Standard +0.8 This question requires students to recognize that the direction of A after collision is ambiguous (could be forward or backward), calculate B's velocity in both cases using conservation of momentum, compute kinetic energy loss for each scenario, and identify the greater loss. The multi-step reasoning with case analysis and the need to recognize the directional ambiguity elevates this above a standard momentum question, though the individual calculations are routine.
Two particles, \(A\) and \(B\), of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, \(B\) is at rest and \(A\) is moving towards \(B\) with speed 8 ms\(^{-1}\). After \(A\) and \(B\) collide, \(A\) moves with speed 2 ms\(^{-1}\).
Find the greater of the two possible total losses of kinetic energy due to the collision. [6]
correct masses with relevant velocities. Their v may be in the
opposite direction.
If g included with the masses:
Allow M1A0A1 for first three marks. Can then score M1M0A0
for final three marks.
38=32+6v
Answer
Marks
Guidance
Or 38=−32+6v
A1
v=3 v=5
A1
Allow finding only v=3, but if both speeds found they must both
be correct
KE
after
=0.5322 +0.56their v 2 =33 if correct
Answer
Marks
Guidance
B
DM1
Allow use of any v even if 0
B
Using speed of 5, KE =0.5322+0.56their 52 =81
after
Candidates may work out the loss for each particle separately
which only scores DM1 when losses subsequently added together.
KE =± ( 0.5382 − ( 0.5322 +0.56their 32))
loss
=96−33
Answer
Marks
Guidance
if correct
DM1
If two speeds found then FT their lower speed, even if later choose
the wrong loss.
If only one speed found then FT their speed.
If the candidate thinks that the particles coalesce then score M0
here
Answer
Marks
Guidance
Loss = 63 [J]
A1
If both losses found, must state which is the greater.
Only award this mark if no errors – e.g. the KE loss for v=5
should be 15 J. If wrong then A0.
Allow −63 [J].
Can score full marks even if only v=3 is found.
6
Answer
Marks
Guidance
Question
Answer
Marks
Question 4:
4 | For attempt at use of conservation of momentum. | *M1 | Must have three non-zero terms. Allow sign errors. Must have
correct masses with relevant velocities. Their v may be in the
opposite direction.
If g included with the masses:
Allow M1A0A1 for first three marks. Can then score M1M0A0
for final three marks.
38=32+6v
Or 38=−32+6v | A1
v=3 v=5 | A1 | Allow finding only v=3, but if both speeds found they must both
be correct
KE
after
=0.5322 +0.56their v 2 =33 if correct
B | DM1 | Allow use of any v even if 0
B
Using speed of 5, KE =0.5322+0.56their 52 =81
after
Candidates may work out the loss for each particle separately
which only scores DM1 when losses subsequently added together.
KE =± ( 0.5382 − ( 0.5322 +0.56their 32))
loss
=96−33
if correct | DM1 | If two speeds found then FT their lower speed, even if later choose
the wrong loss.
If only one speed found then FT their speed.
If the candidate thinks that the particles coalesce then score M0
here
Loss = 63 [J] | A1 | If both losses found, must state which is the greater.
Only award this mark if no errors – e.g. the KE loss for v=5
should be 15 J. If wrong then A0.
Allow −63 [J].
Can score full marks even if only v=3 is found.
6
Question | Answer | Marks | Guidance
Two particles, $A$ and $B$, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, $B$ is at rest and $A$ is moving towards $B$ with speed 8 ms$^{-1}$. After $A$ and $B$ collide, $A$ moves with speed 2 ms$^{-1}$.
Find the greater of the two possible total losses of kinetic energy due to the collision. [6]
\hfill \mbox{\textit{CAIE M1 2024 Q4 [6]}}