Final answer:
The magnitude of the resultant force is determined using vector addition and the Pythagorean theorem, by summing the squared components of each force and taking the square root of that sum.
Step-by-step explanation:
To calculate the magnitude of the resultant force acting on a block (Fr), we use vector addition. For the three forces (F1, F2, and F3), the magnitude of the resultant force is determined by first finding the vector components of each force and then summing these components along their respective axes.
Once we have the resultant components in each direction, we can find the magnitude of Fr by applying the Pythagorean theorem:
Fnet = √(Fx^2 + Fy^2)
In a provided example equation where the components are 30.0 N along the x-axis and 40.0 N along the y-axis, the magnitude of the net force would be 50.0 N, calculated as:
Fnet = |(30.0 N)^² + (40.0 N)^2| = 50.0 N
This method is used regardless of the number of forces involved and can be extended to find the resultant force when dealing with more than two forces.