Resultant Force

Resultant Force is the total force acting on the body. It is defined as the sum of all forces acting on a body and it is the vector sum of all the forces acting on a body. The resultant force is measured in Newton which is the SI unit of force. If the resultant force acting on a body is zero then either it is in uniform motion or it is at rest.

The resultant force acting on an object can be visualized by the example, suppose a box is resting on a table and the force of 10 N is applied to it in the North direction and a force of 8 N is applied to it in the south direction then the resultant force acting on the body is in 2 N (10 N – 8 N). 

In this article, we will learn about, force, the resultant force, and the resultant force formula, its example, and others in detail. Now before learning about the resultant let’s learn about What is Force?

Force Definition

Force is defined as a push or pull of an object. It results in acceleration produced on an object due to external or internal factors. We define force as the product of the mass and acceleration of an object. It is a vector quantity as it has both magnitude and direction. We can not directly add two forces and the resulting force acting on any object is calculated using vector addition.

The force acting on an object is measured in Newton (N). 1 N = 1kgms^-2

Resultant Force Definition

Resultant Force is defined as the resultant force acting on a body. Suppose we apply force on an object in all four directions, then the resultant force acting on the body is the result of all the force applied. We can better understand this concept by the example,

Suppose a block of mass 100 kg is placed on a rough horizontal surface and the maximum friction between the block and the rough surface is 500 N. Now suppose a man applies a force of 200 N to move an object on the rough surface, in this case, a force of 200 N acts opposite to the force applied by the man caused by the friction. Here, the resultant force (200 N – 200 N) acting on the object is zero and hence the object will not move.

Now, if we apply a force of 800 N to move the block then the friction force acting on the block will be at its maximum capacity (500 N) and the resultant force (800 N -500 N) acting on the block is, 300 N on the direction of the applied force.

If the force acting on the object is in a linear direction then it can be easily calculated by taking proper positive and negative signs but when the force acting on the object is perpendicular to each other then either we use Vector Addition or Pythagoras Theorem to find the resultant of the two forces.

Resultant Force Formula

The resultant force formula is the formula that calculated the resultant of all the force acting on the body. If F₁, F₂, F₃,… are the forces acting on a body, the resulting force R_F is calculated using the formula with positive and negative signs used for pair of opposite forces.

F_R = F₁ + F₂ + F₃ . . . 

where,
F₁, F₂, F₃, . . . are the linear forces acting of the body

If F₁ and F₂ are the forces perpendicular to each other then their resultant force is given using the formula,

F_R = √(F₁² + F₂²)

The consequence can be calculated geometrically using the triangle law, parallelogram law, or polygon law of vector addition, depending on the number of forces operating.

It’s worth noting that unless the forces are collinear, they can’t be added or subtracted.

Finding the Resultant Force

The force acting on the object can be found separately in three different scenarios. That includes,

• Forces acting in the SAME Direction
• Forces acting in the OPPOSITE Direction
• Forces acting in ANGULAR Direction

Forces acting in the SAME Direction

If two forces acting on an object are in the same direction then the net force acting on the object is the sum of the individual forces. Suppose two forces acting on an object F₁ and F2 are in the same direction, their resultant force if 

F = F₁ + F₂

This situation is represented in the image shown below. Here the 2 N and the 4 N force is applied to a body in the same direction.

The resultant force applied = 4 N + 2 N = 6N

Forces acting in the OPPOSITE Direction

If two forces acting on an object are in the opposite direction then the net force acting on the object is the difference of the individual forces. Suppose two forces acting on an object F₁ and F₂ are in the opposite direction, their resultant force is 

F = F₁ – F₂

This situation is represented in the image shown below. Here the 2 N and the 4 N force is applied to a body in the opposite direction.

The resultant force applied = 4 N – 2 N = 2N

Forces acting in ANGULAR Direction

In both the above cases the force acting are parallel to each other. Now if two forces acting on an object are in the angular direction then the net force acting on the object can not be directly added or subtracted. It can be achieved by solving the given forces in their respective components and then simplifying them accordingly.

Suppose two forces acting on an object F₁ and F₂ have a 60-degree angle between them, 

This situation where the force is applied at an angle is represented in the image shown below, here 2 N and 4 N force is applied at an angle of 45 degrees. 

Then their resultant force is calculated as,

Taking the component of 2 N

Horizontal component = 2 cos 45° = 2 (1/√2)

Vertical component = 2 sin 45° = 2 (1/√2)

The force 4 N acts horizontally on the body.

Total horizontal force on the body (F_h) = 2 (1/√2)

Total vertical force on the body (F_v) = 2 (1/√2) + 4

Read More,

• Acceleration
• Velocity
• Distance and Displacement

Solved Examples on Resultant Force

Example 1: When three forces, such as 50 N, 90 N, and 40 N, are operating on an object at the same time and the 40 N force is opposite the other two forces, what is the F_R?

Solution:

Given,

• F₁ = 50 N
• F₂ = 90 N
• F₃ = -40 N

We know that the resultant force formula is,

F_R = F₁ + F₂ + F₃

F_R = 50 + 90 – 40

F_R = 100 N

Now the, resultant force acting on the object is, 100 N

Example 2: If perpendicular forces of 7 N and 13 N act on an item. Then calculate the force as a result.

Solution:

Given,

• F₁ = 7 N
• F₂ = 13 N

We know that resultant force formula between perpendicular forces is,

F_R = √(F₁² + F₂²)

F_R = √(7² +13²)

F_R = √218

F_R = 14.76 N

Example 3: If the resultant force F_R acting on an object is 95 N and the force acting on the object are 100 N, 30 N, 20 N and x N, then find the value of 

Solution:

Given,

• F_R = 95 N
• F₁ = 100 N
• F₂ = 30 N
• F₃ = 20 N
• F₄ = x N

We know that the resultant formula is,

F_R = F₁ + F₂ + F₃ + F₄

95 = 100 + 30 + 20 + x

x = (F₄) = -55 N

The force applied on the object is -55 N here, the – sign signifies that this force is opposite in direction to all opposite force.

FAQs on Resultant Force

Q1: What is Force?

Answer:

The force acting on the body is defined as the rate of change of momentum of the body. In simple term we define force as a Push or Pull. The formula to calculate the force is,

F = ma

where
m is the mass of object
a is the acceleration of object

Q2: What is Resultant Force?

Answer:

The sum of all the force acting on the body is called the resultant forces. If the resultant force acting on the body is zero then the body is ether in uniform motion or at rest. While if the resultant force acting on the body is non-zero then the body is accelerating or in non-uniform motion.

Q3: What is Resultant Force Formula?

Answer:

The resultant force formula is the formula which is used to calculate the resultant of the force acting on the body is, if the force acting on the body is are f₁, f₂, and f₃ then the formula for force acting on the body is,

F_R = f₁ + f₂ + f₃

Q4: What is the unit of the Resultant Force?

Answer:

As the resultant force is nothing but the sum of all the forces acting on the body it is measured in the SI unit of force, i.e. Newton(N). It is also measured in kgm^-1s^-2

Q5: What is Net Force?

Answer:

Net Force is nothing but the resultant force acting on the body. It is the resultant of the forces acting on the body.