A square, 0.74m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. This axis is perpendicular to the plane of the square. A force of 26.8N lies in this plane and is applied to the square. What is the magnitude of the maximum torque (in N*m) such that a force could produce?
To find the magnitude of the maximum torque that can be produced by the applied force, we need to first understand the concept of torque.
Torque, denoted by τ (tau), is defined as the rotational equivalent of force. It is a measure of the force's ability to cause an object to rotate about a particular axis. Mathematically, torque is given by the equation:
τ = r × F
Here, r represents the moment arm or the perpendicular distance between the axis of rotation and the line of action of the force F.
In this case, the force lies in the plane of the square, so the moment arm will be the perpendicular distance from the axis of rotation (center of the square) to the line of action of the force. Since it is mounted so that it can rotate about an axis passing through the center, the moment arm will be half the length of one side of the square.
Given that the side length of the square is 0.74m, the moment arm (r) will be equal to 0.74m/2 = 0.37m.
Now we can calculate the maximum torque using the given force of 26.8N:
τ = r × F
= 0.37m × 26.8N
= 9.896N*m
Therefore, the magnitude of the maximum torque that can be produced by the applied force is 9.896 N*m.