two sorces of resultant100N are perpendicular to each other.if one of them makes angle60degree with the resultant calculate the magnitude of the force
To find the magnitude of the force, we can use the Pythagorean theorem and trigonometric ratios. Here's how you can calculate it:
1. Draw a diagram to visualize the forces. Label the two forces as F1 and F2, with the angle between F1 and the resultant force as 60 degrees.
- Let F1 be the force that makes an angle of 60 degrees with the resultant force.
- Let F2 be the other perpendicular force.
2. Apply the Pythagorean theorem to find the magnitude of the resultant force:
Resultant force (F)^2 = F1^2 + F2^2
3. Substitute the given values:
Resultant force (100N)^2 = F1^2 + F2^2
4. Since F1 makes an angle of 60 degrees with the resultant force, we can use trigonometric ratios to find its value:
F1 = F * cos(60)
where F is the magnitude of the resultant force.
5. Substitute the value of F1:
(100N)^2 = (F * cos(60))^2 + F2^2
6. Simplify and solve the equation:
10000N^2 = (F^2 * cos^2(60)) + F2^2
10000N^2 = (F^2 * 1/2) + F2^2 [As cos(60) = 1/2]
10000N^2 = (F^2)/2 + F2^2
Now, let's assume F2^2 as x:
10000N^2 = (F^2)/2 + x
F^2/2 + x = 10000N^2
F^2/2 = 10000N^2 - x
F^2 = 2 * (10000N^2 - x)
F = sqrt(2 * (10000N^2 - x))
7. Substitute the value of x:
F = sqrt(2 * (10000N^2 - F2^2))
8. Solve the equation using the known values:
F = sqrt(2 * (10000N^2 - F2^2))
By following these steps, you can calculate the magnitude of the force. Remember to substitute the value of F2 to get the final result.