Solving Conservation of Energy Problems

[xRadio]

Homework Equations

Total Energy = Kinetic Energy + Potential Energy
T.E = 1/2mv^2 + m(g)(h)

The Attempt at a Solution

T.E at top
= 1/2mv^2 + m(9.8)(h)

T.E at bottom
1/2mv^2 + m(9.8)(h) = 1/2mv^2 + m(9.8)(h/2)

Please help I have no clue what to do

 

[Andy_ToK]

1/2mv^2 + m(9.8)(h) = 1/2mv^2 + m(9.8)(h/2)[\quote]
The speeds of the object are different, so may want to denote the second speed as v2

 

[xRadio]

Oh yeah, I had that on my paper, but forgot to type it in.

 

[hage567]

You look to be on the right track. You just need to solve for v2. Are you having trouble with the algebra? Put "g" back in for the 9.8, to make it clearer.
You can also cancel out m.

 

[xRadio]

1/2mv^2 + m(g)(h) = 1/2m[v]^2 + m(g)(h/2)
v^2 + (g)(h) - (g)(h/2) = [v]^2

Is this right? =/ I really suck at simplifying

 

[hage567]

The first line is good. You can simply your gh terms. If you ignore the gh for a moment, you will see that it is really 1-1/2, which is 1/2.

You have also dropped the 1/2 from the kinetic energy terms again.

 

[xRadio]

1/2mv^2 + 1/2 = 1/2m[v]^2
v^2 + 1 = [v]^2 *multiply both sides by 2 to eliminate 1/2?
v + 1 = [v]

 

[denverdoc]

well the help so far has been on the right track.

you can work this out if you choose, but any increase in energy will come from the additional drop of 1/2y*mg

so 1/2mv'^2=1/2mv^2 +1/2 mgh,
so factoring, gives v'=sqrt(v^2+gh)
may be wrong but don't think you have enough information to solve for h.

 

[robb_]

Okay, I got to ask, Bambi's carcass??!

 

[hage567]

1/2mv^2 + 1/2 = 1/2m[v]^2
v^2 + 1 = [v]^2 *multiply both sides by 2 to eliminate 1/2?
v + 1 = [v]

Oh sorry I should have been clearer...you still need the gh in there. I was just pointing out that gh - (1/2)gh = (1/2)gh. So put a gh in where your 1 is.

Also v must remain as v^2, since you have

v^2 + gh = [v]^2

when you take the square root of both sides, you get

(v^2 + gh)^(1/2) = [v]

You can't take the square root of individual terms like you did. You must take it of the entire left side.

 

[denverdoc]

Okay, I got to ask, Bambi's carcass??!

Robb, I had to laugh as well, I think there is now an industry to make physics problems more entertaining to youth of america. so they dress up the same old dreary problems in ever increasingly bizarre clothes.

 

[hage567]

Okay, I got to ask, Bambi's carcass??!

lol I didn't want to know.

 

[xRadio]

yess thank you I did it again and got this answer, thank you both so much for all your help.