Question

Problem 2. The resultant of two forces in a plane is 400 N at 120. One of the forces is 200 N at 20
Determine the missing force. ​

Answer 1

Answer:

Correct option is

B

20N

Let the other Force be of magnitude x and the angle it makes with resultant be θ.

Now, the components of the two vectors along the resultant should be of magnitude of the resultant and the component of these two vectors resolved in the direction perpendicular to resultant should be zero.

In other words, 20

3

cos30

0

+xcosθ=20

which gives, 20

3

.

2

3

+xcosθ=20

or, 30+xcosθ=20, giving xcosθ=−10 --- (1)

Now, resolving in the perpendicular direction, 20

3

.sin30

0

+xsinθ=0

or, 10

3

+xsinθ=0, giving xsinθ=−10

3

--- (2)

Squaring and adding (1) and (2), we get:

(xcosθ)

2

+(xsinθ)

2

=x

2

=100+300=400 , thus x=20 N