Question

Two forces act on an object. The first force has a magnitude of 360 newtons and acts at an angle of 30° as measured from the horizontal. The second force has a magnitude of 240 newtons and acts at an angle of 135°as measured from the horizontal. Determine the vector v that represents the resultant force.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the resultant force, we can break down each force into its horizontal and vertical components.

For the first force:
Magnitude = 360 N
Angle = 30°

Horizontal component = 360 * cos(30°) = 360 * 0.866 = 311.04 N
Vertical component = 360 * sin(30°) = 360 * 0.5 = 180 N

For the second force:
Magnitude = 240 N
Angle = 135°

Horizontal component = 240 * cos(135°) = 240 * (-0.707) = -169.68 N
Vertical component = 240 * sin(135°) = 240 * 0.707 = 169.68 N

Now, we can add the horizontal and vertical components of both forces to find the total horizontal and vertical components of the resultant force:

Horizontal component of resultant force = 311.04 N + (-169.68 N) = 141.36 N
Vertical component of resultant force = 180 N + 169.68 N = 349.68 N

Finally, we can find the magnitude and direction of the resultant force using the Pythagorean theorem and arctan:

Magnitude of resultant force = sqrt((141.36)^2 + (349.68)^2) = sqrt(19901.53) = 141.14 N
Angle of resultant force = arctan(349.68 / 141.36) = arctan(2.47) = 68.48°

Therefore, the vector v that represents the resultant force is 141.14 N at an angle of 68.48° as measured from the horizontal.