What is the speed of the belt if the tensions in the tight and slack sides of a belt are 14,000 N and 900 N, with a power transmission of 655 kW?

To determine the speed of the belt in a belt drive system, you can use the formula for power transmission, which is given by:

[ P = (T_{tight} - T_{slack}) \times v ]

Where:

• ( P ) is the power transmitted (in watts),

• ( T_{tight} ) is the tension in the tight side of the belt (in newtons),

• ( T_{slack} ) is the tension in the slack side of the belt (in newtons),

• ( v ) is the speed of the belt (in meters per second).

First, we need to convert the power from kilowatts to watts:

[ 655 , kW = 655,000 , W ]

Next, calculate the difference in tension:

[ T_{tight} - T_{slack} = 14,000 , N - 900 , N = 13,100 , N ]

Now, substitute the values into the power equation:

[ 655,000 , W = 13,100 , N \times v ]

To find ( v ), rearrange the equation:

[ v = \frac{655,