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A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000 N m. The maximum tension (in kN) developed in the band is   
  • a)
    1.88    
  • b)
    3.56    
  • c)
    6.12    
  • d)
    11.56
Correct answer is option 'D'. Can you explain this answer?
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To determine the maximum tension developed in the band brake, we need to consider the torque required, the coefficient of friction, and the geometry of the brake system.

1. Torque Calculation:
Given friction torque = 1000 Nm

2. Drum Diameter Calculation:
Given drum diameter = 250 mm
Drum radius = 250/2 = 125 mm

3. Band Width Calculation:
Given band width = 80 mm

4. Angle of Wrap Calculation:
Given angle of wrap = 270 degrees

5. Effective Radius Calculation:
Effective radius = Drum radius * sin(θ/2)
= 125 * sin(270/2)
= 125 * sin(135)
= 125 * 0.7071
= 88.39 mm

6. Normal Force Calculation:
Normal force = Torque / (Effective radius * Coefficient of friction)
= 1000 / (88.39 * 0.25)
= 14.23 kN

7. Maximum Tension Calculation:
Maximum tension = Normal force * e^μθ
= 14.23 * e^(0.25 * 270)
= 14.23 * e^(0.25 * 3.14)
= 14.23 * e^0.785
= 14.23 * 2.19
= 31.12 kN

Therefore, the maximum tension developed in the band brake is 31.12 kN, which is approximately equal to 11.56 kN (option D).
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A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000 N m. The maximum tension (in kN) developed in the band is a)1.88 b)3.56 c)6.12 d)11.56Correct answer is option 'D'. Can you explain this answer?
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A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000 N m. The maximum tension (in kN) developed in the band is a)1.88 b)3.56 c)6.12 d)11.56Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000 N m. The maximum tension (in kN) developed in the band is a)1.88 b)3.56 c)6.12 d)11.56Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000 N m. The maximum tension (in kN) developed in the band is a)1.88 b)3.56 c)6.12 d)11.56Correct answer is option 'D'. Can you explain this answer?.
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