Moderate -0.3 This is a straightforward vector resolution problem requiring students to resolve three forces into components, sum them, and find the magnitude and direction of the resultant. While it involves multiple steps and trigonometry, it's a standard textbook exercise with no conceptual challenges beyond applying the basic method taught in M1.
\includegraphics{figure_2}
Three coplanar forces act at a point. The magnitudes of the forces are \(5 \text{ N}\), \(6 \text{ N}\) and \(7 \text{ N}\), and the directions in which the forces act are shown in the diagram. Find the magnitude and direction of the resultant of the three forces.
[6]
Question 2:
2 | o o
X = 7 + 5cos50 – 6cos30
o o
Y = 5sin50 – 6sin30
2 2 2
R = 5.01.. + 0.83..
θ
tan = 0.8302/5.0178
Magnitude is 5.09 N and
o
direction is 9.4 anti-clockwise
from force of magnitude 7 N | M1
A1
A1ft
M1
M1
A1 6 | For finding component X (3
terms) or component Y (2
terms)
ft for sin/cos instead of cos/sin
o
and/or 70 (100 – 30) instead of
o
60 (90 – 30)
SR (max 1/3) for candidates
who use ΣF + R = 0 or ΣF = 0
(instead of ΣF = R).
X = +5.02 or –5.02 and
Y = +0.83 or -0.83
2 2 2
For using R = X + Y
Y
For using tan θ =
X
2 | o
10.9N and 20.6 anticlockwise
from x-axis
or 3.50 N and 59.0 o clockwise
from x-axis
or 2.15 N and 157.3 o
anticlockwise from x-axis
5.09 N
o
9.4 anticlockwise from the
x-axis | M1
A1
M1
A1
M1
A1 6 | For finding the resultant R (in
1
magnitude and direction) of any
two of the forces.
For finding the magnitude of the
resultant of R and the third
1
force.
For finding the direction of the
resultant of R and the third
1
force.
Page 2 | Mark Scheme | Syllabus | Paper
A AND AS LEVEL – JUNE 2005 | 9709 | 4
2 | 6
R 5
7
R = 5.09 (A2) (or some value
such that 4.9 ≤ R ≤ 5.3 (A1))
9.4 o (A2) (or some value such
that 9 o≤θ ≤ 9.8 o (A1))
anticlockwise from the x-axis | M2
A2
(or
A1)
A2 6
(or
A1) | For correct drawing to scale
\includegraphics{figure_2}
Three coplanar forces act at a point. The magnitudes of the forces are $5 \text{ N}$, $6 \text{ N}$ and $7 \text{ N}$, and the directions in which the forces act are shown in the diagram. Find the magnitude and direction of the resultant of the three forces.
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\hfill \mbox{\textit{CAIE M1 2005 Q2 [6]}}