Question 4

An off-grid hybrid cargo hoist system at a mountain mining site uses a heavy flywheel to store energy and haul a loaded cargo skip up an incline.

The total mass of the loaded cargo skip is $8.50 \times 10^3 \text{ kg}$ .
The incline of the cable track is constant at $12.0∘12.0^\circ$ to the horizontal, and the length of the incline is $\text{ m}$ .
The total resistive force (friction and cable drag) opposing the motion is constant at $\text{ kN}$ .
The hoist's flywheel has a moment of inertia of $\text{ kg m}^2$ .

Calculate the minimum angular speed of the flywheel at the start of the ascent so that the skip can complete the climb using only the energy stored in the flywheel. (Use $\text{ m s}^{-2}$ )

When returning empty skips back down the incline, the hoist system operates in reverse. Suggest two advantages of keeping the flywheel connected to the cable drum during this downhill descent.

The mining company plans to upgrade the system to support longer, steeper tracks. To do this, the flywheel system must be modified to store significantly more energy. Discuss design features of the flywheel that would maximize its energy storage capacity without increasing the overall mass of the hoist assembly.