Question

the sum of the magnitude of two forces acting at a point is 18 and the magnitude of their resultant is 12. The resultant is at 90° with the force of the smaller magnitude then their magnitudes are

Answer 1

Answer

5N and 13 N

Explanation:

Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.

As the resultant force makes 90

∘

with the smaller force P then Q forms the hypotenuse of the triangle.

Thus, it can be written as,

Q

2

−P

2

=R

2

Q

2

−P

2

=(12)

2

Q

2

−P

2

=144 (1)

The sum of magnitudes of two forces is given as,

P+Q=18

Q=18−P (2)

Substituting the value from equation (2) in equation (1), we get

(18−P)

2

−P

2

=144

P=5N

Substituting the value of P in equation (1), we get

Q=18−5

=13N

Thus, the magnitude of the forces are 5N and 13N.