| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Ball bouncing on horizontal surface |
| Difficulty | Standard +0.3 This is a standard projectile motion problem combined with coefficient of restitution, requiring multiple connected steps but using routine M3 techniques: SUVAT for vertical motion to find impact velocity, restitution formula for bounce velocity, and impulse-momentum theorem. All methods are textbook applications with no novel insight required, making it slightly above average difficulty due to the multi-part nature and careful bookkeeping needed. |
| Spec | 3.02h Motion under gravity: vector form6.03e Impulse: by a force6.03f Impulse-momentum: relation6.03j Perfectly elastic/inelastic: collisions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Use of correct formula | M1 | Or by energy |
| Vert speed imm before bounce \(= 2.8\ \text{ms}^{-1}\) | A1 | |
| Time between bounces \(= 0.286\) (s) \((2/7)\) | B1 | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Use of their \(t\) in a correct formula | M1 | Or \(-u = u - 9.8t\) |
| Vert speed imm after bounce \(= 1.4\ \text{ms}^{-1}\) | A1 | |
| Coeff of rest \(= 0.5\) | B1ft | Their values for \(v\) after/\(v\) before; must be worked out to fraction or decimal; \(0 \leq e \leq 1\) |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{Imp} = \text{change of mom}\) | M1 | \(I = 0.3 \times (v) + 0.3 \times (u)\); allow their \(u, v\); allow sign errors for M1, allow if answer implies use of their values |
| \(I = 1.26\) (Ns) | A1 | CAO |
| [2] |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use of correct formula | M1 | Or by energy |
| Vert speed imm before bounce $= 2.8\ \text{ms}^{-1}$ | A1 | |
| Time between bounces $= 0.286$ (s) $(2/7)$ | B1 | |
| **[3]** | | |
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Use of their $t$ in a correct formula | M1 | Or $-u = u - 9.8t$ |
| Vert speed imm after bounce $= 1.4\ \text{ms}^{-1}$ | A1 | |
| Coeff of rest $= 0.5$ | B1ft | Their values for $v$ after/$v$ before; must be worked out to fraction or decimal; $0 \leq e \leq 1$ |
| **[3]** | | |
## Question 2(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Imp} = \text{change of mom}$ | M1 | $I = 0.3 \times (v) + 0.3 \times (u)$; allow their $u, v$; allow sign errors for M1, allow if answer implies use of their values |
| $I = 1.26$ (Ns) | A1 | CAO |
| **[2]** | | |2 A particle of mass 0.3 kg is projected horizontally under gravity with velocity $3.5 \mathrm {~ms} ^ { - 1 }$ from a point 0.4 m above a smooth horizontal plane. The particle first hits the plane at point $A$; it bounces and hits the plane a second time at point $B$. The distance $A B$ is 1 m . Calculate\\
(i) the vertical component of the velocity of the particle when it arrives at $A$, and the time taken for the particle to travel from $A$ to $B$,\\
(ii) the coefficient of restitution between the particle and the plane,\\
(iii) the impulse exerted by the plane on the particle at $A$.
\hfill \mbox{\textit{OCR M3 2013 Q2 [8]}}