Mathematics · May / June 2023 · Paper 51 · Question 2
YMA01
As printed in the paper
The question as text
2. A particle P rests in equilibrium on a smooth horizontal plane. A system of three forces, F1 N, F2 N and F3 N where F1 = (3ci + 4cj) F2 = (–14i + 7j) is applied to P. Given that P remains in equilibrium,
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2(a)[2]
3
F
=
(14
−
3 )
c
i
+ −−
( 7
4 )
c
j
3
Resultant force
2(b)[4]
F
+
F
=
(6 14)
−
i
+
(8
+
7
)
j
1
2
(
j)
= −
8
i
+
15
Find any relevant angle for their (even if they’ve subtracted) resultant
(need not be acute nor positive)
8
15
8
8
any of
tan
−
1
±
,tan
−
1
±
,sin
−
1
±
,cos
−
1
±
,...
15
8
17
17
120o or better (118.0724…) OR 240
or better (241.9276..)
In radians 2.1 or better (2.0607..) OR 4.2 or better (4.2224…)
Use of Pythagoras on their resultant :
( 8)
−
2
+
15
2
2(c)[4]
or their acceleration:
(
−
8
)
2
+
( )
15
2
m
m
Use of their R = 8.5m or their Resultant = ma
A correct equation in m only eg 17
=
m
×
8.5
m =
2
N. B.
2
2
−
8
15
M1
+
8.5
8.5
8
−
i
+
15
j
=
8.5m
M1
2
2
−
8
15
+
= m A1ft
8.5
8.5
2 = m A1
Notes
Accept column vectors throughout apart from answer for (a)
(a)
M1
Uses the vector sum of all 3 forces being equal to zero oe
N.B.
F
=
F
+
F is M0
3
1
2
A1
cao Must be in terms of c, i and j but allow uncollected i’s and j’s and apply isw if
necessary.
(b)
M1
Finds the resultant using
1F +
F or
−
their
F
2
3
M1
Uses trig to find a relevant angle for their resultant
A1ft
Any correct relevant angle (does not need to be acute), ft on their resultant
A1
Cso.
(c)
M1
Use of Pythagoras to find the magnitude of their resultant force or their acceleration
M1
Allow their R = 8.5 m
A1ft
A correct scalar equation in m only eg 17
=
m
×
8.5
, ft on their resultant
A1
cso
1
1.5
=
0
+
2 g t
2
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