Belt Effective Driving Force Calculation

In a belt drive system, power is transmitted due to the difference in tension between the tight side and the slack side of the belt. This difference in tension creates the effective driving force that acts at the circumference of the pulley, causing it to rotate.

The tension on the tight side (where the belt pulls) is greater than the tension on the slack side (where the belt returns). The effective driving force is the net pull exerted by the belt on the pulley.

The formula for the effective driving force (${F_{effective}}$) is given by the difference between the tension in the tight side (${T_1}$) and the tension in the slack side (${T_2}$).

Mathematically, this is expressed as:

$$\text{Effective Driving Force} = \text{Tension on Tight Side} - \text{Tension on Slack Side}$$ $$F_{effective} = T_1 - T_2$$

From the question, we are given the following values:

• Tension in tight side, $T_1 = 3000 \, \text{N}$
• Tension in slack side, $T_2 = 1500 \, \text{N}$

Now, we can calculate the effective driving force using the formula:

$$F_{effective} = T_1 - T_2$$ $$F_{effective} = 3000 \, \text{N} - 1500 \, \text{N}$$ $$F_{effective} = 1500 \, \text{N}$$

Therefore, the effective driving force at the circumference of the driven pulley is 1500 N.

This force is what determines the torque transmitted by the pulley, which in turn relates to the power transmitted by the belt drive.