Define limiting friction and draw free body diagrams for a system with a 20 kg trolley on a surface with rolling friction and a 3 kg hanging block.

Here are the solutions for questions 12.a and 12.b:

12.a) Limiting friction is the maximum static friction that can be exerted between two surfaces before one surface begins to slide over the other. It is the maximum force that opposes the initiation of motion.

12.b)
Free Body Diagrams (FBDs):

• For the 20 kg trolley (W):

  • Weight ($W_T$): Acts vertically downwards. $W_T = M g = 20 \text{ kg} \times 10 \text{ m/s}^2 = 200 \text{ N}$.
  • Normal Force ($N$): Acts vertically upwards, perpendicular to the surface. $N = W_T = 200 \text{ N}$.
  • Tension ($T$): Acts horizontally to the right, due to the string.
  • Rolling Friction ($f_r$): Acts horizontally to the left, opposing the motion. $f_r = \mu_r N$.

• For the 3 kg hanging block:

  • Weight ($W_B$): Acts vertically downwards. $W_B = m g = 3 \text{ kg} \times 10 \text{ m/s}^2 = 30 \text{ N}$.
  • Tension ($T$): Acts vertically upwards, due to the string.

Acceleration of the system: