Question

If one of the components of force 50N is 25N find the other component and angle of force.

Answer 1

• It is given that one component of force is half of force            For component to be half angle may be 30°  or 60° because -- 
• Cos60°=1/2 and sin30°=1/2           
• If Force vector is at 30° from horizontal than it's--
•  horizontal component is Fcos30°  and 
• Vertical component is Fsin30° 
• And value of cos30° = √3/2   and sin30°= 1/2 
• Therefore ,value of horizontal component of force will be 50cos30° = 25√3
• And value of vertical component is 50sin30°= 25 

Answer 2

F= 50N

one of its component = 25

Fsinx=25

sinx=1/2

Fcosx=50*root(3)/2

Answer 3

Let:

• R be the resultant force (50 N),
• A be one component (25 N),
• B be the other component.

According to the Pythagorean theorem:

R² = A² + B²

50² = 25² + B²

2500 = 625 + B²

B² = 2500 − 625 = 1875

B = \(\sqrt{1875}\) ​≈ 43.3 N

The angle θ of the force with respect to the component A:

\(\theta = tan^{-1} (\frac{B}{A})\)

\(\theta = tan^{-1} (\frac{43.3}{25})\)

θ ≈ tan^-1(1.732) ≈ 60°