A boy whose mass is 40kg runs up a flight of 30 steps,each 150mm high,in 6secs.find the average power developed.(take g=10m/s^2.
power is W = J/s = N-m/s
so,
(40*10)*(30*0.15)/6 W
To find the average power developed by the boy, we need to calculate the work done and divide it by the time taken.
1. First, let's calculate the work done by the boy when running up the flight of steps. Work is defined as the force applied multiplied by the distance covered. In this case, the force applied is the weight of the boy, which can be calculated using the formula F = m * g, where m is the mass (40 kg) and g is the acceleration due to gravity (10 m/s^2). Therefore, the weight of the boy is F = 40 kg * 10 m/s^2 = 400 N (Newtons).
2. The distance covered is the height of each step multiplied by the number of steps. In this case, the height of each step is given as 150 mm, which is equivalent to 0.15 m. And the number of steps is 30. Therefore, the total distance covered is 0.15 m * 30 = 4.5 m.
3. Now, we can calculate the work done by multiplying the force applied (weight) by the distance covered. So, the work done is W = F * d = 400 N * 4.5 m = 1800 joules.
4. Next, we need to find the time taken. From the given information, it is mentioned that the boy completes the run in 6 seconds.
5. Now, to find the average power developed, we divide the work done by the time taken. So, the average power is P = W / t = 1800 J / 6 s = 300 watts (W).
Therefore, the average power developed by the boy is 300 watts.