Magnitude Of The Resultant Vector

How- to -calculate the- magnitude- and -direction -of- resultant -force

The resultant forcefulness is 1 of the types of force. Strength is just defined as the pull and push of things. The resultant force is a force used to detect whether the object moves or remains constant. Consider the following scenario. A tug of war is taking place betwixt two groups of individuals, with each grouping pulling on the rope as difficult as they tin.

Finally, who will sally successfully? Another question that may arise is whether 1 group will be able to movement the other. Nosotros need to know how to notice the resultant force to appropriately reply these bug. The resultant force is the single strength that has the aforementioned upshot on an item as the original strength. A rope is an object in this case. In this commodity, we will cover all the nuts and methods of the resultant force.

What is the Resultant Forcefulness?

When numerous forces human activity on an object, the resultant force is the strength that creates the same acceleration as all of the other forces creates combinedly. When two or more forces human activity on a body, the resultant forcefulness or net force is the sum of all the forces that generate the resulting effect. Considering force is a vector, nosotros must calculate the resultant by taking the vector sum of all the forces.

The resultant strength is useful considering it allows us to think about several forces as if they were a single force. This means that determining the influence of several forces on an object is as uncomplicated every bit determining the consequence of a single force.

As we are familiar with the equation of strength as,

F = ma

The resultant force equation is,

R = ma

Here R is the vector sum of vector forces such as F_1,F₂, F₃, …

This formula is just written as,

F_R = F_i + F_ii + F₃

The internet strength acting on an object under several forces is known every bit the resultant forcefulness. The resultant force has both magnitude and direction because force is a vector quantity.

The following diagram is a vector representation of the resultant force:

The formula of the Resultant Force

Nosotros tin calculate the magnitude and direction of the forces by using resultant forcefulness. Both direction and magnitude accept different equations.

The equation for magnitude in resultant forcefulness.

Magnitude of the resultant force = √ ((Σfx)² + (Σfy)² – cos(θ))

Commencement of all, we take to calculate the angle to find the magnitude of the resultant force.

The equation for direction in resultant force.

Direction of the resultant force = arctan (Σfx / Σfy)

How to detect the resultant force magnitude and direction?

First of all, we calculate the resultant strength.

Instance 1
find the resultant force when iii forces such equally 90N, 30N, and 45N are interim on an object concurrently.

Solution

Stride 1: Name the forces.

F₁ = 90N

F₂ = 30N

F_three = 45N

Step 2: Write the full general formula.

F_R = F_one + F₂ + F_iii

Step 3: Put the values.

F_R = 90N + 30N + 45N

F_R = 165N

At present we have taken some examples to calculate the magnitude and direction of the resultant force. The direction and magnitude of the strength can be hands be calculated by using an online tool similar resultant force calculator.

Example two
A bus is existence pulled by 20N at 0 degrees and past 7N at 90 degrees in the forward management calculate the direction and magnitude of the resultant force.

Solution

Step one: Place the values.

F₁= 20N

F₂ = 7N

Angle of F₁ = 0 degree

Bending of F₂ = 90 degrees

Step 2: Calculate the components of forces.

X-complement of F_one = 20cos (0) = xx(1) = xx

Y-component of F_ii = 20sin (0) = 20(0) = 0

10-complement of F₂ = 7cos (90) = vii(0) = 0

Y-component of F_two = 7sin (ninety) = 7(1) = 7

Step 3: Find the sum of 10 components and y components.

Σfx = twenty + 0 = 20

Σfy = 0 + vii = seven

Step four: Find the direction of resultant forcefulness.

Direction of the resultant force = arctan (Σfx / Σfy)

θ = arctan (Σfx / Σfy)

= arctan (twenty/7)

= arctan (2.86)

θ = 71 degree

Footstep v: Now summate the magnitude of the resultant force.

Magnitude of the resultant force = √ ((Σfx)^two + (Σfy)ⁱⁱ – cos(θ))

= √ ((20)^two+ (seven)² – cos (71))

= √ ((400+ 49 – 0.3256)

= √ ((449 – 0.3256)

= √ (448.6744)

= 21.1819

Example iii
A charabanc is being pulled by 19N at 90 degrees and by 17N at 0 degrees in the forward management calculate the direction and magnitude of the resultant forcefulness.

Solution

Step 1: Identify the values.

F₁= 19N

F_ii = 17N

Angle of F₁ = 90 degree

Angle of F_two = 0 degrees

Stride 2: Calculate the components of forces.

10-complement of F₁ = 19cos (xc) = 19(0) = 0

Y-component of F₂ = 19sin (ninety) = nineteen(i) = 19

Ten-complement of F₂ = 17cos (0) = 17(1) = 17

Y-component of F₂ = 17sin (0) = vii(0) = 0

Footstep 3: Find the sum of x components and y components.

Σfx = 0 + 19 = 19

Σfy = 17 + 0 = 17

Step four: Discover the direction of resultant strength.

Direction of the resultant force = arctan (Σfx / Σfy)

θ = arctan (Σfx / Σfy)

= arctan (19/17)

= arctan (1.1176)

θ = 48.1786 degree

Step five: At present summate the magnitude of the resultant force.

Magnitude of the resultant force = √ ((Σfx)² + (Σfy)² – cos(θ))

= √ ((20)²+ (seven)ⁱⁱ – cos (48.1786))

= √ ((361+ 289 + 0.4934)

= √ ((650 + 0.4934)

= √ (650.4934)

= 25.5048

Summary

The force which is used to discover the combined relation is said to be the resultant force. When numerous forces act on an object, the resultant force is the strength that creates the same acceleration as all of the other forces creates combinedly. This forcefulness also tells the magnitude and direction of the forces. We tin easily solve resultant strength-related problems, simply just a piffling effort is required.