A body whose mass is 40kg runs up a flight of 30steps each 150mm high in 6seconds find the average power developed (take g=10m./5)
where did the 9.8 come from
power = work/time = force*distance/time
= (40*9.8N)*(30*0.150m)/6s = 1764/6 N-m/s = 294W
To find the average power developed, we can use the formula:
Power = Work/Time
First, we need to calculate the work done by the body. The work done is equal to the change in potential energy.
Change in potential energy = mass * gravity * height
Given:
mass (m) = 40 kg
gravity (g) = 10 m/s^2
height (h) = 150 mm = 0.15 m
Change in potential energy = mass * gravity * height
= 40 kg * 10 m/s^2 * 0.15 m
= 60 J
Next, we need to calculate the time taken to complete the work.
Given:
time (t) = 6 seconds
Now, we can calculate the average power developed.
Average power = work / time
= 60 J / 6 s
= 10 W
Therefore, the average power developed is 10 Watts.
To find the average power developed, we need to calculate the work done first. The work done is given by the product of force and distance.
The force required to move the body up the flight of steps is equal to the weight of the body. The weight is given by the formula: weight = mass * acceleration due to gravity.
Given:
Mass (m) = 40 kg
Acceleration due to gravity (g) = 10 m/s^2
Weight = m * g = 40 kg * 10 m/s^2 = 400 N
Now, let's calculate the distance traveled. Each step has a height of 150 mm, which is equal to 0.15 meters. The total distance traveled is obtained by multiplying the height of each step with the total number of steps.
Given:
Number of steps (n) = 30
Height of each step (h) = 0.15 meters
Distance (d) = n * h = 30 * 0.15 meters = 4.5 meters
Next, we need to calculate the time taken to climb the steps.
Given:
Time (t) = 6 seconds
Now, we can calculate the average power using the formula: power = work done / time.
The work done is given by the product of force and distance. So,
Work done (W) = force * distance
Substituting the values,
W = 400 N * 4.5 m = 1800 N·m
Now, we can calculate the average power:
Power = Work done / Time = W / t
Substituting the values,
Power = 1800 N·m / 6 s = 300 Watts
Therefore, the average power developed is 300 Watts.