Calculating Force to Lift with Wedge

Aug 20, 2024

Lecture Notes: Calculating Force to Lift a Block Using a Wedge

Introduction

  • Topic: Determining the force required to lift an object using a wedge.
  • Focus: Calculating the minimum force needed to initiate movement (pending motion).

Key Concepts

  • Reactionary Forces: R1 and R2 are reactionary forces, calculated as the vector sum of normal and friction forces.
  • Friction: Coefficient of static friction is 0.35, and it influences the angle between reactionary and normal force.

Calculations Overview

  1. Forces on the Block:

    • Previously calculated forces acting on the block.
    • Found reactionary forces in terms of the block's weight.
    • Angle due to friction calculated as 19.2°.

  2. Forces on the Wedge:

    • Force applied to the wedge, reaction at the bottom (floor) and top (block-wedge interface).
    • R2 at the block's bottom equals R2 at the wedge's top (equal and opposite forces).

Diagram and Vector Analysis

  • Vector sum of forces should equal zero.
  • Angles: Crucial for calculating unknown forces.
    • R3 makes an angle of 19.2° relative to the vertical.
    • Complementary angles calculated:
      • 71° (90° - 19.2°)
      • 62.71° (90° - sum of two angles)
      • 46.58° (180° - sum of other two angles)

Applying the Law of Sines

  • Objective: Find F (force to drive wedge) and R3.
  • Equations:
    • ( F / \sin(46.58°) = R2 / \sin(7.71°) = R3 / \sin(62.71°) )
    • R3: Calculated using ratio of sines.
    • Force F: Calculated using known values of R2.

Results

  • R3:
    • ( R3 = 0.942 \times 1373 \times \text{Weight of Block} \approx 1.29 \times \text{Weight of Block} )
  • Force F:
    • ( F = 0.770 \times 1373 \times \text{Weight of Block} \approx 1.06 \times \text{Weight of Block} )

Conclusion

  • The force required to lift the block is slightly more than its weight due to the high coefficient of static friction.
  • Importance of understanding vector forces and angles in solving mechanics problems.
  • The explanation was split into two parts due to space constraints, emphasizing the need for detailed breakdowns in complex problems.