Question

A 5 newton force and a 7 newton force act concurrently on a point. As the angle between the forces is increased from 0 to 180 the magnitude of the resultant of the two forces changes from

Answer 1

Answer:

The magnitude of the resultant decreases from A+B to A-B

Explanation:

The magnitude of the resultant of two vectors is given by

$R=\sqrt{A^2 +B^2 +2AB cos \theta}$

where

A is the magnitude of the first vector

B is the magnitude of the second vector

$\theta$ is the angle between the directions of the two vectors

In the formula, A and B are constant, so the behaviour depends only on the function $cos \theta$. The value of $cos \theta$ are:

- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is

$R=\sqrt{A^2 +B^2+2AB}=\sqrt{(A+B)^2}=A+B$

- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is

$R=\sqrt{A^2 +B^2+0}=\sqrt{A^2+B^2}$

- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is

$R=\sqrt{A^2 +B^2-2AB}=\sqrt{(A-B)^2}=A-B$