If N forces of equal magnitude F are acting on a body. If angle between adjacent forces is 2π\N, the resultant of the forces is
Answers
Answer:
Explanation:
If the n forces are of equal magnitude and have equal angles between them, which are each equal to 360n degrees. And since the question does not state this particular condition of the angles being equal to 360n degrees, so no, not necessarily.
For example, if there are 3 forces of equal magnitude, they can be oriented such that each makes and angle of 90 degrees with the other 2 (one along x axis, there other two along y and z axes). But, in this case, the net force is not zero, even though each force makes equal angle with each other. But, if the angles between the forces are made to be equal to 3603=120 degrees, then the net force WILL be zero.
This comes out due to the vector laws of addition as force is a vector.
So the actual condition comes out to be the following:
Theorem:
"If n forces of equal magnitude act on an object with equal angles between them, such that each angle is equal to 360n degrees, then the resultant will always be zero."
If you notice, this new condition of 360n degrees, on the angles compels the forces to lie in the same plane (become co-planar). This compulsion is what leads to the resultant becoming zero.
Now remember, converse of the above theorem is NOT true. That is, it does NOT mean that equal magnitude forces with equal angles between them, have to be co-planar to give zero resultant. In certain cases, they can give zero resultant even when they are non-coplanar. Like the case of 4 equal forces aligned like the hydrogen atoms of the methane molecule, making a tetrahedron. These 4 forces are equal in magnitude and have equal angles between them and are NON-coplanar, but still give zero resultant.
Answer:
- The answer of the question is Zero .