Question

Three forces with magnitudes of 80 pounds, 95 pounds, and 125 pounds act on an object at angles of 30°, 45°, and 120°, respectively, with the x-axis. Find the direction and magnitude of the resultant of these forces. (Round your answers to one decimal place.)

Answer 1

• 227.8 pounds
• 71.1°

Explanation:

You want the resultant magnitude and direction when three forces act with magnitudes 80, 95, and 125 pounds in directions 30°, 45°, and 120° relative to the x-axis, respectively.

Sum

A suitable calculator can add these forces directly. This is shown in the second attachment. The resultant is ...

227.8 pounds at an angle of 71.1°

A diagram of the sum is shown in the first attachment.

Components

The x- and y-components of each of the vectors will be ...

(x, y) = M(cos(θ), sin(θ)) . . . . . . where M is the magnitude of the force

Corresponding components of the forces can be added, and the sum converted back to polar form using ...

(a, b) = R∠θ . . . . where R = √(a²+b²) and θ = arctan(b/a)

The third attachment shows the components of the vectors, and the conversion of their sum to polar form. (Final values differ slightly from the second attachment due to the rounding.)