Initial Tension in a Belt

Initial tension is the tension that is applied to the belt before it begins to operate. The purpose of initial tension is to prevent the belt from slipping or losing contact with the pulleys during operation. The initial tension is typically applied by adjusting the position of the idler pulley or by using a tensioning device.

Calculation of Initial Tension

The initial tension in a belt can be calculated using the following formula:

T0 = (T1 + T2)/2 + (μmg)/2

where,
T1 = tight side tension
T2 = slack side tension
μ = coefficient of friction between belt and pulley
m = mass of belt per unit length
g = acceleration due to gravity

Explanation of the Answer

The correct answer is option (a) T0 = (T1 + T2)/2. This formula gives the average tension in the belt between the tight and slack sides. The value of initial tension is important because it affects the power transmission capacity of the belt and the lifespan of the belt. If the initial tension is too low, the belt may slip or lose contact with the pulleys during operation. If the initial tension is too high, it may cause excessive wear on the belt and the pulleys.

It is important to note that the formula for initial tension assumes that the belt is perfectly flat and does not have any curvature or sag between the pulleys. In practice, the belt may have some curvature or sag, which can affect the tension distribution and the power transmission capacity of the belt. Therefore, it is important to design the system with sufficient tension and to periodically check and adjust the tension as needed.