Question

Two forces act on angle of 120 degrees
If the greater force is 100N and their
resultant is perpendicular to the smaller
force, the smaller force is​

Answer 1

Answer:

click the picture for answer of Two fources act on angle of 120° If guteater force is 100N & their Resultant is perpendicular to Smaller fource what is the magnitude of smaller

force.

Answer 2

50 N.

If R is the resultant of the two forces E and F, E being the greater force, α be the angle between them and β be the angle of the resultant from F.

Then, magnitude of resultant is given by,

R = $\sqrt{E^{2} + F^{2} + 2EFcos\alpha }$

and

tan β = $\frac{Esin\alpha }{F+Ecos\alpha }$

∴ We have resultant is perpendicular to F and angle between forces is 120.

ie: β = 90° and α = 120°.

∴ tan 90 = $\frac{Esin\alpha }{F+Ecos\alpha }$

∴ $\frac{1}{0}$ = $\frac{Esin120 }{F+100cos120 }$

∴ cross multiplying,

F + 100×cos120 = 0

∴ F = - 50 N

Here, the negative stands for the direction of the force.