OCR M2 2007 January — Question 2 4 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2007
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeCoalescence or perfectly inelastic collision
DifficultyModerate -0.3 This is a standard direct collision problem requiring conservation of momentum and the elastic collision condition (e = 1 or conservation of kinetic energy). It involves straightforward algebraic manipulation of two simultaneous equations with given masses and initial velocities. While it requires multiple steps, it's a textbook exercise with no novel insight needed, making it slightly easier than average.
Spec6.03c Momentum in 2D: vector form6.03j Perfectly elastic/inelastic: collisions

2 Two smooth spheres \(A\) and \(B\), of equal radius and of masses 0.2 kg and 0.1 kg respectively, are free to move on a smooth horizontal table. \(A\) is moving with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it collides directly with \(B\), which is stationary. The collision is perfectly elastic. Calculate the speed of \(A\) after the impact. [4]

AnswerMarks Guidance
\(e = 1 = (y-x)/4\)B1
\(0.8 = 0.2x + 0.1y\)B1
solving sim. equ.M1 not if poor quad. soln.
\(x = 4/3\) onlyA1 4
OR \(\frac{1}{2}x0.2x^2 + \frac{1}{2}x0.1y^2 = \frac{1}{2}x0.2x4^{2}[B1]\) (if for any 2)
$e = 1 = (y-x)/4$ | B1 |
$0.8 = 0.2x + 0.1y$ | B1 |
solving sim. equ. | M1 | not if poor quad. soln.
$x = 4/3$ only | A1 | 4 |

OR $\frac{1}{2}x0.2x^2 + \frac{1}{2}x0.1y^2 = \frac{1}{2}x0.2x4^{2}[B1]$ (if for any 2) |
2 Two smooth spheres $A$ and $B$, of equal radius and of masses 0.2 kg and 0.1 kg respectively, are free to move on a smooth horizontal table. $A$ is moving with speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ when it collides directly with $B$, which is stationary. The collision is perfectly elastic. Calculate the speed of $A$ after the impact. [4]

\hfill \mbox{\textit{OCR M2 2007 Q2 [4]}}