A man of mass 2000g climbs a flight of stairs of 20 steps, covering a distance of 560mm in 1 hour. Calculate the power expended by the man. Take gravity as 10m/s²
First, we need to convert the mass of the man from grams to kilograms:
2000g / 1000 = <<2000/1000=2>>2 kg
Next, we need to convert the distance covered from millimeters to meters:
560mm / 1000 = 0.56 m
We're given that the time taken is 1 hour, or 3600 seconds.
The work done by the man is given by the formula:
work = force * distance
The force exerted by the man is equal to the weight, calculated as:
weight = mass * gravity
weight = 2 kg * 10 m/s² = 20 N
The work done by the man is:
work = 20 N * 0.56 m = 11.2 J
Finally, we can calculate the power expended by the man using the formula:
power = work / time
power = 11.2 J / 3600 s = 0.00311 W
Therefore, the power expended by the man is approximately 0.00311 watts.
To calculate the power expended by the man, we need to use the formula:
Power = Work / Time
First, let's calculate the work done by the man. The work done is equal to the force applied multiplied by the distance covered. The force applied can be calculated using the man's mass and gravity:
Force = mass * gravity
Force = 2000g * 10
Note: We need to convert the mass from grams to kilograms.
Force = 2000 * (10/1000) (1 gram = 1/1000 kilogram)
Force = 20 kg
Next, let's calculate the distance covered in meters. We have the distance in millimeters, so we need to convert it.
Distance = 560mm
Distance = 560 / 1000 (1 meter = 1000 millimeters)
Distance = 0.56 meters
Now, let's calculate the work done:
Work = Force * Distance
Work = 20 * 0.56
Work = 11.2 joules
Finally, let's calculate the power using the given time:
Time = 1 hour = 3600 seconds
Power = Work / Time
Power = 11.2 / 3600
Power ≈ 0.0031 watts
Therefore, the power expended by the man is approximately 0.0031 watts.