If the two forces are now made to be inclined at 120 to each other find the magintude of the new resultant force
To find the magnitude of the new resultant force, we will use the Law of Cosines.
The Law of Cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c, the following equation holds true:
c^2 = a^2 + b^2 - 2ab*cos(C)
In this case, the two forces make an angle of 120° with each other. Let's call the magnitudes of the two forces A and B. The resultant force (the sum of the two forces) can be represented by a third side, C, of a triangle.
According to the Law of Cosines, we can write the equation for the magnitude of the resultant force (C) as follows:
C^2 = A^2 + B^2 - 2AB*cos(120°)
To find the magnitude of the resultant force, we need the magnitudes of the two forces (A and B).
Without specific values for A and B, we cannot find the exact magnitude of the resultant force.
To find the magnitude of the new resultant force when two forces are inclined at 120 degrees to each other, you can use the law of cosines.
Let's denote the magnitudes of the two forces as F1 and F2.
The law of cosines states that the square of the magnitude of the resultant force (F) is equal to the sum of the squares of the magnitudes of the individual forces, minus twice the product of the magnitudes of the forces and the cosine of the angle between them.
So, using the formula:
F^2 = F1^2 + F2^2 - 2 * F1 * F2 * cos(120)
Since the cosine of 120 degrees is -1/2, we can substitute it into the formula:
F^2 = F1^2 + F2^2 - 2 * F1 * F2 * (-1/2)
F^2 = F1^2 + F2^2 + F1 * F2
Finally, to find the magnitude of the resultant force (F), take the square root of both sides of the equation:
F = sqrt(F1^2 + F2^2 + F1 * F2)
By substituting the values of F1 and F2, you can find the magnitude of the new resultant force.