# Mechanical energy of sliding beads

1. Homework Statement
A 0.5 kg bead slides on a curved wire, starting
from rest at point A as shown in the figure.
The segment from A to B is frictionless, and
the segment from B to C is rough. The point
A is at height 6.9 m and the point C is at
height 1.6 m with respect to point B.
The acceleration of gravity is 9.8 m/s^2 :
http://img376.imageshack.us/img376/2720/motion8pj.gif [Broken]
the image for this problem is fig.2
If the bead comes to rest at C, find the change
in mechanical energy due to friction as it
moves from B to C. Answer in units of J.

2. Homework Equations
mgh=energy of grav.
Force*displacement=diss. energy

3. The Attempt at a Solution
First, I set mgh at point A to mgh at C + diss energy:
(.5)(9.8)(6.9)=.5(9.8)+diss.
diss=26J
the answer above is not right, am i misunderstanding the question?

Last edited by a moderator:

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arildno
Homework Helper
Gold Member
Dearly Missed
Well, isn't the height at C 1.6m above B??

Remember, though that the change of mechanical energy is NEGATIVE.

Last edited:
oh, thanks alot!

since i have fig.1 as well, I might as well post another one of my problem:
1. Homework Statement
A bead slides without friction around a loop-
the-loop. The bead is released from a height
of 9.4 m from the bottom of the loop-the-loop
which has a radius 2 m.
The acceleration of gravity is 9.8 m/s2 :
What is its speed at point A? Answer in
units of m/s.
3.Work
this is basically the same as the first problem, and mass isn't needed because it ends up canceling.
so:
mgh=.5mv^2+mgh <-there is also grav. energy, because A is not the lowest
gh=.5v^2+gh
(9.8)(9.4)=.5v^2+9.8(4)
v=10.3m/s
but that answer is wrong. I'm sure that i have the equation set out right, because at point A kinetic energy is transferred to grav. potential energy.

you did some thing that does not make logical sense. take a look at your plus/minus signs.

so you are saying that one of the value that i plugged in should've been negative?

yep. But don't just change it without understanding why. after it falls, it goes up 4 meters--not down.

i figured out what i did wrong... I rounded wrong. I was off by more than 1% from the real answer, so Utexa's homework service rejected it.

Gyroscope
Those drawings are down in Latex?

no, I copied and edited them on paint :)