# Energy vs Momentum

## 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 dont know why is the differense?
Thanks for any help.

Homework Helper
Gold Member

## 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 dont 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.

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.

Homework Helper
Gold Member