Question

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

Solve and explain briefly....

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Answer 1

Solution

The force of the magnitude is smaller A and larger to B.

The force gives 90 degree angle and smaller force for A and B

So,B is the hypotenuse of the triangle.

Therefore,

B²=R²+A²

R²=B²-A²=12²=144

(A+B=18) and (B=18-A)

Now we need to substitute both A and B

18-A²-A²=144

324-36A+A²-A²=144

So, 36A=324-144=180

A=180/36=5

$therfore \: b = 18 - a = 18 - 5 = 13$

$the \: magnitudes \: of \: the \: two$

$forces \: are \: 5 \: and \: 13$

Answer 2

Answer:

5 N, 13 N

Explanation:

Let the smaller of the two forces is of magnitude P N.

Hence the larger one will be (18 - P) N.

Now,

Given that resultant is at 90° with the force of smaller magnitude.

∴ Q² = S² + P²

⇒ S² = Q² - P² = 12² = 144.

Also,

Given that:

P + Q = 18

⇒ Q = 18 - P

As the resultant 18N is perpendicular to P. we can write

P² + 12² = (18 - P)²

⇒ P² + 144 = 324 + P² - 36P

⇒ 36P = 112

⇒ P = 5 N

Hence, we get

⇒ Q = 18 - 5

⇒ Q = 13 N

Therefore:

Smaller force is 5 N

Larger force is 13 N

Hope it helps!