a girl whose mass is 40kg walk up a fight of steps each 150mm height in second find the average power developed (g=10m/5'2
no answer
no seconds...
p =work / time
p= fxs
p = mgh / t
given that mass= 40kg
height= 150mm × 20 = 300
gram= 10m/s
work done = mgh
40 × 300× 10
=120000
power= w/t
=120000/10
= 12000w
To find the average power developed, we need to use the formula:
Average power (P) = Work done (W) ÷ Time taken (t)
To calculate the work done, we need to determine the change in potential energy as the girl walks up the flight of steps. This can be found using the formula:
Potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
Given:
Mass of the girl (m) = 40 kg
Height of each step (h) = 150 mm = 0.15 m
Acceleration due to gravity (g) = 10 m/s²
First, let's calculate the potential energy for each step:
PE = m × g × h
PE = 40 kg × 10 m/s² × 0.15 m
PE = 60 J (joules)
As the girl climbs the entire flight of steps, she will go through multiple steps. For simplicity, let's assume the flight of steps consists of 10 steps.
Total work done (W) = PE × Number of steps
W = 60 J × 10
W = 600 J
We also need to find the time taken to climb the steps. The question states that she climbs the steps in a second.
Time taken (t) = 1 second
Now, we can calculate the average power developed:
Average power (P) = Work done (W) ÷ Time taken (t)
P = 600 J ÷ 1 s
P = 600 W (Watt)
Therefore, the average power developed by the girl while climbing the flight of steps is 600 Watts.