Mathematics · Oct / Nov 2023 · Paper 51 · Question 1
YMA01
As printed in the paper
The question as text
1. x metres 2 metres A C D B 6 metres Figure 1 Figure 1 shows a beam AB with weight 24 N and length 6 m. The beam is suspended by two light vertical ropes. The ropes are attached to the points C and D on the beam where AC = x metres and CD = 2 m. The tension in the rope attached to the beam at C is double the tension in the rope attached to the beam at D. The beam is modelled as a uniform rod, resting horizontally in equilibrium. Find (i) the tension in the rope attached to the beam at D. (ii) the value of x. (5)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
Form a moments equation
M(A): (2
T
×
x
)
+
T x
(
+
2)
=
(24 3)
×
Form a second equation
vert 3
T =
24
Alternative moments equations in x and T
M(C): 24(3
−
x
)
=
T
×
2
M(G): 2 (3
T
−
x
)
=
T x
(
−
1)
M(D): (2
×
2)
=
24 (
×
−
1)
T
x
M(B): 2 (6
T
−
x
)
+
T
(4
−
x
)
=
(24 3)
×
24
x
x
24(6
−
x
)
(6
−
x
)
M(C):
×
+
2
=
×
T
6
2
6
2
T =
8(N)
7
accept 2.3 or better
x =
3
Notes for question 1
M1
Forms a moments equation in x and T only with the correct no. of terms.
Allow consistent extra g’ s.
M0 if no x.
A1
Correct unsimplified moments equation. Where two moments equations are
used, award this mark for the first correct equation.
Resolves vertically to give equation in T only or a second moments equation
M1
in x and T (M0 if no x.). Must be dimensionally correct with the correct no. of
terms.
Correct value for tension at D
A1
Correct value for x. Accept 2.3 or better
A1
N.B. If T and 2T the wrong way round or they use 24g, can score max
M1A0M1A0A0.
=
+
:
w = + −
8
( 0.5)(4)
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