Can Conservation of Energy Alone Solve Momentum Problems?

[aa_o]

Homework Statement

Homework Equations

Conservation of momentum:
m1*v1 + m2*v2 = k
Conservation of mech. energy
1/2 * m * v^2 + m * g * h = k

The Attempt at a Solution

Why can't i just use conservation of energy to solve this one?
I know that the bullet contains all the kinetic energy before hitting:
K.E = 1/2 * m_b * v_b^2
After hitting we can observe the amplitude of the swing (where kinetic energy is 0 and write):
P.E = (m_b + m_p) * g * h
Where h is the height above the initial position, given by:
h = L * (1 - cos(x))
Solving for v_b we get:
v_b = sqrt[2*(M + m) / m * g * L * (1-cos(x))]

The 'well known' solution to this problem solved with conservation of both energy and yields this solution:
v_b = 2*(M + m) / m * sqrt[g * L * (1-cos(x))]

Which of my assumptions are wrong?

 

[BvU]

Conservation of mech. energy

Is the answer to your question -- as you probably know.
You can calculate the loss of energy from the correct solution and now my question is: where did it go ?

 

[aa_o]

Is the answer to your question -- as you probably know.
You can calculate the loss of energy from the correct solution and now my question is: where did it go ?

It went to making a hole in the pendulum and generating heat in the form of friction?

 

[BvU]

You got it ! deformation of the bullet, and so on.

Compare coins sliding on a table: shoot with one coin at another of the same size. The one moving stops altogether and the other one shoots off at the same speed. Energy and momentum conserved.
With a drop of glue (or two disc magnets) momentum conservation forces the double mass at half the original speed, so ##{1\over 2} mv^2## halves.

There's a lot of discussion on this under Newton's cradle (with or without scholar). Also check out Gauss gun