In this world, everything is in a condition of inertia. Everything will stay in inertial motion, which may include absolute rest if left to its ends. Motion passes from one state to another due to force.

Different forms of forces produce various movements in our environment. In this post, we will learn how to compute the resulting force when two or more of these forces occur on the same body at the same time.

Table of Contents

**What are force and resultant force?**

“Any agent capable of overcoming inertia is referred to as force, and objects are made to move in a non-inertial format.”

“A resultant force is a cohesive group that produces the same impact on the subject as a particular set of forces operating on it.”

Or

“The vector total of all the forces operating on a body at the same time is known as resultant force.”

**SI unit**

The units of force and resulting force are the same. The Newton (N) is used as its system international unit.

**Formula**

If the F_{1 }force is acting on a box with an angle θ_{1} and a force having magnitude F_{2} and angle θ_{2} is also acting on the box at the same time then the resultant of both forces can be written:

**R = √ (fx)**^{2}** + (fy)**^{2}** – cosθ**

Where fx indicates the entire magnitude of both forces’ x components and fy represents the total magnitude of both forces’ y components.

However, the angle θ may be calculated using the following formula:

It is evident from the first equation that to get the magnitude, the angle must first be calculated.

**Explanation**

Several separate forces may be operating on an item, each with varying intensities and directions. However, they may be combined to yield the total force. This is a unified force that has the same impact on the item as all of the other forces combined.

The resulting force is 0 when all of the forces are balanced. In this instance: A stationary item remains still, whereas a moving object continues to move at the same pace and in the same direction.

In the barbell diagram, for example, the resulting force on the rod is zero, therefore the rod does not move. Its descending weight is offset by the weightlifter’s upward pull.

The size of the arrow is directly proportional to the magnitude of force. Since the arrows in the above figure are of the same size that indicates there is no increase in any force.

When any of the two forces increase their magnitude, the resultant force does not remain zero. In the case of imbalanced forces, the body moves in the direction of resultant force.

The resulting force on the bar is not zero in the above weightlifting diagram. The upward force outweighs the descending force. As a result of the resulting force acting upwards, the bar slides upwards.

**How to calculate the resultant force?**

The problems of resultant force can be calculated either by using a formula or Meracalculator (a calculator’s website).

**Example 1:**

A guy pushes a plastic box at an angle of 0 degrees with a force of 15N, while another man pushes the same box at a right angle with a force of 20N. Determine the resulting force.

**Solution: Manual technique**

**Step 1:** Understand the statement and select the given data.

Force of first man = F_{1} = 15N

Force of second man = F_{2} = 20N

Angle of F1 = 0^{0}

Angle of F2 = 90^{0}

**Step 2:** Find the x and y components of the resultant force.

For first force F_{1} = fx = 15cos0^{0} = 15N

For first force F_{1} = fy = 15sin0^{0} = 0N

For second force F_{2} = fx = 20cos90^{0} = 0N

For second force F_{2} = fy = 20sin90^{0} = 20N

**Step 3:** Now write components of both forces in terms of summation.

∑fx = 15N+0N = 15N

∑fy = 0N+20N = 20N

**Step 4:** Now find the angle between fx and fy.

θ = arctan 1.33

θ =53.13

**Step 5:** In the general formula for resultant force, insert the values of fx, fy, and angle.

R = √ (15)^{2} + (20)^{2} – cos53.13

R = √ 225 + 400 – cos53.13

R = 24.98

R = 25N

Hence the resultant force has been calculated.

**Example 2:**

A metal rod is attacked by two forces with the following parameters. Determine the resulting force.

F_{1 }= 8N, F_{2 }= 10N, θ_{1 }= 90 and θ_{2 }= 60

**Solution: Manual technique**

**Step 1:** Understand the statement and select the given data.

F_{1} = 8N

F_{2} = 10N

Angle of F1 = 90^{0}

Angle of F2 = 60^{0}

**Step 2:** Find the x and y components of the resultant force.

For first force F_{1} = fx = 8cos90^{0} = 0N

For first force F_{1} = fy = 85sin90^{0} = 8N

For second force F_{2} = fx = 10cos60^{0} = 5N

For second force F_{2} = fy = 10sin60^{0} = 8.66N

**Step 3:** Now write components of both forces in terms of summation.

∑fx = 0N+5N = 5N

∑fy = 8N+8.66N = 16.66N

**Step 4:** Now find the angle between fx and fy.

θ = arctan 3.32=73.23

**Step 5:** In the general formula for resultant force, insert the values of fx, fy, and angle.

R = √ (5)^{2} + (18.66)^{2} – cos73.23

R = √ 25 + 348.19 – 0.288

R = 17.394N

As a consequence, the resulting force has been determined.

**Summary**

You should now be able to distinguish between force and resultant force after reading this article. With the concept of resultant force defined, it is now simple to determine whether force or resultant force is being discussed.

You can use both manual and calculator methods to calculate the resultant force but the resultant force calculator is highly recommended.