How to Find Net Force: Various Methods, Problems and Facts


The article discusses various methods on how to find net force and its solved problems with some facts.

The net force is the total force on the system, which is discovered by adding up all the forces acting on the system. We use this term when different types of forces act on the system. The net force has the exact characteristics as a single force that accelerates or deaccelerates any object with mass. 

Suppose N number of forces act on an object in all possible directions. What will be its acceleration, and in which direction will it move?

We summed up the all N number of forces acting on the table, which gives the net force as the total number of forces acting on an object.

The basic net force formula is,

Fnet = F1 + F2 + F3 + F4 + …. + FN

Like a single force, Newton(N) is the SI unit of the net force.

 Read more about Net Force.

How to Find Net Force
How to Calculate Net Force

During the tug of war, six unknown forces working on the rope are 5N, 2N, 1N, 7N, 4N, 2N. Find out the net force acting on the rope and which direction it will move.

Given:

F1 = 5N

F2 = 2N

F3 = 1N

F4 = 7N

F5 = 4N

F6 = 2N

To Find: Fnet =?

Formula:

Fnet = F1 + F2 + F3 + F4 + …. + FN

Solution:

The net force acting on rope during tug of war is calculated as,

Fnet = F1 + F2 + F3 + F4 + F5 + F6

Substituting all values,

Fnet = 5 + 2 + 1 + 7 + 4 + 2

Fnet = 22N

The net force acting on the rope is 22N, and since it has a positive value, it accelerates the rope forward direction.

Read more about Net Force Examples.

How do you Find Net Force with Mass?

The net force with mass is determined using Newton’s second law of motion. 

If no force is acting on the system, the net force is also zero. Hence a system having mass will not move or accelerate. But this case is inconceivable in practice, as at least one force always acts on any object in the universe. i.e., gravity force. 

The resistance or friction that resists an object’s motion is negligible during free-fall. Hence, an object with a certain mass falls towards the ground.

The gravity force always operates on us and accelerates us constantly downwards. The gravity force formula is ‘mg’, governed by Newton’s second law of motion F= ma.

How to find Net Force in Free Fall
How to Calculate Net Force with Mass
(credit: shutterstock)

g is the constant acceleration value for all objects. Hence, the larger an object’s mass, the bigger the gravity force and the faster it will fall.

Therefore, the net force formula for a free-fall object is equivalent to the gravity force. i.e., Fnet = Fg = mg

Read more about Gravity Force.

What is the net force acting on the apple having a mass of 2kg, falling freely on the ground (g= 9.8 m/s2)?

Given:

m = 2kg

g = 9.8m/s2

To Find: Fnet =?

Formula:

Fg = mg

Solution:

Since the apple is freely falling, the only gravity force acts on it.

Hence, the net force on free-falling apple is calculated using gravity force formula,

Fnet = mg

Substituting all values,

Fnet = 2 x 9.8

Fnet = 19.6N

The net force on the free-falling apple with mass is 19.6N.

Read more about How to find Gravity?

How do you find Net Force with Two Forces?

The net force with two forces is determined using Newton’s third law of motion: 

When an object is at rest, the ground surface employs the normal force upward on a stationary object as the reaction force to gravity force. Hence, the net force on a stationary object includes two forces such as gravity force and normal force. 

The ground surface employs the normal force to counterpart the gravity force. That means the normal force is equal in magnitude and opposite magnitude of gravity force. Hence, FN = mg

How to Find Net Force with Two Forces
How to Calculate Net Force with Two Forces

Therefore, there is a pair of vertical forces that acts on an object when it stays at rest on the ground surface, giving rise to net force with two forces,

Fnet = FN + Fg

Since the gravity is acting downward, we consider its values as negative. i.e., -Fg.

Hence, the net force formula with two forces is,

Fnet = FN + (-Fg)

Read more about Types of Forces.

Suppose the gravity force of 10N and the normal force of 10N on the man standing on the road. What will be the net force on the standing man?

Given:

Fg = -10N

FN = 10N

To Find: Fnet =?

Formula:

Fnet = F1 + F2 + F3 + F4 + …. + FN

Solution:

The net force acting on the man standing is calculated as,

Fnet = FN + Fg

Fnet = 10 + (-10)

Fnet = 0

The net force on the standing man is zero. That’s why he remains at rest with no net force acting.

Read more about Relative Motion.

How to calculate Net Force in Opposite Directions?

The net force in the opposite direction is determined using Newton’s third law of motion.

When we apply force upward to the stationary object, the air exerts an equal and opposite force called air resistance force. Hence the net force acts in the opposite direction, which opposes the acceleration caused by the applied force.

Previously, we understood that if a pair of forces have the exact magnitude, they balance each other. Hence, an object will not move or accelerate as its net force is zero. That’s why one of the forces needs to have a greater magnitude than the other so that calculated net force can accelerate or deaccelerate an object

When we throw a ball upward, it returns towards the ground more rapidly after going a certain height. It happens because the air resistance force reverses the direction of a ball, and the gravity force accelerates a ball rapidly downward. 

How to Find Net force in Opposite Direction
How to Calculate Net force in Opposite Direction

Since the magnitude of opposite forces becomes greater than the applied force, the net force acts in the opposite direction to the applied force

Read more about Unbalanced Force.

When we apply a force of 10N to a ball by throwing, the air resistance force of 6N and gravity force of 6N are exerted on the ball. Calculate the net force on a ball. 

Given:

Fapp = 10N

Fair = -6N

Fg = -6N

To Find: Fnet =?

Formula:

Fnet = F1 + F2 + F3 + F4 + …. + FN

Solution:

The net force on a ball is calculated as,

Fnet = Fapp + Fair + Fg

Substituting all values,

Fnet = 10 + (-6) + (-6)

Fnet = -2N

The net force on a ball is -2N, acting opposite direction.

How do you find the Net Force of an Angle?

The net force of an angle is determined by using an inclined plane. 

When an object is at an angle with a horizontal surface or inclined plane, the gravity force is resolved into two components. The normal force balances the parallel component. Hence, the net force of an inclined angle comprises the parallel component of gravity. 

In the absence of applied force, the parallel component of gravity force mgsinθ is the only force that accelerates an object downward at an inclined angle. That’s why any object slides quickly on an inclined plane. Since no applied force, there is no friction force acting on an inclined plane. 

Therefore, the net force formula of an inclined angle is,

Fnet = mgsinθ 

 How to Find Net force in an Inclined Angle
How to Calculate Net force of an Angle

Read more about Inclined Plane.

What is the net force on the wheelchair having a mass of 5kg, which slides down on an inclined ramp at an angle of 30°? (g = 9.8m/s2)

Given:

m = 5kg

g = 9.8m/s2

θ = 30°

To Find: Fnet =?

Formula:

Fnet = mgsinθ 

Solution:

The net force on the wheelchair is calculated as,

Fnet = mgsinθ 

Substituting all values,

Fnet = 5 x 9.8 x sin 30°

Fnet = 49/2

Fnet = 24.5N

The net force on the wheelchair at an angle of 30° is 24.5N.

Read more about Friction in an Inclined Plane.

How do you find Net Force with Components?

The net force with components is determined when vertical forces balance each other. 

When we applied force at a specific angle to the horizontal surface, it spilled into two components. The perpendicular component, along with normal force, balances the gravity force. Hence, the net force includes the parallel components of applied force and opposite friction force. 

How to Find Net force with Components
How to Calculate Net force with Components

The horizontal or parallel component of applied force is estimated using trigonometric function as,

Fx = Fapp. Sinθ

Read more about How to Resolve Force into Components.

Suppose we apply a push force of 80N at the angle of 60° to move the box. The ground surface exerts the friction force of 50N to the box. Calculate the net force acting on the box. 

Given:

Fapp = 80N

Ffric = -50N

θ = 60°

To Find: Fnet=?

Formula:

Fnet = F1 + F2 + F3 + F4 + …. + FN

And, Fx = Fapp. Sinθ

Solution:

Before finding the net force on the box, we must find the parallel components of applied force

Fx = Fapp. Sinθ

Fx = 80 x sin 60°

Fx = 80 x 0.86

Fx = 68.8N

The net force formula with parallel component on the box is calculated as,

Fnet = Fx + Ffric

Fnet = 68.8 + (-50)

Fnet = 18.8N

The net force acting on the box due to the parallel component is 18.8N.

How to find Net Force on a Charge?

The net force on a charge is determined using Coulomb’s law

The electrostatic force or Coulomb force between two charges at rest can be acquired using the Coulomb’s law. Since the atom consists of many charged particles, the net force on all charges adds each electrostatic force between pairs of charges.

The electrostatic force Fa,b between charge a and b is given by,

Fa,b=(kqaqb)/r2

Where k is coulomb constant.

qa and qb are charged a and b respectively.

And r is the distance between charges.

Find the net forces on three charges 5μC, 10μC, and 5μC, which are equally separated by a distance of 2cm. (Coulomb constant k = 8.99 x 109)

Given

q1 = 5μC = 5 x 10-6C

q2 = 10μC = 10-5C

q3 = 5μC = 5 x 10-6C

r = 2cm = 2 x 10-2m

k = 8.99 x 109

To Find: Fnet =?

Formula

Fnet = F1 + F2 + F3 + F4 + …. + FN

And Fa,b=(kqaqb)/r2

Solution:

To find the net force on all three charges, we need to find electrostatic forces between them. 

 How to Find Net Force on a Charge
How to Calculate Net Force on a Charge

The electrostatic forces between charge 1 and 2 is, 

F1,2=(kq1q2)/r2

F1,2=(44.95*10-2)/(2*10-2)

F1,2 = 22.47N 

The electrostatic forces between charge 2 and 3 is, 

F2,3=(kq2q3)/r2

F2,3 = 22.47N

The electrostatic forces between charge 1 and 3 is, 

F1,3=(kq1q3)/r2

F1,3 =(224.5*10-3)/(2*10-2)

F1,3 = 11.23N

The net force formula on all three charges is calculated as,

Fnet = F1,2 + F2,3 + F1,3

Fnet = 22.47 + 22.47 + 11.23N

Fnet = 56.17N

The net force acting on charges is 56.17N. 

How do you find Net Force from Velocity Vs Time graph?

The net force from the velocity vs. time graph is determined using Newton’s second law. 

When the various forces act on an object, its velocity changes from time to time. If we plot the graph of its velocity against a time, we estimate its value of acceleration when a net force acts. Therefore, we can calculate net force from velocity using Newton’s second law of motion formula. 

Newton’s second law formula in terms of the net force is,

Fnet = ma

Fnet = m*(Δv/Δt)

Fnet ==m*[(v-v0)/(t-t0)]

Read more about Velocity.

From the below velocity vs. time graph, calculate the net force acting on a car having a mass of 20kg. 

How to Find Net Force from Velocity vs. Time Graph
How to Calculate Net Force from Velocity vs. Time Graph

Given:

m = 20kg

To Find:

a =?

Fnet =?

Formula:

Fnet = ma

Solution,

Before calculating net force, we need to find the car’s acceleration from the velocity vs. time graph.

a=(Δv/Δt)

a=(v-v0)/(t-t0)

From velocity vs time graph,

The car was initially at rest. That means, v0 = 0 and t0 = 0

The final velocity of the car is 80km/hr at the final time 10 min. That means, v = 80km/hr and t= 10 min.

The net force formula is,

Fnet =m*(v/t)

Substituting all values,

Fnet ==20*(80/10)

Fnet = 120N

The net force on the car from its velocity vs. time is 120N.

How to find Net Force with Mass and Velocity?

The net force with mass and velocity is determined using the Work-Energy formula. 

When the net force accelerates an object at rest, it transforms potential energy into kinetic energy. So that an object moves a particular distance, that’s when we said work is done by an object, which enables us to find the net force with its mass and velocity.

As per the Work-Energy formula,

K.E = W

But work done by an object is the product of net force Fnet acting and distance d it travelled. 

(1/2)mv2=Fnetd

Read more about Work Done.

When the footballer kicks the football having a mass of 5kg, it moves with a velocity of 10km/hr at a distance of 8m. What is the net force acting on football? 

Given:

m = 5kg

v= 10km/hr = 10 x 1000/36000 m/sec

d= 8m

To Find: Fnet =?

Formula:

(1/2)mv2=Fnetd

Solution:

The net force on the football is calculate using Work-Energy formula as,

(1/2)mv2=Fnetd

The net force with mass and velocity is,

mv2/2d=Fnet

Substituting all values,

Fnet=5000/368

Fnet = 13.5N

The net force acting on football having a mass and velocity is 13.5N. 

Read more about Potential to Kinetic Energy Conversion.


Manish Naik

Hello, I'm Manish Naik completed my MSc Physics with Solid-State Electronics as a specialization. I have three years of experience in Article Writing on Physics subject. Writing, which aimed to provide accurate information to all readers, from beginners and experts. In my leisure time, I love to spend my time in nature or visiting historical places. I am honoured to be part of LambdaGeeks. Looking forward to connecting you through LinkedIn - https://www.linkedin.com/in/manish-ashok-naik/ Also, for Maharashtra travel guide and heritage conservation articles, visit my website Wandering Maharashtra - https://wanderingmaharashtra.com/travel-blogs/

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