Question

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. Include the formula used.

Answer 1

Answer:

Magnitude: 121.35 pounds

Direction: 21.64°

Explanation:

1) Decompose each force into its x - y components.

2) Force 1, F1: 140 pounds at angle of 30°

x-component: F1,x

F1, x = F1 *cos(30°) = 140 pounds * cos(30°) = 121.24 pounds

y-component: F1,y

F1,y = F1 * sin(30°) = 140 pounds * sin(30°) = 70 pounds.

3) Force 2, F2: 75 poounds at 150°

x-component: F2,x

F2,x = F2 * cos(150°) = 75 pounds * cos(150°) = - 64.95 pounds

y-component: F2,y

F2,y = F2 * sin(150°) = 75 pounds * sin(150°) = 37.5 pounds

4) Resultant Force, Fr

x-component: Fr,x

Fr,x = F1,x + F2,x = 121.24 pounds - 64.95 pounds = 56.29 pounds

y-component: Fr,y

Fr,y = F1,y + F2,y = 70 pounds + 37.5 pounds = 107.5 pounds

4.1) magnitude

|Fr| = √ [ (56.29 pouns)^2 + (107.5 pounds)^2 ] = 121.35 pounds.

4.2) direction

tan(α) = Fr,y / Fr,3 = 56.29 pounds / 107.5 pouns = 0.5236

=> α = arctan(0.5236) = 27.64 °