Mathematics · Oct / Nov 2021 · Paper 51 · Question 2
YMA01
As printed in the paper
The question as text
2. A particle P of mass 2m is moving on a rough horizontal plane when it collides directly with a particle Q of mass 4m which is at rest on the plane. The speed of P immediately before the collision is 3u. The speed of Q immediately after the collision is 2u.
Read automatically from the paper; the printed page above is exact.
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2(a)[3]
I
=
4
m
×
2
u
and
−=
I
2 (
m v
−
3 )
u
AND add to eliminate I
v
= − so speed is u
u
Opposite to its original direction, reversed, in opposite direction, direction QP,
2(b)[1]
opposite direction to Q
Direction changed is B0
2(c)[6]
R = 4mg
F = 4ma ; OR Ft = 4m (0 2u)
4
mg
µ =
4
ma
(their calculated a or unknown a)
−
µ
4
mgt
=
4 (0
m
−
2 )
u
6
u
2
0
2
=
(2 )
u
2
−
2
a
(their calculated a or an unknown a)
g
6
u
2
(0
+
2 )
u t
OR
=
(their calculated t or an unknown t)
g
2
1
µ =
correctly obtained
3
Notes for question 2
M1 Complete method to give equation in m, u and v only, dimensionally
2(a)
correct, correct no. of terms, condone sign errors and consistent cancelled m’s
or extra g’s
A1 Correct equation
A1 u ; must be positive
2(b)
DB1 Dependent on an answer of +u or u in (a)
2(c)
B1 cao Seen anywhere, e.g. on a diagram
M1 Equation of motion (Allow F for friction at this stage)
OR Impulsemomentum equation
A1 Correct equation with F substituted
M1 Use of suvat to obtain an equation in u and a only
OR Use of impulsemomentum to obtain an equation in u and t only
A1 Correct equation ; equations must be consistent to earn both A marks.
A1 Accept 0.33 or better
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