| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find final speed |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question requiring standard application of conservation of momentum (part i) and basic kinematics with constant acceleration (part ii). Both parts follow textbook procedures with no problem-solving insight needed, making it easier than average for A-level. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Momentum before \(= 0.1\times4 - 0.2\times3\) | B1 | or Loss by \(P = 0.1\times4 + 0.1u\) |
| Momentum after \(= -0.1u + 0.2(3.5-u)\) | B1 | or Gain by \(Q = 0.2(3.5-u) + 0.2\times3\) |
| \(0.1\times4 - 0.2\times3 = -0.1u + 0.2(3.5-u)\) | M1 | For using the principle of conservation of momentum |
| \(u = 3\) (positive value only) | A1 | Total: 4 |
| SR: If mgv used for momentum instead of mv, then \(u=3\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| For using \(v^2 = u^2 + 2as\) with \(v=0\) (either case) or equivalent | M1 | |
| \(0 = 3^2 - 10s_1\) and \(0 = 0.5^2 - 10s_2\) | A1ft | ft value of \(u\) from (i) |
| \(0.9 + 0.025\) | M1 | For using \(PQ = s_1 + s_2\) |
| Distance is \(0.925\) m | A1 | Total: 4 |
# Question 3:
## Part (i)
| Momentum before $= 0.1\times4 - 0.2\times3$ | B1 | or Loss by $P = 0.1\times4 + 0.1u$ |
| Momentum after $= -0.1u + 0.2(3.5-u)$ | B1 | or Gain by $Q = 0.2(3.5-u) + 0.2\times3$ |
| $0.1\times4 - 0.2\times3 = -0.1u + 0.2(3.5-u)$ | M1 | For using the principle of conservation of momentum |
| $u = 3$ (positive value only) | A1 | **Total: 4** |
| SR: If mgv used for momentum instead of mv, then $u=3$ | B1 | |
## Part (ii)
| For using $v^2 = u^2 + 2as$ with $v=0$ (either case) or equivalent | M1 | |
| $0 = 3^2 - 10s_1$ and $0 = 0.5^2 - 10s_2$ | A1ft | ft value of $u$ from (i) |
| $0.9 + 0.025$ | M1 | For using $PQ = s_1 + s_2$ |
| Distance is $0.925$ m | A1 | **Total: 4** |
---3 Two small spheres $P$ and $Q$ have masses 0.1 kg and 0.2 kg respectively. The spheres are moving directly towards each other on a horizontal plane and collide. Immediately before the collision $P$ has speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $Q$ has speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Immediately after the collision the spheres move away from each other, $P$ with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $Q$ with speed $( 3.5 - u ) \mathrm { m } \mathrm { s } ^ { - 1 }$.\\
(i) Find the value of $u$.
After the collision the spheres both move with deceleration of magnitude $5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until they come to rest on the plane.\\
(ii) Find the distance $P Q$ when both $P$ and $Q$ are at rest.
\hfill \mbox{\textit{OCR M1 2005 Q3 [8]}}