Lecture on Calculating Forces on a Wedge

Overview

• Goal: Determine the force needed to pull a wedge out.
• Previous Context: In Part 1, forces on the block were analyzed.
• Current Focus: Forces on the wedge and associated calculations.

Forces Acting on the Wedge

• Forces include:
  • Friction on the top and bottom surfaces.
  • Reactionary forces: Vector sum of normal and friction forces.
• Direction
  • Friction force direction: Opposing the motion of pulling out.
  • Normal force: Perpendicular to the inclined surface.
  • Reactionary force (R1): Sum of normal and friction forces.

Equilibrium Condition

• Pending Motion: Static state, forces sum to zero.
• Force Vectors: Need to determine angles between force vectors.

Calculating Angles

• Coefficient of Static Friction: 0.35.
• Angle Calculation:
  • Angle between reactionary force (R1) and normal = 19.29°.
  • Adjust for incline angle (8°) for vertical reference.
  • Resulting angles:
    • Angle with vertical = 11.29°.
    • Complementary angle: 78.71° (90° - 11.29°).

Finding Other Angles

• Angle R3 with Vertical:
  • 90° - 19.29° = 70.71°.
• Third Angle:
  • 180° - (78.71° + 70.71°) = 30.58°.

Using the Law of Sines

• Objective: Find R3 and Force F.
• Formulae:
  • ( F / \sin(30.58°) = R1 / \sin(70.71°) = R3 / \sin(78.71°) )
• Calculation Results:
  • ( R3 = 1.039 R1 )
    • R1 = 0.953 Weight (W)
    • ( R3 = 0.99 W )
  • Force (F):
    • ( F = 0.539 R1 )
    • ( F = 0.51 W )

Conclusion

• Force to Pull Wedge Out: Approximately 51% of the block's weight.
• Comparison: More force was needed to push the wedge in than to pull it out.
• Insight: Demonstrates calculation approach for static equilibrium and vector forces.