Lecture on Friction and Torque

Example: Bracket on a Pole

• Scenario:
  • A bracket with two rings is attached to a pole.
  • A load is applied to the bracket.
• Objective: Determine the minimum distance (X) from the pole's center where a 100 N load can be applied without the bracket sliding.

Key Concepts

• Torque and Friction:
  • Torque depends on the distance from the load to the point of rotation.
  • More distance increases torque, which increases friction due to higher normal forces on the rings.
• Static Friction:
  • Assumed that nothing slides, using the static coefficient of friction.
  • Friction force (F_f) = Normal force (N) x Coefficient of friction (\mu_s).

Calculations

1. Normal Forces:
   • (F_{fA} = N_A \times \mu_s)
   • (F_{fB} = N_B \times \mu_s)
   • (N_A = N_B) since the sum of forces in the X-direction equals zero.
2. Sum of Forces in Y-Direction:
   • (F_{load} = F_{fA} + F_{fB})
   • (F_{load} = 2 \times N_A \times \mu_s)
   • Given (\mu_s = 0.2), solve for (N_A):
     • (100 N = 2 \times N_A \times 0.2) ➜ (N_A = 250 N)
   • Thus, (N_A = N_B = 250 N).
3. Calculating Moments:
   • Moments about point A must sum to zero:
     • Clockwise moment: (-100 N \times (X - 0.025 m))
     • Counterclockwise moments:
       • (+250 N \times 0.1 m) for normal force at B.
       • (-50 N \times 0.05 m) for friction force at B:
         • (50 N = 250 N \times 0.2)
   • Solve for (X):
     • (0 = 100 N \times X - 2.5 Nm + 25 Nm - 2.5 Nm)
     • (100 N \times X = 25 Nm)
     • (X = 0.25 m = 25 cm)

Conclusion

• The minimum distance (X) to apply a 100 N load without sliding is 25 cm from the center of the pole.
• Closer than 25 cm will not provide enough torque to maintain the static friction required to hold the load.