Water slide energy dissipation problem

[psruler]

Can anyone help me get started with this problem:

A 50kg man at a water park shows off by going down a long, winding waterslide of varying slope. THe slide is a total of 25m tall from start to finish, and the man starts from rest. DEspite all the attempts to minimize friction with rushing water, there remains some friction between the man and the slide. If he shoots out of the end of the slide at only 8.0m/s instead of the speed you found in part (a) how many joules of energy were dissipated by friction on his way down? what percentage of his initial total energy does this represent?

THANKS!

 

[Guybrush Threepwood]

At the end of the slide the potential energy equals the kinstic energy of the man plus the lost energy due to friction.

You can find out the kinetic energy because you know the man's wight and final speed. And also the potential energy because you know the height from which he started.
I suppose you solved point (a) already

 

[psruler]

Hi Guybrush Threepwood,
Ok for part (a) i got 22.1 m/s for the final speed when he reaches the end of the slide. I don't know if that is correct and i used this formula: v=2gh^1/2. Also, friction is neglected at this part.

the second question is asking how many joules of energy were dissipated by friction and i got, 12050J. I used this equation to get that answer, mgh = 1/2mv^2 + Fd, where F is the friction force. Is that right and how do i figure the percentage of his initial total energy?

thanks!

 

[Guybrush Threepwood]

well I got :
mgh = 50*9.81*25 = 12262.5 J
mv²/2 = 50*64/2 = 1600 J

so the energy loss to friction is 10662.5 J. Check again anyway...

ther percentage is really easy though:
(energy lost / total energy)*100 = aprox 87%

 

[psruler]

Also can you help me on one more question:

if his trip down the slide took a total of 25s, what was the average power dissipated by fricton, in watts?

THANKS SO MUCH AGAIN!

 

[Guybrush Threepwood]

power = energy / time