Question

Two forces act on an object. The first force has a magnitude of 17.0 N and is oriented 78.0° counterclockwise from the + ‑axis, whereas the second force has ‑ and ‑components (−21.0 N,12.5 N). Express the magnitude and direction of the net force.

a) 20.8 N at 53.2° counterclockwise
b) 5.5 N at 120.5° clockwise
c) 25.0 N at 15.5° counterclockwise
d) 17.2 N at 78.0° counterclockwise

Answer 1

The net force can be found by adding the individual forces together. The magnitude and direction of the net force can be determined using the Pythagorean theorem and the inverse tangent function, respectively.

Step-by-step explanation:

The net force can be found by adding the individual forces together.

The first force has components of 17.0 N*cos(78.0°) in the x-direction and 17.0 N*sin(78.0°) in the y-direction.

The second force has components of -21.0 N in the x-direction and 12.5 N in the y-direction.

To find the net force, add the x-components and the y-components separately.

The magnitude of the net force can be found using the Pythagorean theorem, and the direction can be found using the inverse tangent function.

a) 20.8 N at 53.2° counterclockwise