List five minerals and five nutritional compositions for plant and animal materials. Define angle of repose and coefficient of static friction, and explain their relevance in machine design.

Here's the solution for Question 3:

3(a) Five Minerals and Five Nutritional Compositions

Plant Materials:

• Minerals:
  1. Calcium (Ca)
  2. Potassium (K)
  3. Magnesium (Mg)
  4. Iron (Fe)
  5. Phosphorus (P)
• Nutritional Compositions:
  1. Carbohydrates
  2. Proteins
  3. Fats/Lipids
  4. Vitamins
  5. Fiber

Animal Materials:

• Minerals:
  1. Calcium (Ca)
  2. Phosphorus (P)
  3. Sodium (Na)
  4. Potassium (K)
  5. Iron (Fe)
• Nutritional Compositions:
  1. Proteins
  2. Fats/Lipids
  3. Vitamins
  4. Minerals
  5. Water

3(b) Angle of Repose and Coefficient of Static Friction

The angle of repose ($\phi$) is the steepest angle at which a granular material can be piled without slumping. It reflects the internal friction and interlocking of particles. The coefficient of static friction ($\mu_s$) is the ratio of the maximum static friction force to the normal force, indicating the resistance to initial motion between a material and a surface.

In machine design, the angle of repose is critical for designing storage structures like hoppers and silos to ensure materials flow out smoothly without bridging or blockages. The coefficient of static friction is used to design conveyors, chutes, and processing equipment to ensure materials slide or grip appropriately, preventing jams or slippage. Both properties are essential for efficient material handling and equipment performance.

3(c) Angle of Repose of Prosopis africana seeds