| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.2 This is a standard M4 oblique collision problem requiring resolution of velocities parallel and perpendicular to the line of centres, application of conservation of momentum and the restitution equation. While it involves multiple steps and careful algebraic manipulation, it follows a well-established method taught in Further Maths M4 with no novel insight required. The 90° deflection provides a helpful constraint that simplifies the algebra. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| VIIIV SIHI NI IIIIM I I O N OA | VIIV SIHI NI IIIHM ION OO | VI4V SIHI NI JIIIM IONOO |
1.
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\caption{Figure 1}
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A smooth uniform sphere $A$ of mass $m$ is moving on a smooth horizontal plane when it collides with a second smooth uniform sphere $B$, which is at rest on the plane. The sphere $B$ has mass $4 m$ and the same radius as $A$. Immediately before the collision the direction of motion of $A$ makes an angle $\alpha$ with the line of centres of the spheres, as shown in Figure 1. The direction of motion of $A$ is turned through an angle of $90 ^ { \circ }$ by the collision and the coefficient of restitution between the spheres is $\frac { 1 } { 2 }$
Find the value of $\tan \alpha$.\\
1.
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VIIIV SIHI NI IIIIM I I O N OA & VIIV SIHI NI IIIHM ION OO & VI4V SIHI NI JIIIM IONOO \\
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\hfill \mbox{\textit{Edexcel M4 2016 Q1 [8]}}