container factory uses a 450 W motor to operate a conveyor belt that lifts containers from one
floor to another. To lift 250 1-kg containers a vertical distance of 2.4 m, the motor runs for 45 s.
What is the efficiency of the motorized conveyor system?
energy output= 250g*2.4
energy input= 450*45s
efficiency= output/input
To calculate the efficiency of the motorized conveyor system, we need to find both the useful work done and the total work done.
First, let's calculate the useful work done:
Useful work = Force × Distance
The force required to lift the containers can be calculated using the equation:
Force = mass × gravity
where mass is the total mass of the containers (250 containers × 1 kg/container) and gravity is the acceleration due to gravity (approximately 9.8 m/s²).
Force = 250 kg × 9.8 m/s²
Next, we calculate the actual distance lifted by multiplying the vertical distance (2.4 m) by the total mass (250 kg).
Distance = 2.4 m × 250 kg
Now, we can calculate the useful work done:
Useful work = Force × Distance
Next, let's calculate the total work done:
Total work = Power × Time
The power of the motor can be calculated using the equation:
Power = Work / Time
Power = Total work / Time
Since we know the motor runs for 45 seconds and has a power of 450 W, we can substitute these values into the equation to find the total work done.
Total work = Power × Time = 450 W × 45 s
Finally, we can calculate the efficiency using the formula:
Efficiency = (Useful work / Total work) × 100
Substituting the values we calculated earlier, we can find the efficiency of the motorized conveyor system.