Mathematics · May / June 2024 · Paper 51 · Question 6
YMA01
As printed in the paper
The question as text
6. (m) θ Figure 3 A box of mass m lies on a rough horizontal plane. The box is pulled along the plane in a straight line at constant speed by a light rope. The rope is inclined at an angle θ to the plane, as shown in Figure 3. The coefficient of friction between the box and the plane is 1 3 The box is modelled as a particle. Given that tan 3 4
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
6(a)[7]
R
T
mg
T
cos
θ−
F
=
0
1
=
F
R
3
Solve for T, in terms of mg
(T) = 1
3 mg
1
6(b)[5]
F
=
mg
3
= ±
OR W.D. = Fd
±
F
ma
2
2
1
1
1
1
1
=
2
−
2(
1
)
=
2
−
DM1A1
u
u
g d
m
u
mu
mgd
2
3
2
2
2
3
9
2
9
2
u
u
d
=
oe
d
=
oe
8
g
8
g
Notes
M1: Vertical resolution, with correct terms, condone sign errors and
6(a)
sin/cos confusion. Allow if they use
sin( ) or similar.
3
5
A1: Correct equation
M1: Horizontal resolution, with correct terms, condone sign errors and
sin/cos confusion. Allow if they use
cos( ) or similar.
4
5
A1: Correct equation
B1: Seen anywhere, including on a diagram
DM1: Dependent on both M’s
A1:cao. Accept 0.33 mg or better.
6(b)
B1: Seen anywhere, including on a diagram
B1: F
= ±
ma
where F is friction, (allow + or −) OR Fd
DM1: Complete method, dependent on the previous B mark, using a
new dimensionally correct acceleration, to produce an equation, with
correct no. of terms, in d, u and g, condone sign errors.
OR, using workenergy principle using Fd , where F is friction, to
produce an equation, with correct no. of terms, in d, u and g, condone
sign errors
A1: Correct equation
A1: cao (must be d = , seen or implied, but allow s in the working)
N.B. Answers to (a) and (b) should be in terms of i and j, but only
penalise once. Column vectors can be used in working.
v
=
(20sin )
α
i
+
(20cos )
α
j oe e.g. use of Pythagoras but must get
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