2 forces acting at a point make angles of 25 and 65 degrees respectively with their resultant which has a magnitude of 150 N .Find the magnitude of the two components.
The two components lie on opposite sides of the resultant. Call them a and b. Let a be the vector that is 25 degrees from the resultant.
Then these two equations must be satisfied:
a cos25 + b cos65 = 150
a sin25 - b sin65 = 0
a/b = sin65/sin25 = 2.1445
1.9436b + 0.4266b = 150
This leads to b = 63.39 and a = 135.95
The units of a and b are Newtons, since we are adding forces with reulstant 150 N.
Want to be cleared about magnitude in vectors.
To find the magnitudes of the two components, we need to use trigonometry and break down the resultant force into its components using the given angles.
Let's call the magnitudes of the two forces F1 and F2.
First, we can find the horizontal component of the resultant force (Rx) using trigonometry. We can use the cosine function since the given angle is adjacent to the horizontal component:
Rx = Resultant force * cos(angle)
Rx = 150 N * cos(65 degrees)
Next, we can find the vertical component of the resultant force (Ry) using the sine function since the given angle is opposite to the vertical component:
Ry = Resultant force * sin(angle)
Ry = 150 N * sin(65 degrees)
Similarly, we can find the horizontal and vertical components for the other force, which makes an angle of 25 degrees with the resultant:
Fx = F1 * cos(25 degrees)
Fy = F1 * sin(25 degrees)
Now, we have two equations for the horizontal components:
Rx = F1 * cos(25 degrees)
Rx = F2 * cos(65 degrees)
And two equations for the vertical components:
Ry = F1 * sin(25 degrees)
Ry = F2 * sin(65 degrees)
We can substitute the found values of Rx and Ry into the equations to get:
150 N * cos(65 degrees) = F1 * cos(25 degrees)
150 N * sin(65 degrees) = F1 * sin(25 degrees)
Now, we can solve these two equations simultaneously to find the magnitude of the two components, F1 and F2.