Question

The tension T in the cable AB is maintained at a constant value of 120 N. Determine the moment of this tension about point O when θ=0 and θ=45.

a) 0 Nm
b) 60 Nm
c) 84.85 Nm
d) 120 Nm

Answer 1

The moment of the tension about point O when θ=0 is 0 Nm (a), and when θ=45 it is 84.85 Nm (c), calculated by the product of the tension in the cable, the distance to the point, and the sine of the angle between the force and the lever arm.

Step-by-step explanation:

The moment of a force (also known as torque) about a point is a measure of the tendency of that force to rotate an object about the point. The formula for the moment (torque) is given by T = rF sin(θ), where T is the torque, r is the distance from the point to the line of action of the force, F is the magnitude of the force, and θ is the angle between the force and the lever arm. When θ=0°, sin(θ) is 0, so the torque is 0 Nm. When θ=45°, sin(θ) is √2/2, so assuming the distance from point O to the line of action of tension is constant and using a cable tension T of 120 N, we must multiply 120 N by √2/2 to get the torque, which equals 84.85 Nm. Therefore, the answer to the student's question for θ=0° is (a) 0 Nm, and for θ=45° (c) 84.85 Nm.