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Question

Two forces, while acting on a particle in opposite; directions, have the resultant of 10N. If they act at right angles to each other, the resultant is found to be 50N. Find the two forces.

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Solution

Step 1: Resultant force when the forces are opposite [Ref. Fig. 1]
Let F1 and F2 are the magnitudes of two forces
R1=F21+F22+2F1F2cosθ
10N=F21+F22+2F1F2cosθ1800
10=(F1)2+F222F1F2
10=F1F2 .....(1)

Step 2: Resultant force when the forces are at right angle [Ref. Fig. 2]
R2=F21+F22+2F1F2cos900
50=F21+F22
2500=F21+F22 ....(2)

Step 3: Solving equations
From eq (1) substitute the value of F1 in eq (2)
2500=(F2+10)2+(F22)
F22+10F21200=0
(F2+40)(F230)=0
F2=30N [Since the magnitude of force can't be negative , so we will not consider negative value]

Substituting this value of F2 in eq (1)
10=F130F1=40N

Hence, the Magnitudes of two forces are 40N and 30N.


2110357_984347_ans_aa4fdd4940b845bd86d8913bcafe2076.png

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