1. a).
The figure shows a force of magnitude F and two of its components
of magnitude F1 and F2 which are mutually perpendicular. What is the
resultant force in terms of F, F1 and F2.
Horizontal Component
Vertical Component
Resultant force
[3]
= F2Sin𝜃
= F1Cos𝜃
= F2Sin𝜃 + F1Cos𝜃
b) The vector diagram below shows two forces Y and Z acting at a point X.
The vector F represents the force which must be applied at X to maintain
equilibrium. Draw a diagram to show the correct vector F.
[3]
c) For each of the figures below. express the vector R in terms of vectors P and Q.
[4]
2. Forces 5 N, 4 N and 3 N are in equilibrium. Assuming that sin 37° = 0·6. Find the angle
between the 5 N force and the 3 N force.
[3]
Since the forces are in equilibrium, they can be represented by the sides of a triangle taken in
order.
Also, 52 = 42 + 32
Therefore, the triangle is a right-angled triangle.
∴ the angle between the 5 N force and 3 N force is
𝑎 = (900 + 370 ) = 1270
3. a)
The forces acting on a point O are shown in the figure below.
Find the magnitude and direction of the resultant.
[7]
The best way to represent this is using a table.
Force
H. Component
V. Component
A
4 Cos 15
4 Sin 15
B
3 Cos 30
3 Sin 30
C
- 3 Cos 60
3 Cos 120
D
- 2 Cos 45
2 Cos 225
3 Sin 60
3 Sin 120
2 Sin 225
- 2 Sin 45
b) The figure above shows a point O in equilibrium under the action of 5 coplanar forces.
Calculate the values for 𝜃 and 𝑥.
2
[7]
Since the forces are in Equilibrium, the algebraic sum of all the forces gives us zero.
Resolving Horizontally
3𝑥 𝑆𝑖𝑛𝜃 + 2𝑥𝑆𝑖𝑛𝜃 = 4𝑥
5𝑥 𝑆𝑖𝑛𝜃 = 4𝑥
4
𝑆𝑖𝑛𝜃 =
5
4
𝜃 = 𝑆𝑖𝑛−1 = 53.1
5
Resolving Vertically
13 + 2𝑥𝐶𝑜𝑠
𝑖𝑓
𝑆𝑖𝑛𝜃 =
3
4
𝑎𝑙𝑠𝑜
5
𝐶𝑜𝑠𝜃 =
3
5