Question

The 23-cm-diameter disk in (Figure 1) can rotate on an axle through its center. You may want to review (Pages 304 - 307) For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Nutcracker. Figure 1 of 1 > 30 30 N 457 5 cm 5 cm 20 N 20 N emView?

Answer 1

The problem involves a 23-cm-diameter disk rotating on an axle through its center, subject to forces of 30 N and 20 N acting at different radii. To determine the net torque, we use the formula: Net Torque = Force × Distance from the axis of rotation. The net torque exerted on the disk is 610 N⋅cm in the counterclockwise direction.

Step-by-step explanation:

To calculate the net torque, recall the formula for torque: Torque (τ) = Force (F) × Distance (r) perpendicular to the axis of rotation. Given the forces of 30 N and 20 N acting at distances of 5 cm and 457 cm from the axis of rotation, respectively, the torques exerted by these forces are calculated as follows:

For the 30 N force at 5 cm radius:

τ₁ = F₁ × r₁ = 30 N × 5 cm = 150 N⋅cm

For the 20 N force at 457 cm radius:

τ₂ = F₂ × r₂ = 20 N × 457 cm = 9140 N⋅cm

The net torque is the sum of these torques, considering their respective directions. Given the counterclockwise direction of both torques, the net torque is obtained by subtracting the smaller torque from the larger one:

Net Torque = |τ₂ - τ₁| = |9140 N⋅cm - 150 N⋅cm| = 8990 N⋅cm ≈ 610 N⋅cm

The net torque exerted on the disk is 610 N⋅cm in the counterclockwise direction. This indicates the tendency of the combined forces to rotate the disk in a counterclockwise direction about its axis of rotation. Understanding torque and its calculation is crucial in analyzing rotational motion and mechanical systems, as seen in this problem involving forces acting at different radii on a rotating disk.