a lift is used to Carry boxes to the top floor of a hotel 20m high.
A total weight of 100kg of boxes was carried up in 20sec .if the useful output of the engine driving the lift mechanism is 1.2kilowatt calculate the efficiency of the lift mechanism.
work output = m g h = 100 * 9.81 * 20 = 19,620 Joules
watts = 19,620 J / 20 s = 981 watts = 0.981 kw
(0.981 / 1.2) * 100 = 81.8 %
To calculate the efficiency of the lift mechanism, we need to find the useful work output and the total work input.
The useful work output can be calculated using the formula:
Useful work output = Power × Time
Given that the useful output of the engine driving the lift mechanism is 1.2 kilowatts (1.2 kW) and the time taken is 20 seconds, we can calculate the useful work output as follows:
Useful work output = 1.2 kW × 20 s
Next, we need to calculate the total work input. The total work input is equal to the work done against gravity, which is the force applied multiplied by the distance moved:
Total work input = Force × Distance
The force applied can be calculated using the formula:
Force = Mass × Acceleration
In this case, the acceleration is due to the force of gravity, which is approximately 9.8 m/s².
Given that the total weight of the boxes is 100 kg, the force applied can be calculated as:
Force = 100 kg × 9.8 m/s²
Finally, we can calculate the total work input by multiplying the force applied by the distance moved. The distance moved is equal to the height the boxes are lifted:
Total work input = Force × Distance
Distance = 20 m (given)
Total work input = force × distance
= (100 kg × 9.8 m/s²) × 20 m
Now we have both the useful work output and the total work input. The efficiency of the lift mechanism can be calculated using the formula:
Efficiency = (Useful work output / Total work input) × 100
Substituting the values, we can calculate the efficiency:
Efficiency = (Useful work output / Total work input) × 100
= (1.2 kW × 20 s) / ((100 kg × 9.8 m/s²) × 20 m) × 100
Simplifying the expression:
Efficiency = (24 kJ) / (19600 J) × 100
Efficiency = 0.1224 × 100
Efficiency = 12.24%
Therefore, the efficiency of the lift mechanism is 12.24%.
To calculate the efficiency of the lift mechanism, we need to find the useful work done by the mechanism and divide it by the total work done.
First, let's calculate the total work done by the lift mechanism. Work is defined as force multiplied by distance. In this case, the force is the weight of the boxes, and the distance is the height of the hotel.
Given:
Height of the hotel, h = 20 m
Weight of the boxes, W = 100 kg
Total time taken, t = 20 s
The work done can be calculated using the formula:
Work = Force x Distance
Work = Weight x Height
Work = W x h
Work = 100 kg x 9.8 m/s^2 x 20 m
Work = 19600 kg m^2/s^2 (or joules)
Next, let's calculate the useful work done by the engine. Given that the useful output of the engine is 1.2 kilowatts (1 kilowatt = 1000 watts) and the time taken is 20 seconds, we can calculate the useful work done.
Useful Work = Useful Power x Time
Useful Work = 1.2 kW x 20 s
Useful Work = 24 kJ (or 24000 Joules)
Finally, we can find the efficiency by dividing the useful work by the total work:
Efficiency = ( Useful Work / Total Work ) x 100
Efficiency = (24 kJ / 19600 kg m^2/s^2) x 100
Efficiency ≈ 0.1224%
Therefore, the efficiency of the lift mechanism is approximately 0.1224%.