An elevator can lifts 10 people up 12 floors. Each person weighs approximately 60 kg. each floor is 3m high, and it takes 15s to reach the 12th floor from the ground floor without stopping. How much work does the elevator do? How much power does the elavator use?
W=60kg*9.8m/s= 5880kg.m/s*36m
W= 211,680 kg.m/s
P=W/t
P= 211,680kg.m/s / 15s
P= 14,112kg.m/s
To calculate the work done by the elevator, we need to determine the total weight it lifts and the vertical distance it covers.
Firstly, let's calculate the total weight lifted:
Each person weighs approximately 60 kg, and the elevator can lift 10 people. Therefore, the total weight lifted is 60 kg/person * 10 people = 600 kg.
Secondly, let's calculate the total distance traveled:
Each floor is 3m high, and the elevator travels from the ground floor (floor 1) to the 12th floor. Therefore, the total distance traveled is 3m/floor * 12 floors = 36m.
Now, we can calculate the work done by the elevator using the formula:
Work = Force * Distance
Since weight is the force acting against gravity, we can use the weight lifted as the force:
Work = Weight * Distance
Work = 600 kg * 9.8 m/s^2 * 36m
Work = 211,680 Joules
Now, let's move on to calculating the power used by the elevator.
Power is the rate at which work is done. We can use the time taken by the elevator to travel from the ground floor to the 12th floor to determine the power.
Power = Work / Time
Given that the time taken is 15s, we can calculate the power:
Power = 211,680 Joules / 15s
Power = 14,112 Watts
So, the elevator does 211,680 Joules of work and uses 14,112 Watts of power.
work = force * distance, so assuming European conventions, where the ground floor is floor zero,
work = 60*9.8*10 * 3*12 Joules
power = work/time, so
p = work/12 Watts