horizontal table and collide directly. Immediately before the collision, the speed of \(A\) is 6 m s\(^{-1}\) and the speed of \(B\) is 2 m s\(^{-1}\). As a result of the collision, the direction of motion of \(B\) is reversed and its speed immediately after the collision is 3 m s\(^{-1}\). Find

(a) the speed of \(A\) immediately after the collision, stating clearly whether the direction of motion of \(A\) is changed by the collision, (4)

(b) the magnitude of the impulse exerted on \(B\) in the collision, stating clearly the units in which your answer is given. (3)

Diagram: 0.4 kg with speed 6 and 0.3 kg with speed 2 moving towards each other; after the collision speeds v and 3 in the same direction — Mark scheme (a)

Scheme	Marks
CLM: \(0.4 \times 6 - 0.3 \times 2 = 0.4 \times v + 0.3 \times 3\)	M1 A1
\(\Rightarrow v = (+)\ 2.25\) m s\(^{-1}\)	A1
(‘+’ \(\Rightarrow\)) direction unchanged	A1ft
	(4)

Mark scheme (b)

Scheme	Marks
\(I = 0.3 \times (2 + 3) = 1.5\), Ns (o.e.)	M1 A1, B1
	(3)
	(7 marks)

Notes

(b) M1 – need (one mass) \(\times\) (sum or difference of the two speeds associated with the mass chosen)

A1 – answer must be positive

B1 allow o.e. e.g. kg m s\(^{-1}\)