To find the power transmitted by the belt, we can use the formula:
Power = (Tension × Velocity) / 1000
First, let's calculate the velocity of the belt running over the pulley. The circumference of the pulley is given by:
Circumference = π × diameter
Circumference = π × 120 cm
Circumference ≈ 376.99 cm
The distance traveled by the belt in one revolution is equal to the circumference of the pulley. Since the pulley is rotating at 200 revolutions per minute (r.p.m), the belt's velocity can be calculated as:
Velocity = Circumference × r.p.m
Velocity = 376.99 cm/rev × 200 rev/min
Velocity ≈ 75,398 cm/min
Next, we need to convert the velocity to meters per second (m/s) because the tension is given in Newtons (N) and power is typically measured in watts (W). There are 100 centimeters in a meter and 60 seconds in a minute, so:
Velocity = (75,398 cm/min) × (1 m/100 cm) × (1 min/60 s)
Velocity ≈ 12.57 m/s
Now we can calculate the power transmitted by the belt using the given maximum tension:
Power = (3000 N × 12.57 m/s) / 1000
Power ≈ 37.71 W
Therefore, the power transmitted by the belt is approximately 37.71 watts.
