Question

The value of initial tension in belts is equal to
1. Tension in the tight side of the belt 
2. Tension in the slack side of the belt
3. Sum of the tension in the tight side and slack side of the belt
4. Average tension of the tight side and slack side of the belt 

Answer 1

Correct Answer - Option 4 : Average tension of the tight side and slack side of the belt 

Explanation:

Initial tension (T_o):

When a belt is first fitted to a pair of pulleys, an initial tension T_o is given to the belt when the system is stationary. When transmitting power, the tension on the tight side increases to T₁ and that on the slack side decreases to T₂.

It is assumed that the material of the belt is perfectly elastic, i.e. the strain in the belt is proportional to the stress in it and the total length of the belt remains unchanged. Therefore, the tension on the tight side will increase by the same amount as the tension on the slack side decreases.

Tension on tight side T₁ = T_o + δT

Tension on slack side T₂ = T_o - δT

where T_o is the initial tension and T₁ and T₂ is the tension on the tight and slack side respectively.

Mathematically initial tension is

\(T_o= \frac{{T_1 + T_2 }}{2}\)

Considering centrifugal tension:

\(T_o= \frac{{T_1 + T_2 +2T_c }}{2}\)