Why momentum and energy give different bullet speeds after plastic collision

[vadbol]

Homework Statement

A bullet hits balk of 5kg on a rope of 2m lenths. Bullets mass 2gr, velocity unknown. Plastic collission, balk goes upat 45 degrees.

Homework Equations

When i solve it with energy equations i get
h=2-2cos45=0.58m
V(of balk and bullet) = sqrt(2gh)=3.38 m/s. (potential energy of total mass)

Now i need to find a velocity of bullet at t(0).
Here is the trick
when i solve it using momentum i get:
mv=(m+M)V
v=8450 m/s
But! when i solve it using energy i got
m*sqr(v)/2=(m+M)*g*h
v=168.5 m/s.
Thinking about that we used the potential energy to calculate a balk speed and taking into account an absolute plastic collision i don't know why is the differense?
Thanks for any help.

 

[PhanthomJay]

Homework Statement

A bullet hits balk of 5kg on a rope of 2m lenths. Bullets mass 2gr, velocity unknown. Plastic collission, balk goes upat 45 degrees.

Homework Equations

When i solve it with energy equations i get
h=2-2cos45=0.58m
V(of balk and bullet) = sqrt(2gh)=3.38 m/s. (potential energy of total mass)

Now i need to find a velocity of bullet at t(0).
Here is the trick
when i solve it using momentum i get:
mv=(m+M)V
v=8450 m/s
But! when i solve it using energy i got
m*sqr(v)/2=(m+M)*g*h
v=168.5 m/s.
Thinking about that we used the potential energy to calculate a balk speed and taking into account an absolute plastic collision i don't know why is the differense?
Thanks for any help.

During a plastic (totally inelastic) or inelastic collision, momentum is always conserved, but energy is not (there is energy loss from friction, heat, etc.). Your first approach seems correct, although that bullet speed seems enormously high.

 

[vadbol]

Ok, thanks for reply.
But to solve it using momentum approach i took velocity of balk and a bullet after collision which i got using the very energy equation. So if the energy is not saved totally as you say how can we use that velocity of balk to calculate velocity of bullet?
I mean when the bullet hits the balk it gives it its total energy and balk goes up - converting kinetic energy into potential. Now using the height of rising we got velocity of balk using energy equations. So the energy the bullet gave to balk - the bullet had at the fire moment - a kinetic.
The difference between results is too big for thinkinf about heat etc.

 

[PhanthomJay]

Ok, thanks for reply.
But to solve it using momentum approach i took velocity of balk and a bullet after collision which i got using the very energy equation. So if the energy is not saved totally as you say how can we use that velocity of balk to calculate velocity of bullet?
I mean when the bullet hits the balk it gives it its total energy and balk goes up - converting kinetic energy into potential. Now using the height of rising we got velocity of balk using energy equations. So the energy the bullet gave to balk - the bullet had at the fire moment - a kinetic.
The difference between results is too big for thinkinf about heat etc.

Momentum is conserved during the collision, energy is not. Energy is conserved after the collision, momentum is not.

During the collision, there are no external forces acting on the system, that is why momentum is conserved. But energy is not conserved during the collision, because of the fact that there are non-conservative forces acting in bringing the bullet to a stop as it penetrates the balk.

After the collision takes place in a very short impulse of time, now energy must be conserved, because only the gravity force...a conservative force..is acting. But since gravity is an external force, momentum is not conserved after the collision.

 

[vadbol]

Thanks , now i got it. :)