Two forces acting in the opposite direction have a resultant of 10N. If they act at the right angles to each other the resultant is 50N .the magnitude of the forces are
30N and 40N
To find the magnitudes of the forces, we can use the Pythagorean theorem.
Let's call the magnitudes of the two forces F1 and F2.
When two forces are acting in opposite directions and have a resultant of 10N, they form a right angle. According to the Pythagorean theorem, the square of the resultant is equal to the sum of the squares of the magnitudes of the two forces:
(Resultant)^2 = (F1)^2 + (F2)^2
Substituting the given values, we get:
10^2 = (F1)^2 + (F2)^2
100 = (F1)^2 + (F2)^2 ----(Equation 1)
Now, let's consider the second situation where the resultant is 50N when the forces act at right angles to each other. In this case, the magnitude of the resultant force is the hypotenuse of a right triangle formed by the two forces:
(Resultant)^2 = (F1)^2 + (F2)^2
Substituting the given values, we get:
50^2 = (F1)^2 + (F2)^2
2500 = (F1)^2 + (F2)^2 ----(Equation 2)
We now have two equations with two unknowns. We can solve this system of equations by subtracting equation 1 from equation 2:
2500 - 100 = (F1)^2 + (F2)^2 - ((F1)^2 + (F2)^2)
2400 = 0
This equation is absurd and does not have a solution.
Therefore, there are no magnitudes of forces that satisfy both conditions simultaneously.
50N & 90N
x - y = 10
x ² + y ² = 50 ²
Solve for x and y.