Lecture on Belt Drive System

Key Components

• Pulley A and Pulley B: Pulley B drives Pulley A.
• Drive Belt: Tension is applied by Pulley D turning.

Tension and Forces

• Maximum Tension (T2): 800 Newtons. This is the limit to avoid breaking the belt.
• Objective: Calculate the maximum moment applicable on Pulley A.

Calculating Tension

• Tension Equation:
  • ( \frac{T2}{T1} = e^{\mu \theta} )
  • Given: Coefficient of static friction (( \mu )).
  • Angle of contact (( \theta )) needs to be calculated

Angle of Contact Calculation

• Angle Details:
  • Each angle with the horizontal is 20 degrees.
  • Angle of contact ( \beta ) on Pulley B is 180 degrees (half a turn) minus 2 times 20 degrees = 140 degrees.
  • Convert degrees to radians using ( \pi/180 ).

Calculate T1

• Formula: ( T1 = \frac{T2}{e^{\mu \beta}} )
• Calculation:
  • ( T1 = \frac{800}{e^{0.3 \times 140 \times \frac{\pi}{180}}} )
  • Calculated ( T1 = 384 ) Newtons.

Maximum Moment Calculation on Pulley A

• Net Tension: ( 800 - 384 = 416 ) Newtons.
• Moment Arm: Radius of Pulley = 15 cm = 0.15 meters.
• Moment on A:
  • ( 416 \times 0.15 )
  • Result: 62.4 Newton-meters.

Summary

• Pulley B induces tension on the belt.
• The angle of contact and the coefficient of static friction are used to find the tension ( T1 ).
• Calculate the moment by finding the net tension difference and multiplying by the moment arm.
• Key takeaway is understanding how tension and angles affect the belt drive system's ability to transfer force effectively.

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These notes provide an overview of the calculations necessary to determine the maximum moment on Pulley A in a belt drive system, taking into account the frictional forces and the geometry of the system.