Question

Example 7 The sum of the magnitudes of two forces
acting a point is 18 and the magnitude of their resultant is 12.
If the resultant is at 90° with the force of smaller magnitude.
what are the magnitudes of forces?​

Answer 1

Answer:

S1 21

Explanation:

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Answer 2

Answer:

5,13.

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.