Four forces are acting on an object. Force 1 has a magnitude of 5N at an angle of 70° above the +x-axis; force 2 has a magnitude of 8N at an angle of 35° above the +x-axis; force 3 has a magnitude of 4N at an angle of 20° above the -x-axis; force 4 has a magnitude of 7N at an angle of 25° to the left of the -y-axis. Find the magnitude and direction of the

resultant of these four forces.

This is my work:
V1: 1.7 (x) 4.7(y)
V2: 6.5 (x) 4.5 (y)
V3: -3.8 (x) 1.4 (y)
V4: -6.3 (x) 2.9 (y)
R: -1.9 (x) 13.5 (y)

tan-1(13.5/-1.9) = -81.9

I really don't understand this question!

See current post: Sat, 10-11-14, 11:51AM

To find the magnitude and direction of the resultant of the four forces, you need to calculate the sum of the individual force vectors.

Let's break down the calculation step by step:

1. Resolve each force into its x and y components:
- Force 1: magnitude of 5N at an angle of 70° above the +x-axis.
- x-component: 5N * cos(70°) = 1.7N in the positive x-direction.
- y-component: 5N * sin(70°) = 4.7N in the positive y-direction.
- Force 2: magnitude of 8N at an angle of 35° above the +x-axis.
- x-component: 8N * cos(35°) = 6.5N in the positive x-direction.
- y-component: 8N * sin(35°) = 4.5N in the positive y-direction.
- Force 3: magnitude of 4N at an angle of 20° above the -x-axis.
- x-component: 4N * cos(180° - 20°) = -3.8N in the negative x-direction.
- y-component: 4N * sin(180° - 20°) = 1.4N in the positive y-direction.
- Force 4: magnitude of 7N at an angle of 25° to the left of the -y-axis.
- x-component: 7N * cos(90° + 25°) = -6.3N in the negative x-direction.
- y-component: 7N * sin(90° + 25°) = 2.9N in the positive y-direction.

2. Add up the x and y components separately:
- x-components sum: 1.7N + 6.5N - 3.8N - 6.3N = -1.9N.
- y-components sum: 4.7N + 4.5N + 1.4N + 2.9N = 13.5N.

3. Determine the magnitude of the resultant:
- Magnitude = √((-1.9N)^2 + (13.5N)^2) = √(3.61N^2 + 182.25N^2) = √(185.86N^2) = 13.62N.

4. Determine the direction of the resultant:
- tan^(-1)(13.5N / -1.9N) = -81.9° (rounded to one decimal place).
- The negative sign indicates the direction in the negative x-axis, and the value of 81.9° is the angle with respect to the positive x-axis.

Therefore, the magnitude of the resultant force is 13.62N, and its direction is -81.9° (with respect to the positive x-axis). Note that direction is usually measured counterclockwise from the positive x-axis in the range of -180° to 180°.