Question

if two forces act in opposite direction then their resultant is 10 N and of they act mutually perpendicular then their resultant is 50n .find the magnitude of both the forces
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Answer 1

Answer:

Case 1: when F1 is opposite to F2.

Here we deal only with magnitude

Given:

F1 - F2 =10 ----------------------------> (1)

Case 2 :

when both forces are perpendicular to each other

And ((F1)2+(F2)2)^1/2=50 -------> (2)

By squaring eq. 2 we get

(F1)2+(F2)2=2500 -----------------> (3)

On solving eq. 1 and eq. 3

(F1−F2)2=(F1)2+(F2)2−2(F1)(F2)

(10)2=2500−2(F1)(F2)

2(F1)(F2) = 2500 - 100=2400

(F1)(F2) = 1200 ----------------------> (4)

Now we can easily solve eq.1 and eq.4

(F1+F2)2=(F1)2+(F2)2+2(F1)(F2)

F1 + F2 = 70 -----------> (5)

By adding eq.1 and eq.5,

2(F1) = 10+70=80

F1 = 40 N

and F2 = 70 - 40 = 30 N

F2 = 30 N