An elevator carries 10 people of average mass 70kg each to a height of 5 meters in 2 minutes. What is the power generated by the elevator
Well, let's break it down, shall we? Elevators are like little weightlifting champions, carrying people and their weight up. So, to calculate the power generated by the elevator, we need to consider the work done and the time it takes.
The work done by the elevator can be calculated using the formula: work = force × distance. In this case, the force is the combined weight of the people in the elevator, which is 10 people × 70 kg = 700 kg. The distance traveled is 5 meters.
So the work done is: work = 700 kg × 5 m = 3500 kg·m.
Now, we need to consider the time it takes. The time given is 2 minutes, but we should convert it to seconds for our calculations. 2 minutes × 60 = 120 seconds.
So, the power generated by the elevator is: power = work / time = 3500 kg·m / 120 s = 29.17 kg·m/s.
Now, I have to clown around a bit here. Why is the power generated by the elevator always positive? Well, because elevators are always lifting people up, not them bringing people down! That's the power of elevators – they always stay positive!
To calculate the power generated by the elevator, we need to use the formula:
Power = Work / Time
First, let's calculate the work done by the elevator. The work done is equal to the force applied (mass multiplied by gravity) multiplied by the distance traveled.
Force = mass * gravity
mass = 10 people * 70 kg/person
= 700 kg
gravity = 9.8 m/s^2 (approximation)
Force = 700 kg * 9.8 m/s^2
= 6860 N
Distance = 5 meters
Work = Force * Distance
= 6860 N * 5 m
= 34300 J
Next, let's calculate the time taken:
Time = 2 minutes = 2 * 60 seconds
= 120 seconds
Now, we can substitute the values into the power formula:
Power = Work / Time
= 34300 J / 120 s
≈ 285.8 watts
Therefore, the power generated by the elevator is approximately 285.8 watts.