A 46.4-N force is applied to the outer edge of a door of width 1.26 m in such a way that it acts (a) perpendicular to the door (b) at an angle of 43.0 degrees with respect to the door surface, (c) so that the line of action of the force passes through the axis of the door hinges. Find the torque for these three cases
(a) M= F•W =46.6•1.26 = ...
(b) M= F•W•sinα =46.6•1.26 •sin43°=
(c) M=0
To find the torque in each case, we need to calculate the moment of the force applied to the door. The moment of a force is given by the product of the force magnitude and the perpendicular distance between the axis of rotation and the line of action of the force.
(a) When the force is applied perpendicular to the door:
In this case, the perpendicular distance between the axis of rotation (hinges) and the line of action of the force is equal to the half-width of the door. Let's assume the width of the door is given by 'W'.
Therefore, the perpendicular distance is W/2.
The torque is given by the formula: Torque = Force * Perpendicular Distance
So, Torque in this case = 46.4 N * (W/2)
(b) When the force is applied at an angle of 43.0 degrees with respect to the door surface:
To find the torque in this case, we need to calculate the perpendicular distance between the axis of rotation and the line of action of the force. This distance can be found using trigonometry.
Let's call the perpendicular distance 'D'.
From the given information, we have an angle of 43.0 degrees, and the width of the door is given by 'W'.
Using trigonometry, we can express 'D' in terms of 'W' and the angle:
D = W * sin(angle)
The torque is then given by: Torque = Force * Perpendicular Distance
So, Torque in this case = 46.4 N * D
(c) When the line of action of the force passes through the axis of the door hinges:
In this case, the perpendicular distance between the axis of rotation and the line of action of the force is zero. The torque is also zero because there is no lever arm.
To summarize:
(a) Torque = 46.4 N * (W/2)
(b) Torque = 46.4 N * (W * sin(angle))
(c) Torque = 0 N (No torque as there is no perpendicular distance)
Please note that I have used 'W' to represent the width of the door without any specific numerical value. You can substitute the value of 'W' into the formulas to calculate the torque for each case.