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?

Work output = 250*g*2.4 = 5880 joules

(g=9.8)

Work input = 450*45 = 20,250 joules

For the efficiency, take the output/input ratio

To calculate the efficiency of the motorized conveyor system, we need to first determine the work done by the motor.

The work done (W) can be calculated using the formula:
W = force × distance.

The force required to lift the containers can be found using the formula:
force = mass × gravity.

Given:
Mass of each container (m) = 1 kg.
Number of containers (n) = 250.
Vertical distance (d) = 2.4 m.
Acceleration due to gravity (g) = 9.8 m/s^2.

Let's calculate the force required to lift the containers:
force = m × g
= 1 kg × 9.8 m/s^2
= 9.8 N.

Now, we can calculate the work done by the motor:
W = force × distance
= 9.8 N × 2.4 m
= 23.52 Joules.

The efficiency of a motorized system is given by the equation:
Efficiency = (useful output energy / input energy) × 100%.

Since the motor's input energy is given by the power (P) and time (t), we can calculate it using the formula:
Input energy = P × t.

Given:
Power of the motor (P) = 450 W.
Time (t) = 45 s.

Now, let's calculate the input energy:
Input energy = P × t
= 450 W × 45 s
= 20250 Joules.

Finally, we can calculate the efficiency of the motorized conveyor system:
Efficiency = (useful output energy / input energy) × 100%
= (23.52 J / 20250 J) × 100%
≈ 0.116% (rounded to three decimal places).

Therefore, the efficiency of the motorized conveyor system is approximately 0.116%.

To calculate the efficiency of the motorized conveyor system, we need to know the input power and the output power.

First, let's calculate the input power, which is the power provided to the system. In this case, the input power can be calculated using the formula:

Input Power = Voltage × Current

Since the question does not provide information about the voltage or current, we can assume it to be given in terms of power directly. Here, the power is given as 450 W, which is the input power.

Next, let's calculate the output power, which is the power used to lift the containers. Power is equal to work done divided by time taken. The work done is given by the formula:

Work Done = Force × Distance

The force applied to lift the containers can be calculated using the formula:

Force = Mass × Acceleration

Acceleration here will be the acceleration due to gravity, which is approximately 9.8 m/s^2.

Given that the mass of each container is 1 kg, the force applied will be:

Force = 1 kg × 9.8 m/s^2 = 9.8 N

Now, let's calculate the work done:

Work Done = Force × Distance = 9.8 N × 2.4 m = 23.52 Nm

Finally, let's calculate the output power:

Output Power = Work Done / Time Taken = 23.52 Nm / 45 s = 0.52 W

Now that we have both the input power (450 W) and the output power (0.52 W), we can calculate the efficiency of the motorized conveyor system. Efficiency is defined as the ratio of output power to input power.

Efficiency = (Output Power / Input Power) × 100

Efficiency = (0.52 W / 450 W) × 100 = 0.1156 %

Therefore, the efficiency of the motorized conveyor system is approximately 0.1156%.