what are the maximum and minimum resultants of the two forces?
when they act in parallel, either in the same direction or in opposite directions.
When they act in parallel either in the same direction or opposite directions
To determine the maximum and minimum resultants of two forces, we need to understand the concept of vector addition.
Step 1: Determine the magnitudes and directions of the two forces.
For example, let's assume force A has a magnitude of 10 Newtons and is directed at an angle of 30 degrees from the positive x-axis, while force B has a magnitude of 15 Newtons and is directed at an angle of 60 degrees from the positive x-axis.
Step 2: Convert the forces into their horizontal and vertical components.
To do this, we use trigonometry. For force A, its horizontal component is A * cos(theta) and its vertical component is A * sin(theta), where A is the magnitude of the force and theta is the angle the force makes with the positive x-axis. Similarly, for force B, its horizontal component is B * cos(theta) and its vertical component is B * sin(theta).
Step 3: Add the horizontal components together to get the resultant horizontal component, and add the vertical components together to get the resultant vertical component.
Let's assume the horizontal components of the forces are Ax and Bx, while the vertical components are Ay and By. The resultant horizontal component, Rx, is Ax + Bx, and the resultant vertical component, Ry, is Ay + By.
Step 4: Calculate the magnitude of the resultant vector using the Pythagorean theorem.
The magnitude of the resultant vector, R, is given by the formula: R = sqrt(Rx^2 + Ry^2).
Step 5: Determine the maximum and minimum resultants.
The maximum resultant occurs when the two forces are in the same direction, while the minimum resultant occurs when the two forces are in opposite directions. In this case, the maximum resultant would be the magnitude of the larger force plus the magnitude of the smaller force. The minimum resultant would be the magnitude of the larger force minus the magnitude of the smaller force.
So, by following these steps and plugging in the given values, you can calculate the maximum and minimum resultants of the two forces.