Two forces 12N and 16N are acting upon a body. What can be the maximum and minimum resultant force on the body?

Expert Answers

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Let's assume that both forces are apllied to the same point. In another case they would cause rotation of a body and it would be unclear what the net force is.

Forces are vectors. Two vectors a and b with the same starting point are always lie in the same two dimensional plane. The magnitude of their sum is the square root of the dot product:

`sqrt((a + b)(a + b)) = sqrt(|a|^2 + |b|^2 + 2|a|*|b|*cos(c)),`

where c is the angle between a and b.

The maximum value of this magnitude is reached when cos(c) = 1, this means the vectors have the same direction. The value is actually |a| + |b| = 12 N + 16 N = 28 N.

The minimum is reached when cos(c) = -1, when the vectors have opposite directions. And this minimum value is ||a| - |b|| = 16 N - 12 N = 4 N.

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