Find the magnitude and direction of the resultant of two forces of 250 pounds and 45 pounds at angles of 25 degrees and 250 degrees with the x-axis, respectively.
This is a standard vector addition problem.
Add the x and y components of the two vectors separately. The x component sum is
Fx = 250 cos 25 + 250 cos 250) = 226.6 -85.5 = 137.1
The y component sum is
Fy = 250 sin 25 + 250 sin 250 = -129.3
Use the Pythagorean theorem for the magnitude of the resultant. Its direction in quadrant IV. Use the
tan^-1 Fy/Fx for the direction
To find the magnitude and direction of the resultant of two forces, we can use vector addition. The given forces are 250 pounds and 45 pounds at angles of 25 degrees and 250 degrees with the x-axis. Let's break them down into their x and y components.
Force 1 (250 pounds at 25 degrees):
The x-component can be found using the equation:
F1x = F1 * cos(theta1)
F1x = 250 * cos(25 degrees)
The y-component can be found using the equation:
F1y = F1 * sin(theta1)
F1y = 250 * sin(25 degrees)
Force 2 (45 pounds at 250 degrees):
The x-component can be found using the equation:
F2x = F2 * cos(theta2)
F2x = 45 * cos(250 degrees)
The y-component can be found using the equation:
F2y = F2 * sin(theta2)
F2y = 45 * sin(250 degrees)
Once we have the x and y components of both forces, we can add them together to get the x and y components of the resultant force.
Resultant x-component:
Rx = F1x + F2x
Resultant y-component:
Ry = F1y + F2y
Now that we have the x and y components of the resultant force, we can find its magnitude using the Pythagorean theorem:
Magnitude of the resultant force:
R = sqrt(Rx^2 + Ry^2)
To find the direction of the resultant force, we can use the inverse tangent function:
Direction of the resultant force:
θ = arctan(Ry / Rx)
Now, we can proceed to calculate the values.