A boy whose mass is 40kg runs up a flight of 30 steps each.150mm,in 6secs find d average power developed (take g
=10m/s sguaree)
m g h / time
40 * 10 * 30 * .15 / 6
in Joules per second or watts
To find the average power developed by the boy while running up the flight of steps, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the boy. The work done is equal to the force applied multiplied by the distance traveled. In this case, the force is equal to the weight of the boy, which can be calculated using the formula:
Weight = mass * gravity
where the mass is given as 40 kg and the acceleration due to gravity, g, is given as 10 m/s². Substituting these values, we get:
Weight = 40 kg * 10 m/s² = 400 N
Now, to calculate the distance traveled, we need to find the total vertical distance covered by the boy when running up the flight of steps. The height of each step is given as 150 mm. Since there are 30 steps, the total vertical distance covered can be calculated as:
Distance = height of each step * number of steps
Distance = 150 mm * 30 = 4500 mm
However, it is more convenient to have the distance in meters. So, we need to convert 4500 mm to meters by dividing it by 1000:
Distance = 4500 mm / 1000 = 4.5 m
Now that we have the force and the distance, we can calculate the work done:
Work = force * distance
Work = 400 N * 4.5 m = 1800 Nm (or Joules)
Finally, we can substitute the value of work and the given time of 6 seconds into the formula for power:
Power = Work / Time
Power = 1800 Nm / 6 s = 300 Watts (or Joules per second)
Therefore, the average power developed by the boy while running up the flight of steps is 300 Watts.