A pupil of mass 50kg runs a flight of 20 stairs each 25cm high in a time of 20 seconds,[Take g=10/kg ] calculate the pupil's gain in potential energy and the useful power developed by the pupil in climbing the stairs.
20 * 0.25 = 20/4 = 5 meters up
gain in PE = m g h = 50 * 10 * 5 = 2500 Joules
power = energy/time = 2500 Joules / 20 seconds = 250/2 = 125 watts
Well, well, well, it seems we have a budding stair-climbing champion here! Let's get calculating, shall we?
First, let's find the pupil's gain in potential energy. The potential energy is given by the formula E = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the stairs.
Since we have the mass (m = 50 kg), the height of each stair (h = 0.25 m), and the acceleration due to gravity (g = 10 m/s²), we can plug in the values and calculate:
E = 50 kg * 10 m/s² * 0.25 m
E = 125 Joules
So the pupil's gain in potential energy is 125 Joules. Now, onto the useful power developed by the pupil.
Power is defined as the rate at which work is done or energy is transferred. In this case, the useful power developed by the pupil will be the potential energy gained divided by the time taken:
Power = Energy / Time
Power = 125 J / 20 s
Power = 6.25 Watts
Voila! The pupil's gain in potential energy is 125 Joules, and the useful power developed is 6.25 Watts. Keep climbing those stairs and developing your superpowers, my stair-scaling friend!
To calculate the pupil's gain in potential energy, we need to determine the change in height and multiply it by the pupil's mass and the acceleration due to gravity.
The change in height can be calculated by multiplying the height of each step (25 cm) by the number of steps (20). Converting 25 cm to meters gives us 0.25 m, so the total change in height is 0.25 m * 20 = 5 meters.
Thus, the gain in potential energy can be calculated as follows:
Potential energy = mass * gravity * height
= 50 kg * 10 m/s^2 * 5 m
= 2500 J (joules)
Now let's calculate the useful power developed by the pupil in climbing the stairs. Power is the rate at which work is done, and in this case, the work done is the gain in potential energy.
Power = Work / time
= Potential energy / time
= 2500 J / 20 s
= 125 W (watts)
Therefore, the pupil's gain in potential energy is 2500 joules, and the useful power developed by the pupil in climbing the stairs is 125 watts.
To calculate the pupil's gain in potential energy, we can use the formula:
Potential Energy = Mass * Gravitational Acceleration * Height
Here, the mass of the pupil is given as 50 kg, the height of each stair is 25 cm, and the gravitational acceleration is given as g = 10 m/s^2.
First, we need to convert the height of each stair from centimeters to meters:
Height = 25 cm = 25/100 = 0.25 m
Now, we can calculate the potential energy:
Potential Energy = 50 kg * 10 m/s^2 * 0.25 m
Potential Energy = 125 Joules
Therefore, the pupil's gain in potential energy while climbing the stairs is 125 Joules.
To calculate the useful power developed by the pupil, we can use the formula:
Useful Power = Work Done / Time
Here, the work done is equal to the change in potential energy, which is given by the formula:
Work Done = Potential Energy Final - Potential Energy Initial
Since the initial potential energy is zero (at the bottom of the stairs) and the final potential energy is 125 Joules (at the top of the stairs), the work done can be calculated as:
Work Done = 125 Joules - 0 Joules
Work Done = 125 Joules
Now, we can calculate the useful power:
Useful Power = 125 Joules / 20 seconds
Useful Power = 6.25 Watts
Therefore, the pupil has developed a useful power of 6.25 Watts while climbing the stairs.