Question

Two forces F1 and F2 are acting on a body . One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is ?

Answer 1

Given:
Let F1=F
F2=2F
Resultant force= Fnet= 2F
By parallelogram of vector addition ,
F net =√F₁²+F₂²+2F₁F₂CosΘ
2F=√F²+ 2F²+2x Fx(2F)CosΘ
4F²=5F²+4F²CosΘ
4CosΘ=-1
CosΘ=-1/4
Θ=Cos⁻¹(-1/4)
Θ=180⁰ - Cos⁻¹(1/4)
Θ=104.375⁰

∴The angle between the two forces is 104.375⁰

Answer 2

Answer

Given:

Let F1=F

F2=2F

Resultant force= Fnet= 2F

By parallelogram of vector addition ,

F net =√F₁²+F₂²+2F₁F₂CosΘ

2F=√F²+ 2F²+2x Fx(2F)CosΘ

4F²=5F²+4F²CosΘ

4CosΘ=-1

CosΘ=-1/4