Calculating Belt Power Transmission

This question asks us to determine the amount of power a belt drive system can transmit, given the tensions on both sides of the belt and its running speed. Power transmission in belt drives depends on the net effective pull exerted by the belt and the speed at which it moves.

Understanding the Concepts

• Tight Side Tension ($T_1$): This is the tension in the belt on the side that is being pulled towards the driven pulley.
• Slack Side Tension ($T_2$): This is the tension in the belt on the side that is returning from the driven pulley to the driver pulley. It's typically lower than the tight side tension.
• Belt Speed ($v$): This is the linear velocity of the belt as it moves between the pulleys.
• Net Effective Tension: The difference between the tight side and slack side tensions creates the effective force that drives the pulley.

Formula for Power Transmission

The power transmitted by a belt ($P$) is calculated by multiplying the net effective tension by the belt speed. The formula is:

$$ P = (T_1 - T_2) \times v $$

Where:

• $P$ is the power transmitted (in Watts, W).
• $T_1$ is the tension on the tight side (in Newtons, N).
• $T_2$ is the tension on the slack side (in Newtons, N).
• $v$ is the belt speed (in meters per second, m/s).

Given Data

From the question, we have the following values:

• Tension on the tight side, $T_1 = 25$ N
• Tension on the slack side, $T_2 = 15$ N
• Belt speed, $v = 10$ m/s

Step-by-Step Calculation

First, we calculate the net effective tension in the belt:

$$ \text{Net Effective Tension} = T_1 - T_2 $$

Substituting the given values:

$$ \text{Net Effective Tension} = 25 \text{ N} - 15 \text{ N} = 10 \text{ N} $$

Now, we use this net tension and the belt speed to calculate the power transmitted:

$$ P = (\text{Net Effective Tension}) \times v $$

Substituting the calculated net tension and the given speed:

$$ P = 10 \text{ N} \times 10 \text{ m/s} $$

$$ P = 100 \text{ N} \cdot \text{m/s} $$

Since 1 Newton-meter per second (N·m/s) is equal to 1 Watt (W), the power transmitted is:

$$ P = 100 \text{ W} $$

Conclusion

The calculated power transmitted by the belt is 100 W. This matches one of the provided options.