Question

What is the resultant of three coplanar forces : 300 N at 0°, 400 N at 30° and 400 N at 150°?

(a) 500 N

(b) 700 N

(c) 1100 N

(d) 300 N​

Answer 1

Solution:

Let us assume that the angles are with respect to the positive 'x' direction.

The 'x' component of the resultant force,

Fx = 300 × cos0° + 400 × cos30° + 400 × cos 150°

Fx = 300 + 400 × √3/2 - 400 × √3/2

Fx = 300 + 200√3 - 200√3

Fx = 300 N

Also,

Fy = 300 × cos90° + 400 × sin30° + 400 × sin30°

Fy = 300 × 0 + 400 × 1/2 + 400 × 1/2

Fy = 0 + 200 + 200

Fy = 400 N

Now,

F = √( Fx^2 + Fy^2 )

F = √( 300^2 + 400^2 )

F = √( 90,000 + 1,60,000 )

F = √2,50,000

F = 500 N

Answer: (a) 500 N is the correct answer.

Answer 2

Answer:

f= 500N

Explanation:

a) is the correct answer.