OCR M1 2005 January — Question 2 8 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Year2005
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeMultiple sequential collisions
DifficultyStandard +0.3 This is a standard two-collision momentum problem requiring straightforward application of conservation of momentum twice. Part (i) involves a single collision with given masses and velocities, requiring basic algebraic manipulation. Part (ii) repeats the process with an unknown mass. While it requires careful sign convention and multiple steps, it's a routine textbook exercise with no conceptual challenges beyond applying the momentum formula correctly—slightly easier than average for M1.
Spec6.03b Conservation of momentum: 1D two particles
2 \includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-2_221_1153_1340_497} Three small uniform spheres \(A , B\) and \(C\) have masses \(0.4 \mathrm {~kg} , 1.2 \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively. The spheres move in the same straight line on a smooth horizontal table, with \(B\) between \(A\) and \(C\). Sphere \(A\) is moving towards \(B\) with speed \(6 \mathrm {~ms} ^ { - 1 } , B\) is moving towards \(A\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(C\) is moving towards \(B\) with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). Spheres \(A\) and \(B\) collide. After this collision \(B\) moves with speed \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards \(C\).
  1. Find the speed with which \(A\) moves after the collision and state the direction of motion of \(A\).
  2. Spheres \(B\) and \(C\) now collide and move away from each other with speeds \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Find the value of \(m\).
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\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-2_221_1153_1340_497}

Three small uniform spheres $A , B$ and $C$ have masses $0.4 \mathrm {~kg} , 1.2 \mathrm {~kg}$ and $m \mathrm {~kg}$ respectively. The spheres move in the same straight line on a smooth horizontal table, with $B$ between $A$ and $C$. Sphere $A$ is moving towards $B$ with speed $6 \mathrm {~ms} ^ { - 1 } , B$ is moving towards $A$ with speed $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $C$ is moving towards $B$ with speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (see diagram). Spheres $A$ and $B$ collide. After this collision $B$ moves with speed $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ towards $C$.\\
(i) Find the speed with which $A$ moves after the collision and state the direction of motion of $A$.\\
(ii) Spheres $B$ and $C$ now collide and move away from each other with speeds $0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. Find the value of $m$.

\hfill \mbox{\textit{OCR M1 2005 Q2 [8]}}
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