Mathematics · May / June 2022 · Paper 51 · Question 3
YMA01
As printed in the paper
The question as text
3. A tractor of mass 6 tonnes is dragging a large block of mass 2 tonnes along rough horizontal ground. The cable connecting the tractor to the block is horizontal and parallel to the direction of motion. The cable is modelled as being light and inextensible. The driving force of the tractor is 7400 N and the resistance to the motion of the tractor is 200 N. The resistance to the motion of the block is R newtons, where R is a constant. Given that the tension in the cable is 6000 N and the tractor is accelerating,
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Show the answer and mark scheme
3(a)[6]
a
7400
−
200
−
=
8000
Any two of these three equations
R
a
6000
−
=
2000
R
a
N.B. 6000 (N) must be used as the tension to earn an M mark.
R = 5600
N.B. If they consistently use tonnes in their equations treat as a MR i.e.
max M1A0M1A0M1A1
Wrong figs. for mass, e.g. 6000000 etc or just m, can score M mark in
that equation.
Same acceleration for the tractor and the block
3(b)[1]
Notes for question 3
N.B. Enter marks on ePen in the order in which the equations appear.
M1 Correct no. of terms, condone sign errors
3(a)
(use mass to determine which equation is being attempted)
A1 Correct equation
M1 Correct no. of terms, condone sign errors
A1 Correct equation
DM1 Solve for R, dependent on both M marks
A1 cao
B1 Any equivalent statement e.g ‘both have the same acceleration’ but
not just ‘same acceleration’. Need to say ‘both’ or mention the tractor
and the block. Allow ‘they have the same acceleration’.
3(b)
Allow ‘same acceleration throughout the system’ and ‘both particles
have the same acceleration’.
N.B. B0 if extra wrong answers are included.
( )
=
5
−
14si
n3
0
o
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