The resultant of two forces X and Y will be the greatest when the angle between X and Y is:
0, of course.
They add in the same direction.
Think of the law of cosines, and draw the parallelogram. The long diagonal is longest when they are parallel.
The resultant of two forces X and Y will be the greatest when the angle between X and Y is 180 degrees or a straight line.
To determine the angle between two forces X and Y that will result in the greatest resultant, we need to understand the concept of vector addition.
When two forces act on an object, their resultant can be found by adding the two forces vectorially. This is done by adding the components of the two forces in the same direction.
The magnitude of the resultant force can be calculated using the formula:
Resultant = √(X^2 + Y^2 + 2XYcosθ)
Where:
- X and Y are the magnitudes of the forces X and Y
- θ is the angle between X and Y
Since we want to find the angle that gives us the greatest resultant, we need to maximize the value of the expression under the square root. It is important to note that cosθ can take values from -1 to +1.
To maximize the expression, we need cosθ to be as close to +1 as possible. This occurs when θ is equal to 0 degrees or 180 degrees.
Therefore, the angle between X and Y that will result in the greatest resultant is either 0 degrees or 180 degrees. In other words, the two forces need to be acting either in the same direction or in opposite directions to have the greatest resultant.