# Horizontal Plane With Friction And Incline Plane With no Friction

1. Dec 20, 2011

### amgoda

1. A body with mass m = 5 kg and initial velocity = 5 m/s moves along a horizontal plane with length 10 m, where the friction coefficient is μ=0.1, After passing the part with friction, the body moves up along a tilted plane wich has no friction. What is the maximum height of body elevation along the tilted plane?

http://imageshack.us/photo/my-images/15/physicso.png/

i tired to get the final velocity before it goes up the inclined plane and got (2.32) but i think i got it wrong

2. Dec 20, 2011

### Dick

You should really show how you got 2.32m/s. And no, you didn't get it wrong. But you never really needed to find the velocity. What you needed to find is the kinetic energy before it goes up the ramp. How is that related to the height it climbs?

3. Dec 20, 2011

### amgoda

alright .. here is how i thought about it ..
N=mg
Fκ=μk.N
a=(μk.mg)/-m=-.98m/s^s
vf^2=V0+2a(x-x0)
vf^2=5^2+(2*-.98*10)= 2.32
and i thought that the final velocity on the horizontal plane is the initial velocity for the inclined plane ..

4. Dec 20, 2011

### Dick

That is perfectly fine. I don't think it's the most economical route to the answer but you are doing very well. But now how do you use the initial velocity up the ramp to find the height you climb?

5. Dec 20, 2011

### amgoda

that's the problem .. i just got to this point and i don't know what to do afterwards ...
btw thanks for the fast replies

6. Dec 20, 2011

### Dick

Do you know how to use energy conservation to do it? Gravitational potential energy at a height h up the ramp is mgh. That must be equal to the kinetic energy you started with. Yes?

7. Dec 20, 2011

### amgoda

ahaa .. so it should equal to the kinetic energy at the end of the horizontal plane .. so will it be .5*m*v^2=mgh .5*5*2.32^2=5*9.8*h
h=0.63 meters ?

8. Dec 20, 2011

### Dick

Exactly, except I don't get h=0.63m. Can you try that once more? And think about whether you really needed to find v at all. You just need the KE at the start of the ramp. Can you think of a simpler way to find that?

Last edited: Dec 20, 2011
9. Dec 20, 2011

### amgoda

ahaaa .. here we go .. i dont know why i havent thought of this
Wnet=μk.mg.Δx = change in KE
then KE at the bottom = 13.5 =mgh
h= .027
and i recalculated H in the First method i used and i got 0.27 also ..
thanks alot u drew my attention to the easier way .. thanks

10. Dec 20, 2011

### Dick

Very welcome. Energy conservation is often the easy way to go. And both are h=0.27, right?

11. Dec 20, 2011

### amgoda

yup.. i just messed up in the first calculation