Belts: belt speed for maximum power transmission Assume a flat belt with maximum permissible belt tension T and belt mass per unit length m. Find the belt speed condition that maximizes power transmitted. Choose the correct expression.
Mechanical Engineering
Machine Design
Difficulty: Medium
Choose an option
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Av = √(T/m)
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Bv = √(3T/m)
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Cv = √(T/2m)
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Dv = √(T/3m)
Answer
Correct Answer: v = √(T/3m)
Explanation
Given/Notation
- T = maximum permissible belt tension (N)
- m = mass per unit length of belt (kg/m)
- v = belt speed (m/s)
ApproachPower P = (T1 − T2)·v. With centrifugal tension Tc = m v² acting, the available tight-side tension is limited by T = T1 + Tc. Maximizing P with respect to v leads to the classical condition Tc = T/3.
Step-by-step outlineLet Tc = m v².At optimum, Tc = T/3 ⇒ m v² = T/3.⇒ v = √(T/(3m)).
VerificationThis condition is standard: at maximum power, centrifugal tension equals one-third of the maximum allowable belt tension.
Common pitfallUsing √(T/m) or √(T/2m); those ignore the power optimum and set centrifugal tension too high.
Final Answerv = √(T/3m)