Question

Three teenagers push a heavy crate across the floor. Dion pushes with a force of 185 N at 0°. Shirley exerts a force of 165 N at 30°, while Joan pushes with a 195 N force at 300°. What is the resultant force on the crate?

Answer 1

The resultant force on the crate is approximately 247.87 N at an angle of -21.86°.

Step-by-step explanation:

To find the resultant force on the crate, we will use vector addition. We'll start by breaking down each force into its x and y components using trigonometry.

Dion's force of 185 N at 0° has an x-component of 185 N and a y-component of 0 N. Shirley's force of 165 N at 30° has an x-component of 142.53 N and a y-component of 82.5 N. Joan's force of 195 N at 300° has an x-component of -97.5 N and a y-component of -167.95 N.

Adding up these components, we get an x-component of 185 N + 142.53 N - 97.5 N = 230.03 N, and a y-component of 0 N + 82.5 N - 167.95 N = -85.45 N. Using the Pythagorean theorem, we can find the magnitude of the resultant force: √((230.03 N)² + (-85.45 N)²) = 247.87 N. The direction of the resultant force can be found using the inverse tangent function: tan^(-1)((-85.45 N)/(230.03 N)) = -21.86°. Therefore, the resultant force on the crate is approximately 247.87 N at an angle of -21.86°.