The sum of all the forces acting on an object is called as is the net force. A mass can be accelerated by a net force. A body at rest or in motion has some other force on it. The term Net force is used in a system where the number of forces is numerous in quantity.

Formula for Net Force

If N is the number of forces acting on a body, then the formula for net force is given as,

Where,

F1, F2, F3…FN is the force acting on a body.

When the body is at rest, then the formula for net force is given as,

Where,

Fa = applied force,

Fg = gravitational force.

When the force is applied to the body, not only the applied force is acting, there are many other forces like gravitational force  Fg, frictional force Ff and the normal force that balances the other force.

Therefore, the net force formula is given by,

Where,

• Fa is applied force,

• Fg is the gravitational force,

• Ff is the frictional force,

• FN is a normal force.

Solved Examples 

Example 1: In a tug of war, a fat man pulls with a force of 100 N on a side, and a lean man pulls with 90 N on the other side. Determine the net force.

Solution:

Given,

Force F1= 100 N

Force F2 = -90 N

The net force formula is given by

FNet = F1 + F2

FNet  = 100 – 90

FNet  = 10 N

Thus the net force is 10 N.

Example 2: A toy bus is stationary and a force of 70 N is exerted on it. The friction force about the surface is given as 20 N, determine the net force.

Solution:

Applied force Fa = 70 N

Frictional force Ff = -20 N

The equation for net force is given by

FNet = Fa + Ff

FNet = 70 – 20

FNet  = 50 N

Hence the net force is 50 N