Lecture Notes: Force Analysis on Block and Wedge

Objective

• Determine the force needed to cause a block to slide down a wedge.
• Remove the wedge and calculate the pending downward force required.

Key Concepts

1. Freebody Diagram:

   • Analyze forces acting on the block.
   • Weight of the block acts downward.
   • Friction between the wedge and block causes lateral movement into the wall.
   • Reactionary force is the sum of normal and friction forces.

2. Static Friction Coefficient:

   • Given as 0.35.
   • Influences the reactionary force at an angle of 19.29 degrees.

3. Angles and Force Components:

   • Friction between block and wedge influences the normal force at an 8-degree angle to the vertical.
   • Reaction force makes a 19.29-degree angle with the horizontal.
   • Calculate angles between forces:
     • Angle R1: 11.29 degrees relative to vertical.
     • Angle R2: 90 - 19.29 = 70.71 degrees.
     • Third angle in triangle: 180 - 11.29 - 70.71 = 98 degrees.

Calculations

• Use the Law of Sines to determine values for reactionary forces (R1 and R2).

  • Weight is divided by the sine of 90 degrees (angle directly opposite weight).

  • Equate R1 to the sine of 70.71 degrees and R2 to the sine of 11.29 degrees.

  • Formula:

    [ \frac{\text{Weight}}{\sin(90)} = \frac{R1}{\sin(70.71)} = \frac{R2}{\sin(11.29)} ]

• Results:

  • [ R1 = \text{Weight} \times \frac{\sin(70.71)}{\sin(98)} \approx 0.953 \times \text{Weight} ]
  • [ R2 = \text{Weight} \times \frac{\sin(11.29)}{\sin(98)} \approx 0.198 \times \text{Weight} ]

Next Steps

• These R1 and R2 values are crucial for the next part of the analysis.
• In Part 2, draw a Freebody diagram for the wedge to calculate the force required to pull it out.

Conclusion

• Understanding force components and angles is essential for calculating the necessary forces to initiate movement in mechanical systems.