Belt Drive Power Calculation

In a belt drive mechanism, power is transmitted from one pulley to another due to the difference in tension between the tight side and the slack side of the belt and the velocity of the belt.

The formula for the power transmitted (\(P\)) by a belt drive is given by:

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

where:

• \(T_1\) is the tension in the tight side of the belt.
• \(T_2\) is the tension in the slack side of the belt.
• \(v\) is the velocity of the belt.

Given Values

From the question, we are given the following values:

• Velocity of the belt, \(v = 5 \text{ m/s}\)
• Tension in the tight side, \(T_1 = 2000 \text{ N}\)
• Tension in the slack side, \(T_2 = 1000 \text{ N}\)

Calculating Power Transmitted

Now, we can substitute these values into the power transmission formula:

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

\( P = (2000 \text{ N} - 1000 \text{ N}) \times 5 \text{ m/s} \)

\( P = (1000 \text{ N}) \times 5 \text{ m/s} \)

\( P = 5000 \text{ Nm/s} \)

Since 1 Nm/s is equal to 1 Watt (W), the power transmitted is 5000 W.

To express the power in kilowatts (kW), we divide by 1000:

\( P = \frac{5000 \text{ W}}{1000 \text{ W/kW}} = 5 \text{ kW} \)

Final Power Result

The power transmitted in the belt drive mechanism is 5 kW.

This calculated value matches one of the provided options.