Question

Three forces with magnitudes of 65 pounds, 90 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

The diagram of forces is shown below

We would express each vector in component form. We have

For F1 = 65 pounds,

F1 = <65Cos30, 65Sin30>

F1 = <56.2917, 32.5>

For F2 = 90 pounds,

F2 = <90Cos45, 90Sin45>

F2 = <63.6396, 63.6396>

For F3 = 125 pounds

F3 = <125Cos120, 125Sin120

F3 = <- 62.5, 108.2532>

Fnet = F1 + F2 + F3

Fnet = <56.2917, 32.5> + <63.6396, 63.6396> + <- 62.5, 108.2532>

Fnet = <56.2917 + 63.6396 - 62.5, 32.5 + 63.6396 + 108.2532>

Fnet = <57.4313, 204.3928>

Magnitude of resultant force = √(57.4313^2 + 204.3928^2)

Magnitude of resultant force = 212.3 pounds

Direction, θ = tan^-1(204.3928/57.4313)

θ = 74.3 degrees