How Does Friction Affect Mechanical Energy in a Bead Slide?

[notsam]

Homework Statement

A 0.5 kg bead slides on a curved wire, starting
from rest at point A.
The segment from A to B is frictionless, and
the segment from B to C is rough. The point
A is at height 4.9 m and the point C is at
height 1 m with respect to point B.
The acceleration of gravity is 9.8 m/s2 .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.

Homework Equations

K=.5mv^2, P=mgh

The Attempt at a Solution

Ok so here is where I'm at. I know that the Kenetic energy at point "B" will be 24.01 J. So once it it climbs up to point "c" the ball stops which means that the veolocity is 0 m/s. So there is no kenetic energy at point "C". At point "C" the potential energy will be P=mgh, (.5)(9.8)(1)= 4.9 J And the K= 0 Only at point "c". I know that all of the energy must be conserved so-- K at b= P at c+ K at c + Energy due to friction. So the "Change in Mechanical Friction" should be my energy due to friction. Yes? or No?

 

[PhanthomJay]

Homework Statement

A 0.5 kg bead slides on a curved wire, starting
from rest at point A.
The segment from A to B is frictionless, and
the segment from B to C is rough. The point
A is at height 4.9 m and the point C is at
height 1 m with respect to point B.
The acceleration of gravity is 9.8 m/s2 .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.

Homework Equations

K=.5mv^2, P=mgh

The Attempt at a Solution

Ok so here is where I'm at. I know that the Kenetic energy at point "B" will be 24.01 J. So once it it climbs up to point "c" the ball stops which means that the veolocity is 0 m/s. So there is no kenetic energy at point "C". At point "C" the potential energy will be P=mgh, (.5)(9.8)(1)= 4.9 J And the K= 0 Only at point "c". I know that all of the energy must be conserved so-- K at b= P at c+ K at c + Energy due to friction. So the "Change in Mechanical Friction" should be my energy due to friction. Yes? or No?

You have the correct equation, but the wrong terms. From your equation, the energy due to friction is the change in mechanical energy, where mechanical energy is defined as P + K .