Three Fixed pulleys with a common center have the following radi of Ra=16cm, Rb=24cm and Rc=36cm with the applied forces <- Fc; /Fa (pointing southwest); and Fb (pointing southeast).
Find the Resultant Torque given Fa=25N; Fb=75N; and Fc=120N.
To find the resultant torque in this scenario, we need to first calculate the moment arm for each force using the given radii. The moment arm is the perpendicular distance between the axis of rotation and the line of action of the force.
Moment arm for Fa:
The moment arm for Fa can be calculated by taking the distance between the axis of rotation and the line along which it is acting. As it is pointing southwest, the line of action is perpendicular to the radius Ra and can be drawn by extending the radius in the southwest direction. The moment arm for Fa will be the length of this line, which is the same as the radius Ra since the force is acting at the same distance.
Moment arm for Fb:
Similarly, the moment arm for Fb can be calculated by taking the distance between the axis of rotation and the line along which it is acting. As it is pointing southeast, the line of action is perpendicular to the radius Rb and can be drawn by extending the radius in the southeast direction. The moment arm for Fb will be the length of this line, which is the same as the radius Rb since the force is acting at the same distance.
Moment arm for Fc:
The moment arm for Fc can be calculated by taking the distance between the axis of rotation and the line along which it is acting. The line of action for Fc is directly opposite to the radius Rc, extending in the north direction. The moment arm for Fc will be the length of this line, which is the same as the radius Rc since the force is acting at the same distance.
Now, we can calculate the resultant torque using the following formula:
Resultant Torque = (Fa * Moment arm for Fa) + (Fb * Moment arm for Fb) + (Fc * Moment arm for Fc)
Substituting the given values:
Resultant Torque = (25N * 16cm) + (75N * 24cm) + (120N * 36cm)
Resultant Torque = 400cmN + 1800cmN + 4320cmN
Finally, adding the torques gives us:
Resultant Torque = 6520cmN
Therefore, the resultant torque is 6520 centimeter-newtons (cmN).