A body is under the action of two forces 7N and 10N , find the resultant of the two vectors if the two forces are inclined at the angle of 60° to each other.
I would use the law of sines to find another angle, then use the sum of angles is 180 to find the last angle, then finally, law of sines to find the resulstant
To find the resultant of the two vectors, you can use the graphical method or the component method.
Let's first use the component method to solve this problem:
1. Resolve the forces into their x and y components:
Force1 (7N) = 7N * cos(60°) in the x-direction and 7N * sin(60°) in the y-direction.
Force2 (10N) = 10N * cos(60°) in the x-direction and 10N * sin(60°) in the y-direction.
2. Add the x-components and y-components separately:
x-components: 7N * cos(60°) + 10N * cos(60°)
y-components: 7N * sin(60°) + 10N * sin(60°)
3. Calculate the magnitude of the resultant:
Resultant = √[(x-components)² + (y-components)²]
Substitute the values:
Resultant = √[(7N * cos(60°) + 10N * cos(60°))² + (7N * sin(60°) + 10N * sin(60°))²]
Evaluate the expression to find the magnitude of the resultant.
4. Calculate the direction of the resultant:
The angle at which the resultant is inclined can be found using trigonometry.
Angle = tan⁻¹[(y-components)/(x-components)]
Substitute the values:
Angle = tan⁻¹[(7N * sin(60°) + 10N * sin(60°))/(7N * cos(60°) + 10N * cos(60°))]
Evaluate the expression to find the angle of the resultant.
By following these steps, you will be able to determine the magnitude and direction of the resultant of the two vectors.