Question

two forces f1 and f2 acting simultaneously on a particle are measured as f1= 36+- 0.3 N and f2=23+-0.5 N what will be the resultant if they act in same and opposite direction​

Answer 1

Answer:

F1 = 40 N

F2 = 70 - 40 = 30 N

Explanation:

Case 1 when F1 is opposite to F2.

Here we deal only with magnitude

Given: F1 - F2 =10 _____(1)

case2 when both forces are perpendicular to each other

And (F1)2+(F2)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

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Answer 2

Answer:

After solving using Parallelogram Law of Vector Addition:

F1= 40N

F2= 30N