Mathematics · May / June 2023 · Paper 51 · Question 6
YMA01
As printed in the paper
The question as text
6. P N α Figure 3 A particle of weight W newtons lies at rest on a rough horizontal surface, as shown in Figure 3. A force of magnitude P newtons is applied to the particle. The force acts at an angle α to the horizontal, where tan α = 4 3 The coefficient of friction between the particle and the surface is 1 4 Given that the particle does not move, show that W P 5 8 (7)
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Show the answer and mark scheme
Vertical
R
−
P
sin
α
=
W
Horizontal
F
=
P
cos
α
OR
F
cos
P
α
MAX
1
1
F
R
or
F
=
R
seen or implied
4
4
Produce a dimensionally correct inequality or equation in P and W
only, trig does not need to be substituted
Reach the given answer, with exact working.
W
5
* or 5
W
P
P
8
8
Notes for Question 6
M1
Equation for vertical equilibrium. Correct number of terms, forces resolved
where appropriate, condone sign errors and sin/cos confusion. M0 for an
inequality
A1
Correct unsimplified equation.
M1
Equation for horizontal equilibrium. Correct number of terms, forces resolved
where appropriate, condone sign errors and sin/cos confusion.
N.B. Allow
F
cos
P
α
A1
cos
Either
F
=
P
α
may be implied by use of 1
or
F
cos
P
α
where
F
4 R
MAX
MAX
M1
1
1
1
M0 for
F
< 4
R
or
F
> 4
R
or
F
R
4
M1
Eliminate F and R to form an inequality or equation in P and W only but allow
trig to be unsubstituted.
e.g. 1 (
or 1 (
4 W
P
sin
cos
P
4 W
P
sin
cos
P
+
α
)
α
+
α
) =
α
1
1
1
M0 for use of
F
< 4
R
or
F
> 4
R
or
F
R
to form their inequality
4
A1* cso
Reach the given answer with at least one line of working. Must come from
exact working and correct use of the inequality
Whole system:
(
)
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