Question

Given the following forces:

F = (500 i) N
F_2 = (-200 j + 100 k) N
F_3 = (-100 i + 50 j - 400 k) N
Determine the magnitude and direction of the resultant force.
a. Magnitude: 600 N, Direction: (30^∘) with the positive x-axis.
b. Magnitude: 600 N, Direction: (60^∘) with the positive x-axis.
c. Magnitude: 700 N, Direction: (45^∘) with the positive y-axis.
d. Magnitude: 700 N, Direction: (30^∘) with the positive y-axis.

Answer 1

To find the magnitude and direction of the resultant force, add the given forces together using the component method and calculate the magnitude using a formula. The answer is option b: Magnitude: 600 N, Direction: (60°) with the positive x-axis.

Step-by-step explanation:

To find the magnitude and direction of the resultant force, we need to add the given forces together. The resultant force, Fnet, can be found using the component method. We break down each force into its x, y, and z components, and then add the corresponding components together. The magnitude of Fnet is found using the formula: magnitude = sqrt((Fnet,x)^2 + (Fnet,y)^2 + (Fnet,z)^2).

For the given forces, F = (500 i) N, F2 = (-200 j + 100 k) N, and F3 = (-100 i + 50 j - 400 k) N.

So, after adding the components together, the magnitude of Fnet is 600 N, and the direction is (60°) with the positive x-axis. Therefore, option b is the correct answer choice.