Question 5.2: This example illustrates two methods for solving problems in...
This example illustrates two methods for solving problems involving forces in equilibrium. With experience, you will find it easier to judge which method is best for a particular problem.
A sign of mass 10 kg is to be suspended by two strings arranged as shown in the diagram opposite. Find the tension in each string.
The force diagram for this situation is given below.
Method 1: Resolving forces
Vertically (\uparrow) : T_{1} sin 30° + T_{2} sin 45° – 10g = 0
0.5 T_{1} + 0.707 T_{2} = 98 ①
Horizontally (→) : – T_{1} cos 30° + T_{2} cos 45° = 0
-0.866 T_{1} + 0.707 T_{2} = 0 ②
Subtracting ② from ① 1.366 T_{1} = 98
T_{1} = 71.74
Back substitution gives T_{2} = 87.87
The tensions are 71.7 N and 87.9 N (to 1 d.p.).
Method 2: Triangle of forces
Since the three forces are in equilibrium they can be represented by the sides of a triangle taken in order.
