A body is at equilibrum under the action of three forces.one force is 10N acting due east and one is 5N in the direction 60degree north east.what is the magnitude and direction of the third force
sum these two forces. Then the equilibrant is the negative of that sum
15n 60°
To find the magnitude and direction of the third force, we can use vector addition. Here's how to do it step by step:
Step 1: Draw a diagram of the problem.
Draw a coordinate system and mark the east direction as positive x-axis and the north direction as positive y-axis. Label the forces accordingly.
Step 2: Resolve the forces into their x and y components.
The force of 10N due east has no vertical component and has a horizontal component of 10N in the positive x-direction.
The force of 5N in the direction 60 degrees north-east can be resolved into its x and y components. The angle formed with the positive x-axis is 60 degrees. To find the x and y components, you can use trigonometry:
x-component = 5N * cos(60°)
y-component = 5N * sin(60°)
Step 3: Add up the x and y components separately.
To find the x-component of the third force, we add the x-components of the other two forces.
x-component of the third force = 10N + 5N * cos(60°)
To find the y-component of the third force, we add the y-components of the other two forces.
y-component of the third force = 5N * sin(60°)
Step 4: Calculate the magnitude and direction of the third force.
To find the magnitude of the third force, use the Pythagorean theorem:
Magnitude of the third force = √(x-component^2 + y-component^2)
To find the direction of the third force, use trigonometry:
Angle with the positive x-axis = arctan(y-component / x-component)
By plugging in the values from step 3 into these formulas, you can calculate the magnitude and direction of the third force.