IB Physics HL A.2 Forces and momentum questions

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Question 1

Multiple choiceHard1 mark

A body of mass $M$ moves at speed $u$ along the $+x$ -direction and explodes into two pieces of masses $\alpha M$ and $(1-\alpha)M$ where $0<\alpha<1$ The piece of mass $\alpha M$ moves at speed $v$ perpendicular to the original motion. The external impulse during the explosion is negligible. What is the speed of the other piece divided by $u$

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Answer: C. Total momentum is conserved as a vector. The other piece must have momentum components $Mu$ and $-\alpha Mv$ so its speed is

\frac{\sqrt{(Mu)^2+(\alpha Mv)^2}}{(1-\alpha)M}.

Dividing by $u$ gives $\dfrac{\sqrt{1+\alpha^2(v/u)^2}}{1-\alpha}$

A: assigns mass $\alpha M$ rather than $(1-\alpha)M$ to the other piece.
B: adds the perpendicular momentum components as scalar magnitudes.
D: uses only the $x$ -component and omits the momentum needed to cancel the first piece’s perpendicular component.
Remember: conserve momentum in each perpendicular direction before finding a resultant speed.

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