Question

Two forces of 58 newtons and 32 newtons act simultaneously on an

object. The angle between the two forces is 22°. Find the magnitude of

the resultant, to the nearest 10th of a newton. Find the measure of the

angle between the resultant and the smaller force, to the nearest 10th

of a degree.

Answer 1

Answer: To find the magnitude of the resultant, we can use the formula:

R = sqrt(F1^2 + F2^2 - 2F1F2*cos(theta))

where F1 and F2 are the magnitudes of the two forces and theta is the angle between them in radians.

So,

R = sqrt(58^2 + 32^2 - 25832cos(22)) = sqrt(3364 + 1024 - 21856*0.9135) = sqrt(4388) = 66.18

To find the measure of the angle between the resultant and the smaller force, we can use the formula:

theta = atan2(F2sin(theta), F1 + F2cos(theta))

So,

theta = atan2(32sin(22), 58 + 32cos(22)) = atan2(15.49, 81.49) = 16.89 degree

The magnitude of the resultant to the nearest 10th of a newton is 66.2 newton.

Final Answer = The measure of the angle between the resultant and the smaller force, to the nearest 10th of a degree, is 16.9 degree

Explanation: