Mathematics · May / June 2023 · Paper 51 · Question 1
YMA01
As printed in the paper
The question as text
1. A particle A has mass 4 kg and a particle B has mass 2 kg. The particles move towards each other in opposite directions along the same straight line on a smooth horizontal table and collide directly. Immediately before the collision, the speed of A is 2u m s –1 and the speed of B is 3u m s –1 Immediately after the collision, the speed of B is 2u m s –1 The direction of motion of B is reversed by the collision.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[3]
2u 3u
A (4 kg) B (2 kg)
v 2u
(
) (
)
(
)
CLM:
4 2
×
u
+ −
3
u
×
2
=
4
v
+
2 2
×
u
OR
Equating impulses: (
)
2 2 3
u
−−
u
=
4(
−−−
v
2 )
u
1
(
)
2 u
m s
−
1
1(b)[1]
The direction of motion is reversed.
(
)
I
= ±
2 2 3
u
−−
u
For B:
1(c)[3]
u
OR For A:
I
= ±
4
2
−−
u
2
I
=
10 Ns
u
or 10u
kgms−
1
Notes
(a)
M1
Dimensionally correct CLM equation or equating of impulses equation.
Allow consistent extra g’s. Ignore sign errors. May be +v or v
−
A1
Correct unsimplified equation
A1
Cao. Must be positive.
(b)
B1
Accept opposite direction. Do not accept changed or to the left or
backwards, away from B
N.B. This mark is dependent on correctly obtaining 1
1
2 u or
2 u
−
in (a)
(c)
M1
Dimensionally correct impulsemomentum equation using A or B.
Condone sign errors with appropriate velocities. M0 if g is included
A1
Correct unsimplified equation
A1
Cao with units. Accept kg m/s
F
+
(3
c
i
+
4 )
c
j
+ −
( 14
i
+
7 )
j
=
0 oe
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