How to Calculate Resultant Force with Given Magnitude and Angle

What are the magnitudes of forces Q and P? How can we find the resultant force using vector addition?

The magnitude of force Q is 60N, while the magnitude of force P is 40N at an angle of 20 degrees with respect to the x-axis (AE). To calculate the resultant force, we need to resolve force P into its x and y components, and then add the components of forces Q and P separately.

Calculating Resultant Force:

Force Q: Magnitude = 60N

Force P: Magnitude = 40N, Angle = 20 degrees

To find the resultant force, we first need to resolve force P into its x and y components:

X-component of P (Px) = Force P * cos(angle)

Y-component of P (Py) = Force P * sin(angle)

Next, we can add the x-components and y-components of forces Q and P separately:

Resultant force in the x-direction (Rx) = Q + Px

Resultant force in the y-direction (Ry) = Py

Using the Pythagorean theorem, we can find the magnitude of the resultant force (R):

R = sqrt(Rx^2 + Ry^2)

By substituting the values and performing the calculations, we can determine the magnitude of the resultant force.