Standard +0.3 This is a straightforward momentum conservation problem with two spheres colliding. Students must apply conservation of momentum to find B's final speed, then check the coefficient of restitution constraint (0 ≤ e ≤ 1) to determine which solutions are physically valid. It requires standard A-level mechanics techniques with one additional step beyond basic collision problems, making it slightly above average difficulty.
\includegraphics{figure_2}
Two small uniform smooth spheres A and B have masses 0.5 kg and 2 kg respectively. The two spheres are travelling in the same direction in the same straight line on a smooth horizontal surface. Sphere A is moving towards B with speed \(6 \text{ m s}^{-1}\) and B is moving away from A with speed \(2 \text{ m s}^{-1}\) (see diagram). Spheres A and B collide. After this collision A moves with speed \(0.2 \text{ m s}^{-1}\).
Determine the possible speeds with which B moves after the collision. [4]
errors and a slip in one value only – allow mgv for M
marks only
Answer
Marks
Guidance
v = 3 .4 5 (m s-1)
A1
1.1
0 .5 ( 6 ) + 2 ( 2 ) = 0 .5 ( − 0 .2 ) + 2 v
M1
3.1b
compared to first application of CLM must be the
same total momentum before collision but different
sign of 0.2 in expression for total momentum after the
collision
Answer
Marks
Guidance
v=3.55(m s-1)
A1
1.1
[4]
Question 2:
2 | 0 .5 ( 6 ) + 2 ( 2 ) = 0 .5 ( 0 .2 ) + 2 v | M1 | 3.3 | Use of CLM – correct number of terms – allow sign
errors and a slip in one value only – allow mgv for M
marks only
v = 3 .4 5 (m s-1) | A1 | 1.1
0 .5 ( 6 ) + 2 ( 2 ) = 0 .5 ( − 0 .2 ) + 2 v | M1 | 3.1b | Use of CLM (again) – correct number of terms. When
compared to first application of CLM must be the
same total momentum before collision but different
sign of 0.2 in expression for total momentum after the
collision
v=3.55(m s-1) | A1 | 1.1
[4]
\includegraphics{figure_2}
Two small uniform smooth spheres A and B have masses 0.5 kg and 2 kg respectively. The two spheres are travelling in the same direction in the same straight line on a smooth horizontal surface. Sphere A is moving towards B with speed $6 \text{ m s}^{-1}$ and B is moving away from A with speed $2 \text{ m s}^{-1}$ (see diagram). Spheres A and B collide. After this collision A moves with speed $0.2 \text{ m s}^{-1}$.
Determine the possible speeds with which B moves after the collision. [4]
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2023 Q2 [4]}}