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.

Given/Notation

• T = maximum permissible belt tension (N)
• m = mass per unit length of belt (kg/m)
• v = belt speed (m/s)

Approach
Power P = (T₁ − T₂)·v. With centrifugal tension T_c = m v² acting, the available tight-side tension is limited by T = T₁ + T_c. Maximizing P with respect to v leads to the classical condition T_c = T/3.

Step-by-step outline
Let T_c = m v².At optimum, T_c = T/3 ⇒ m v² = T/3.⇒ v = √(T/(3m)).

Verification
This condition is standard: at maximum power, centrifugal tension equals one-third of the maximum allowable belt tension.

Common pitfall
Using √(T/m) or √(T/2m); those ignore the power optimum and set centrifugal tension too high.

Final Answer
v = √(T/3m)