Let's assume that the smaller force is represented by vector A and the larger force is represented by vector B. We are given that the magnitude of vector B is 80 Newtons and that the angle between the two forces is 120°.
We can use vector addition to find the resultant of the two forces. If the resultant is perpendicular to vector A, it means that the two forces are parallel and in opposite directions.
First, we represent vector A using Cartesian coordinates: A = (Ax, Ay). Since the resultant is perpendicular to vector A, its x-component must be equal in magnitude but opposite in direction to the x-component of vector A. Therefore, the x-component of the resultant is -Ax.
Next, we represent vector B using Cartesian coordinates: B = (80cos(120°), 80sin(120°)).
Now, we can find the x-component of the resultant by adding the x-components of vector A and vector B: -Ax = 80cos(120°) + Ax
Simplifying this equation: 2Ax = 80cos(120°)
Ax = 40cos(120°) = -20.
Since vector A is represented by (Ax, Ay), we know that Ay must equal zero for the resultant to be perpendicular to vector A.
Thus, the smaller force represented by vector A is 20 Newtons.
Two forces act at an angle of 120°,the bigger force is of 80newton and the resultant is perpendicular to the smaller one.find the smaller one.
1 answer