Two forces are acting at a point make angle of 25 and 65 respectively with their resultant which is of magnitude 15N.Find the magnitude of two components forces
Fx = 15cos25 = 13.6N
Ft = 15sin65 = 13.6N
To find the magnitude of the two component forces, we can use trigonometry.
Let's consider the two forces as vectors A and B, and their resultant as vector R.
Given that the magnitude of the resultant force R is 15N, we need to find the magnitudes of forces A and B.
Now, let's break down the resultant force R into its components.
We can use the concept of vector addition and resolve the resultant force R into its components along the directions of the given angles.
The component of the resultant force R in the direction of the first angle (25 degrees) is given by R1 = R * cos(angle1).
R1 = 15 * cos(25).
Similarly, the component of the resultant force R in the direction of the second angle (65 degrees) is given by R2 = R * cos(angle2).
R2 = 15 * cos(65).
The magnitude of force A is equal to the magnitude of the first component R1, and the magnitude of force B is equal to the magnitude of the second component R2.
So, the magnitude of force A is 15 * cos(25) N, and the magnitude of force B is 15 * cos(65) N.
Solve
Say resultant is in x direction
A at +25 and B at -65
so
Rx = 15 and Ry = 0
and
Rx = A cos 25 + B cos 65 = 15
Ry = A sin 25 - B sin 65 = 0
solve for A and B