A girl of mass 60kg runs up a flight of 20 steps each of 0.5m high in 10sec.find the average power developed (g=10m/s^2
To find the average power developed by the girl, we can use the formula:
Average Power = Work / Time
First, let's find the work done by the girl. The work done to climb a step can be calculated as the product of the force applied and the distance moved. In this case, the force applied is equal to the weight of the girl, which can be calculated as:
Force = mass * acceleration due to gravity
Force = 60kg * 10m/s^2
Force = 600N
The distance moved when climbing one step is given as 0.5m. Therefore, the work done to climb one step is:
Work = Force * Distance
Work = 600N * 0.5m
Work = 300 Joules
Next, we need to find the total work done by the girl to climb up all the steps. Since there are 20 steps, the total work done can be calculated as:
Total Work = Work per Step * Number of Steps
Total Work = 300 Joules * 20
Total Work = 6000 Joules
Finally, we can calculate the average power developed by the girl using the given time of 10 seconds:
Average Power = Total Work / Time
Average Power = 6000 Joules / 10 seconds
Average Power = 600 Watts
Therefore, the average power developed by the girl is 600 Watts.
A body of mass of 10kg is acted upon by a constant force of 30N for 2sec.calculate the kinetic energy gained by the body
To calculate the kinetic energy gained by the body, we can use the formula:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's find the acceleration of the body using the given force and mass. According to Newton's second law:
Force = mass * acceleration
Rearranging the formula, we can solve for acceleration:
acceleration = Force / mass
acceleration = 30N / 10kg
acceleration = 3 m/s^2
Next, let's calculate the final velocity of the body using the formula:
velocity = initial velocity + acceleration * time
Since the initial velocity is 0 (assuming the body starts from rest), the equation simplifies to:
velocity = acceleration * time
velocity = 3 m/s^2 * 2 sec
velocity = 6 m/s
Now, we can calculate the kinetic energy gained by the body using the formula mentioned earlier:
Kinetic Energy = 1/2 * mass * velocity^2
Kinetic Energy = 1/2 * 10kg * (6m/s)^2
Kinetic Energy = 1/2 * 10kg * 36 m^2/s^2
Kinetic Energy = 180 Joules
Therefore, the kinetic energy gained by the body is 180 Joules.
To find the average power developed by the girl, we can use the formula:
Power = Work / Time
First, we need to calculate the work done. The work done is equal to the force applied multiplied by the distance covered. In this case, the force applied is the girl's weight, which is equal to her mass multiplied by the acceleration due to gravity (g=10m/s^2).
Work = Force * Distance
The distance covered is equal to the height of each step (0.5m) multiplied by the number of steps (20).
Distance = Height * Number of Steps
Now we can calculate the work done:
Distance = 0.5m * 20 = 10m
Work = Force * Distance
Work = (mass * g) * Distance
Work = 60kg * 10m/s^2 * 10m
Work = 6000 Joules
Next, we can substitute the value of work into the power formula:
Power = Work / Time
Power = 6000 J / 10 s
Power = 600 Watts
Therefore, the average power developed by the girl is 600 Watts.