two current forces acts at an angle 30 degree . the resultant force is 15 N and one of the forces is 10 N . find the other force
a body is under of 2 forces 7n and 10n find the
resultant of 2 forces ...
To find the magnitude of the other force, we can use the concept of vector addition.
Let's denote the magnitude of the other force as F. We know that the resultant force is 15 N and one of the forces is 10 N.
Using trigonometry, we can break down the resultant force into its x and y components. Since the angle between the two forces is given as 30 degrees, we can see that the x-component of the resultant force is given by:
Rx = 15 N * cos(30 degrees)
Similarly, the y-component of the resultant force is given by:
Ry = 15 N * sin(30 degrees)
Now, we can break down the 10 N force into its x and y components. Since the angle between the 10 N force and the resultant force is also 30 degrees, we can see that the x-component of the 10 N force is given by:
Ax = 10 N * cos(30 degrees)
Since the other force acts in the opposite direction to the 10 N force, its x-component will have the same magnitude but opposite sign:
Bx = -Ax = -10 N * cos(30 degrees)
Now, we can calculate the x-component of the other force:
Rx = Ax + Bx
15 N * cos(30 degrees) = 10 N * cos(30 degrees) + Fx
Simplifying the equation, we get:
15 N * cos(30 degrees) - 10 N * cos(30 degrees) = Fx
5 N * cos(30 degrees) = Fx
Using the cosine function, we can find the value of Fx:
Fx = 5 N * cos(30 degrees)
Similarly, we can calculate the y-component of the other force:
Ry = Ay + By
15 N * sin(30 degrees) = 10 N * sin(30 degrees) + Fy
Simplifying the equation, we get:
15 N * sin(30 degrees) - 10 N * sin(30 degrees) = Fy
5 N * sin(30 degrees) = Fy
Using the sine function, we can find the value of Fy:
Fy = 5 N * sin(30 degrees)
Finally, we can find the magnitude of the other force using the Pythagorean theorem:
F = sqrt(Fx^2 + Fy^2)
F = sqrt((5 N * cos(30 degrees))^2 + (5 N * sin(30 degrees))^2)
Substituting the values and calculating, we can find the magnitude of the other force.