Solved Examples on Equilibrium of Bodies

Example 1. Calculate the force acting on a body of mass 2 kg with an acceleration of 3 m/s².

Solution:

We have,

m = 2

a = 3

Using the formula we have,

F = ma

= 2 (3)

= 6 N

Example 2. Three forces P, Q, and R are in equilibrium with each other acting at a place. Angles between P and Q, Q and R, and P and R have a ratio of 1:2:3. Find the ratio of the forces, P:Q:R.

Solution:

Suppose the angles are a, 2a and 3a.

=> x + 2x + 3x = 360^o

=> x = 60^o

Using Lamis theorem we get,

P/sin 120^o = Q/sin 180^o = R/sin 60^o

P/(√3/2) = Q/0 = R/(√3/2)

So, we get P:Q:R = √3/2 : 0 : √3/2.

Example 3. A body is subjected to two perpendicular forces of 4 N and 3 N. Find the magnitude of the resultant force on the body.

Solution:

We have,

F₁ = 4

F₂ = 3 

Using the formula we have,

F = √(F₁² + F₂²)

= √(4² + 3²)

= √25

= 5 N

Example 4. Calculate the mass of a body whose acceleration is 2 m/s² subjected to two perpendicular forces of 8 N and 6 N.

Solution:

We have,

a = 2

F₁ = 8

F₂ = 6

Using the formula we have,

F = √(F₁² + F₂²)

= √(8² + 6²)

= √100

= 10 N

We know,

m = F/a

= 10/2

= 5 kg

Example 5. Calculate the acceleration of a body whose mass is 3 kg subjected to two perpendicular forces of 5 N and 12 N.

Solution:

We have,

m = 3

F₁ = 5

F₂ = 12

Using the formula we have,

F = √(F₁² + F₂²)

= √(5² + 12²)

= √169

= 13 N

We know,

a = F/m

= 13/3

= 4.33 m/s² 

The laws of motion, which are the foundation of old-style mechanics, are three explanations that portray the connections between the forces following up on a body and its movement. They were first expressed by English physicist and mathematician Isaac Newton. The motion of an item is related to the forces operating on it by Newton’s equations of motion. According to the first law, until a force acts on an item, it will not alter its motion. According to the second law, an object’s force equals its mass times its acceleration.

First Law Of Motion

According to Newton’s first law, Everybody continues to be in its state of rest or uniform motion until and unless an external force acts on the body. This law is also called as Law of Inertia. This is the most practical law which we can experience daily while driving a bike or travelling on a bus.

Second Law Of Motion

According to Newton’s second law, For an object of constant mass, the rate of change of momentum is the force acting on the body. Thus the product of mass and acceleration gives the magnitude of the force acting on the body.

F = d/dt(mv)

= m.(dV/dt)

= m.a

Hence, F = m.a m/s²

Third Law Of Motion

According to Newton’s third law, Every action on a body has an equal and opposite reaction. Example: Shooting using a rifle, Frictional force acting on the shoe while we walk.