CAIE M1 2022 June — Question 1 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2022
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeLoss of kinetic energy in collision
DifficultyModerate -0.8 This is a straightforward two-part momentum and energy question requiring only standard application of conservation of momentum and kinetic energy formulas. Part (a) involves setting up one equation with the given speed relationship, and part (b) is direct calculation of KE before and after. No problem-solving insight or novel approach needed—purely routine mechanics.
Spec6.02d Mechanical energy: KE and PE concepts6.03b Conservation of momentum: 1D two particles
Small smooth spheres \(A\) and \(B\), of equal radii and of masses \(5\text{kg}\) and \(3\text{kg}\) respectively, lie on a smooth horizontal plane. Initially \(B\) is at rest and \(A\) is moving towards \(B\) with speed \(8.5\text{ms}^{-1}\). The spheres collide and after the collision \(A\) continues to move in the same direction but with a quarter of the speed of \(B\).
  1. Find the speed of \(B\) after the collision. [3]
  2. Find the loss of kinetic energy of the system due to the collision. [2]
Question 1:
AnswerMarks Guidance
1(a)Conservation of momentum M1
3 terms; allow M1 if speed of A after collision is 8.5.
4
Allow 58.55X 3Y where X and Y are different
which may be seen by later work. If X and Y are
subsequently used as being equal then M0.
AnswerMarks Guidance
58.550.25v3vA1 OE e.g. 58.55V 34V
Speed of B 10 ms1A1 Do not award if 10 from using mgv, maximum 2/3
–10 is A0 as speed required not velocity
3
AnswerMarks
1(b)1
KE before  58.52180.625
2
1 1
KE after  52.52  310215.625150165.625
AnswerMarks Guidance
2 21 Attempt at any of the 3 terms for KE, using their 10 ms1
1 1
538.52, 532.52
Not not
2 2
1
not 53102 unless X  Y seen
2
AnswerMarks Guidance
KE loss 180.625165.62515 JA1 Accept ‒15, AWRT 15.0
2
AnswerMarks Guidance
QuestionAnswer Marks 
Question 1:
--- 1(a) ---
1(a) | Conservation of momentum | M1 | 1
3 terms; allow M1 if speed of A after collision is 8.5.
4
Allow 58.55X 3Y where X and Y are different
which may be seen by later work. If X and Y are
subsequently used as being equal then M0.
58.550.25v3v | A1 | OE e.g. 58.55V 34V
Speed of B 10 ms1 | A1 | Do not award if 10 from using mgv, maximum 2/3
–10 is A0 as speed required not velocity
3
--- 1(b) ---
1(b) | 1
KE before  58.52180.625
2
1 1
KE after  52.52  310215.625150165.625
2 2 | 1 | Attempt at any of the 3 terms for KE, using their 10 ms1
1 1
538.52, 532.52
Not not
2 2
1
not 53102 unless X  Y seen
2
KE loss 180.625165.62515 J | A1 | Accept ‒15, AWRT 15.0
2
Question | Answer | Marks | Guidance
Small smooth spheres $A$ and $B$, of equal radii and of masses $5\text{kg}$ and $3\text{kg}$ respectively, lie on a smooth horizontal plane. Initially $B$ is at rest and $A$ is moving towards $B$ with speed $8.5\text{ms}^{-1}$. The spheres collide and after the collision $A$ continues to move in the same direction but with a quarter of the speed of $B$.

\begin{enumerate}[label=(\alph*)]
\item Find the speed of $B$ after the collision. [3]

\item Find the loss of kinetic energy of the system due to the collision. [2]
\end{enumerate}

\hfill \mbox{\textit{CAIE M1 2022 Q1 [5]}}
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