WJEC Further Unit 6 2024 June — Question 1

Exam BoardWJEC
ModuleFurther Unit 6 (Further Unit 6)
Year2024
SessionJune
PaperDownload PDF ↗
TopicOblique and successive collisions
TypeOblique collision, vector velocity form
DifficultyStandard +0.8 This is a multi-part oblique collision problem from Further Mechanics requiring conservation of momentum in 2D, coefficient of restitution calculations, angle deflection, and impulse-momentum theorem. While systematic, it demands careful vector component work, understanding that perpendicular components are unchanged in oblique collisions, and multiple connected calculations across four parts—more demanding than standard A-level mechanics but follows established procedures without requiring novel insight.
Spec6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts
  1. Two smooth spheres \(A\) and \(B\) are moving on a smooth horizontal plane when they collide obliquely. When the spheres collide, the line joining their centres is parallel to the vector \(\mathbf { j }\), as shown in the diagram below.
Immediately before the collision, sphere \(A\) has velocity ( \(6 \mathbf { i } - 3 \mathbf { j }\) ) \(\mathrm { ms } ^ { - 1 }\) and sphere \(B\) has velocity \(( - 4 \mathbf { i } + 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). Sphere \(A\) has mass 6 kg and sphere \(B\) has mass 2 kg . \includegraphics[max width=\textwidth, alt={}, center]{36112cfa-20c4-4ba8-b972-6b7b44e5182f-02_595_972_753_534} Immediately after the collision, sphere \(B\) has velocity \(( - 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\).
  1. Find the velocity of \(A\) immediately after the collision.
  2. Calculate the coefficient of restitution between \(A\) and \(B\).
  3. Find the angle through which the direction of motion of \(B\) is deflected as a result of the collision. Give your answer correct to the nearest degree.
  4. After the collision, sphere \(B\) continues to move with velocity \(( - 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) until it collides with another sphere \(C\), which exerts an impulse of \(( - 20 \mathbf { i } + 18 \mathbf { j } )\) Ns on \(B\). Find the velocity of \(B\) after the collision with \(C\).
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Question 1:
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\begin{enumerate}
  \item Two smooth spheres $A$ and $B$ are moving on a smooth horizontal plane when they collide obliquely. When the spheres collide, the line joining their centres is parallel to the vector $\mathbf { j }$, as shown in the diagram below.
\end{enumerate}

Immediately before the collision, sphere $A$ has velocity ( $6 \mathbf { i } - 3 \mathbf { j }$ ) $\mathrm { ms } ^ { - 1 }$ and sphere $B$ has velocity $( - 4 \mathbf { i } + 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$. Sphere $A$ has mass 6 kg and sphere $B$ has mass 2 kg .\\
\includegraphics[max width=\textwidth, alt={}, center]{36112cfa-20c4-4ba8-b972-6b7b44e5182f-02_595_972_753_534}

Immediately after the collision, sphere $B$ has velocity $( - 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$.\\
(a) Find the velocity of $A$ immediately after the collision.\\

(b) Calculate the coefficient of restitution between $A$ and $B$.\\

(c) Find the angle through which the direction of motion of $B$ is deflected as a result of the collision. Give your answer correct to the nearest degree.\\

(d) After the collision, sphere $B$ continues to move with velocity $( - 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$ until it collides with another sphere $C$, which exerts an impulse of $( - 20 \mathbf { i } + 18 \mathbf { j } )$ Ns on $B$.

Find the velocity of $B$ after the collision with $C$.\\

\section*{PLEASE DO NOT WRITE ON THIS PAGE}

\hfill \mbox{\textit{WJEC Further Unit 6 2024 Q1}}
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