Question

Use a trigonometric solution to find the magnitude of the resultant of the following coplanar forces

Answer 1

The magnitude of the resultant force from coplanar forces can be found using trigonometry by resolving the forces into components and applying the Pythagorean theorem.

Step-by-step explanation:

To find the resultant of the coplanar forces F1 and F2, one can use trigonometry. This process involves isolating components of the individual forces along the x and y axes, and then combining these components to calculate the magnitude of the total force, Ftot. To demonstrate these principles, we will walk through the calculation of the magnitude, assuming we have the necessary values for F1 and F2.

Steps to Calculate the Resultant Force:

1. Resolve each force into its x and y components using sine and cosine functions.
2. Add the x-components of F1 and F2 together to find the resultant x-component (Fx).
3. Add the y-components of F1 and F2 together to find the resultant y-component (Fy).
4. Use the Pythagorean theorem to find the magnitude of the resultant force: Ftot = √(Fx² + Fy²).
5. If required, find the direction of the resultant using the tangent function: θ = tan⁻¹(Fy/Fx).

By following this method, one can also show graphically that the same Ftot is obtained regardless of the order in which F1 and F2 are added, demonstrating the commutative property of vector addition.

Answer 2

To find the magnitude of the resultant of 60N at 90 degrees, 80N at 120 degrees and 100 N at 270 degree, you will just minus 180 degrees to 180 degrees since the remaining angle is the resultant velocity of the unmeasured side of the angle. Since there is a given of 30 degrees, then 180 degrees-30 degree = 150 degrees. Th magnitude is Ncos150 where N=squareroot of A^2+B^2 and the answer is 128.06
SO magnitude= 128.06cos150
=110.91
or 111