## amistre64 3 years ago Object sliding down a ramp .... PE and KE

1. amistre64

|dw:1348751150306:dw|

2. amistre64

oh, and time it takes to slide to the bottom of the ramp is 1.638 seconds Potential energy = .0025*9.8*.46 Kinetic energy at the bottom of the ramp is?

3. amistre64

this problem involves friction

4. imron07

I think we can use work-kinetic energy theorem.

5. amistre64

hopefully :) I seem to come up with 2 different answers; and i know one of them is wrong.

6. imron07

The aceleration must be constant right?

7. amistre64

$a=\frac{2d}{t^2}$ $v=at=\frac{2d}{t}$ $K_e=\frac12mv^2$ energy lost to friction $P_e-K_e$

8. amistre64

assume a constant acceleration yes

9. imron07

You're did it correct i think

10. rajathsbhat

do you know the co-efficient of sliding friction?

11. amistre64

not outright; but that can be calculated with given information i believe

12. imron07

Hmm, actually we don't need $$\mu$$ since time is known.

13. rajathsbhat

mmm true.

14. amistre64

$\mu_k=\frac{g~sin\theta-a}{g~cos\theta}$ $F_k=\mu_k*\vec n=\frac{g~sin\theta-a}{g~cos\theta}*mg~cos\theta$ $F_k=m(g~sin\theta-a)$ $W_f=F_k*d=md~(g~sin\theta-a)$

15. rajathsbhat

hey you know that v=2d/t^2. So KE is just 1/2 mv^2.

16. rajathsbhat

i mean, what else do you want?

17. amistre64

just working it thru a couple of ways. When I first tried to work this out; I used: Pe = mgh = 0.01127 J in a frictionless system; Ke = Pe at the bottom of the ramp mgh = mv^2/2 gh = v^2/2 sqrt(2gh) = v v = 3.0027 m/s right?

18. imron07

The problem maybe 1.638 sec isn't the correct time :)

19. rajathsbhat

yes, v=3m/s in that case.

20. amistre64

its pretty good, we slid the penny 5 times and averaged it out

21. amistre64

at first the velocity of the Ke i just worked out threw me for a loop

22. rajathsbhat

you actually measured 3m/s!?

23. amistre64

i couldnt see why the velocity from v=2d/t wasnt matching up :)

24. amistre64

the 3 m/s was not measured, it was calculated

25. rajathsbhat

oh i thought you performed an experiment with a penny..

26. amistre64

i spose my question is; is using the velocity of 2d/t a proper way to determine the kinetic energy in the system at the bottom of the ramp?

27. rajathsbhat

yes. This works no matter what the friction is (even 0).

28. amistre64

thanks :) so if it was a frictionless system, then the kinetic energy at the bottom of the ramp would still equal the potential energy from the start of it; and all that would change is the final velocity of the object then.

29. amistre64

..and a change in time, but thats a given :)

30. rajathsbhat

yes.

31. rajathsbhat

Here's a nice video of an extreme case where the object slides with uniform velocity: http://www.youtube.com/watch?v=84DXjumAxNQ&feature=plcp

32. amistre64

lol, great; i minute ten watching a sock slide down a banister ....

33. rajathsbhat

x)