Find the magnitude of the two forces, such that if they act at right angles, their resultant is 10 N . But if they Act at 60, their resultant is 13 N .
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Hi Debasis,
Let the forces be F1 and F2
F1^2 + F2^2 = 10
as the angle between them is 90 degrees
when angle is 60
F1^2 + F2^2 + 2 * F1 * F2 *cos(60)=13
10 + F1 * F2=13
3 = F1 * F2
(F1 + F2)^2 = F1^2 + F2^2 + 2 * F1 * F2 = 10 + 6 = 16
F1 + F2 = 4...............(1)
F1 - F2 = √( ( F1 + F2)^2 - 4F1 * F2) = 2.......(2)
from eq.(1) and (2) We get
F1 = 3N ,and F2 = 1 N
Feel free to ask doubts in the Comment Section.
I hope this information helps you.
Good Luck!
Hello!
We can assume the two forces to be f1 and 2
Therefore, f1²+f2²=10
Since the angle between them is 90 degrees
when angle is 60
f1²+f2²+2*f1*f2*cos(60)=13
10+f1*f2=13
3=f1*f2
(f1+f2)²=f1²+f2²+2*f1*f2=10+6=16
f1+f2=4........................................(1)
f1-f2=√((f1+f2)²-4f1*f2)=2...........(2)
Therefore,
from (1) and (2) u get
f1= 3 N
f2= 1 N
Hope this helps you!
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