Mathematics · May / June 2024 · Paper 51 · Question 1
YMA01
As printed in the paper
The question as text
1. Two particles, A and B, have masses m and 3m respectively. The particles are connected by a light inextensible string. Initially A and B are at rest on a smooth horizontal plane with the string slack. Particle A is then projected along the plane away from B with speed U. Given that the common speed of the particles immediately after the string becomes taut is S
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[2]
OR
and
:
3
AND eliminate I to give
A
:
−=
I
m S
(
−
U
)
B I
=
mS
−
3
=
(
−
)
oe
mS
m S
U
1
=
or 0.25 U
S
U
4
1
1(b)[3]
For A:
±
(
−
)
m
U
U
4
3
4 mU
1
For B:
Alternative
±
3
m
U
4
3
4 mU
Notes
1(a)
M1: CLM equation with correct terms, condone sign errors and cancelled m’s or
consistent extra g’s
N.B. If they use 2 impulsemomentum equations, each equation must have the
correct terms but condone sign errors.They must then eliminate the impulse to
produce an equation in m, U and S only.
N.B. Allow the use of v or similar for S in the working but must use S for their
answer.
A1: cao (A0 if m’s not cancelled)
1(b)
M1: Impulsemomentum for A or B, with correct terms, condone sign errors and
allow S for final speed but M0 if m omitted or extra g
A1ft: Correct expression in terms of m and U, ft on the magnitude of their S.
A1 cao (must be positive and a multiple of mU)
Make a free account to save your answers and see your weak topics and ask the AI why a wrong answer is wrong.