# Thread: power, mass, speed, time and height

1. ## power, mass, speed, time and height

A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?

This is one of the first exercises I have had to tackle concerning power, so I'm pretty sure its meant to be simple. However, in terms of power both force x velocity and work/time i have no idea where to start.

Without the child's starting speed, horizontal distance covered or total distance run I'm at a loss for what to use and what to look for...any suggestions would help.

2. ## Re: power, mass, speed, time and height

Originally Posted by furor celtica
A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?

This is one of the first exercises I have had to tackle concerning power, so I'm pretty sure its meant to be simple. However, in terms of power both force x velocity and work/time i have no idea where to start.

Without the child's starting speed, horizontal distance covered or total distance run I'm at a loss for what to use and what to look for...any suggestions would help.
Note that the initial speed is assumed to be zero.

Power = Change in energy per unit time = (PE + KE)/time = 30(9.8*3 + 1/2 *2^2)/6 = 5(29.4 + 2) = 157 W

3. ## Re: power, mass, speed, time and height

then why am i given the height of the flight of steps?

4. ## Re: power, mass, speed, time and height

Originally Posted by furor celtica
then why am i given the height of the flight of steps?
I used the height to find the PE.

5. ## Re: power, mass, speed, time and height

PE and KE being potential and kinetic energy? I'm pretty sure I'm not supposed to be using those in this exercise.
Why don't you just use 0.5m(v^2) - 0.5m(u^2)?

6. ## Re: power, mass, speed, time and height

Originally Posted by furor celtica
PE and KE being potential and kinetic energy?
Yes.

Why don't you just use 0.5m(v^2) - 0.5m(u^2)?
Because the child has potential energy in addition to kinetic energy.

7. ## Re: power, mass, speed, time and height

Hi alexmahone.
Shouldn't the KE power be 60 Watts not 10 Watts

8. ## Re: power, mass, speed, time and height

Originally Posted by bjhopper
Hi alexmahone.
Shouldn't the KE power be 60 Watts not 10 Watts
I have got KE = 30*1/2*2^2 = 60 J

9. ## Re: power, mass, speed, time and height

So why was your total power 157 Watts not 207 Watts

10. ## Re: power, mass, speed, time and height

Originally Posted by bjhopper
So why was your total power 157 Watts not 207 Watts
Why should it be 207 W?

11. ## Re: power, mass, speed, time and height

It' the sum of the power of the PE/6 + KE/1 = 147 +60 Watts

12. ## Re: power, mass, speed, time and height

Originally Posted by bjhopper
It' the sum of the power of the PE/6 + KE/1 = 147 +60 Watts
You need to divide the KE by 6 as well.

13. ## Re: power, mass, speed, time and height

Originally Posted by furor celtica
A child of mass 30 kg runs up a flight of stairs in 6 seconds. The top of the flight is 3 metres above the bottom, and at the top he is running at 2ms^-1. What average power does he need to produce?
$\displaystyle P_{avg} = \frac{total \, work}{total \, time}$

$\displaystyle P_{avg} = \frac{\Delta PE_g + \Delta KE}{total \, time}$

$\displaystyle P_{avg} = \frac{mg(h_f-h_0) + \frac{1}{2}m(v_f^2 - v_0^2)}{total \, time}$

$\displaystyle P_{avg} = \frac{30g(3) + 15(4)}{6} = 157 \, J/s$