Question

Two forces are such that the sum of their magnitude is 18N and their resultant is 12N which is perpendicular to the smaller force. Then the magnitude of the forces are

Answer 1

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Answer 2

Answer:

The magnitude of the forces are 13N and 5N.

Explanation:

Let B be the smaller force and A be the larger force, with C being the result.

A,B,C simply form a right-angled triangle with B as the base vector and A as the hypotenuse.

So you only have one equation: A+B=18

A² = B² + C²

A²- C² = B²

(A+B) (A-B) = 144

(A-B) 18 = 144

(A-B) = 144 ÷ 18 = 8

So, by simply solving both equations, A-B=8 and A+B=18 are obtained.

By combining both:

2A = 26

A = 13

B = 5

Hence, the answer is 13N and 5N.

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