Video Lesson

Lesson objective

Dear learners,

At the end of the lesson you will be able to

• Define the term equilibrium
• Explain the first condition of equilibrium
• Apply the first condition of equilibrium to solve practical problems.

Brainstorming question

What will happen to an object when it is under the action of balanced set of forces?

Key Terms and Concepts

Equilibrium

• Equilibrium: is a state in which an object or system does not accelerate.
• This means that the net force and net torque acting on the object or system are zero.
• First condition of equilibrium: It is also known as the condition for translational equilibrium. It states that for a body to be in translational equilibrium, the net force acting on it must be zero.
• Second condition of equilibrium: It is also known as the condition for rotational equilibrium. It states that for a body to be in rotational equilibrium, the net torque acting on it must be zero.
• If a body is at rest or moves at a constant speed in a fixed direction (constant velocity) then it is in translational equilibrium. This statement defines the first condition of equilibrium.
• If an object is in equilibrium, its acceleration is zero and according to Newton’s second law of motion, the vector sum of all the forces acting on it must be zero.
• ∑$\overrightarrow{F}$=0 (The first condition of equilibrium)
• For n number of forces acting on a object, we write
• $\overrightarrow{F_{1}}+\overrightarrow{F_{2}}+\overrightarrow{F_{3}}+…+\overrightarrow{F_{n}}$ = 0
• This equation can be written component wise as
• ∑$\overrightarrow{F_{x}}$=0 and ∑$\overrightarrow{F_{y}}$

Examples 4.1

A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support, as in Figure 4.33a. The upper cables make angles of 37° and 53° with the horizontal. Find the tension in each of the three cables

Figure 4.6 A traffic light suspended from two strings solution

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Examples 4.2

Mass m= 10kg is supported by two strings is in equilibrium as shown in Figure 4.34. Find the tension in the horizontal string. Take θ = 53^o

Figure 4.7 A mass in equilibrium

Solution: