The resultant of two forces 1 and P, is perpendicular to 1 and equal to 1. What is the value of 'P' and angle between the forces?
To find the value of 'P' and the angle between the forces, we can use the principles of vector addition and trigonometry.
First, let's represent the two forces graphically:
Let force 1 be represented by vector A, and force P be represented by vector B. Since the resultant of the two forces is perpendicular to force 1 (A), it means that force P (B) must be perpendicular to force 1 (A).
Now, since the resultant is equal to force 1 (A), the magnitude of vector A is equal to the magnitude of the resultant.
Let's denote the magnitude of force 1 (A) as |A| = 1.
Therefore, the magnitude of the resultant (R) is also 1.
Using the Pythagorean theorem for right triangles, the magnitude of vector B can be calculated as:
|B| = √(R^2 - |A|^2)
= √(1^2 - 1^2)
= √0
= 0
So, the magnitude of P (|B|) is 0. This means that the value of 'P' is 0.
Now, let's calculate the angle between the forces:
Since vector B is perpendicular to vector A, the angle between them is 90 degrees (or π/2 radians).
Therefore, the value of 'P' is 0, and the angle between the forces is 90 degrees (or π/2 radians).
without loss of generality, we can set it up so that the two unit vectors are along the x and y axes. So, if P = <x,y>
<0,1>+<x,y> = <1,0>
<x,y> = <1,0>-<0,1>
<x,y> = <1,-1>
I think you can take it from there, eh?