# Principles of Conservation

1. Aug 26, 2008

### ritwik06

1. The problem statement, all variables and given/known data
A bullet of mass 50 g is fired from below into the bob of mass 450 g of a long simple pendulum. The bullet remains inside the bob and the bob rises through a height of 1.8 m. Find the speed of the bullet. Take g=10

2. Relevant equations
Momentum remains conserved
Energy remains conserved

3. The attempt at a solution
I tried to solve this using two methods and thereby I got two differnt answers. Tell me where am I wrong.

Using Kinematics:
Let th speed of the bullet be v. Let the velocity after th bullet is embeed is V. by the principle of conservation of linear momnetum:
$$V=\frac{(0.05 Kg)v}{0.45+0.05}=\frac{v}{10}$$

Using v^2=u^2+2ax
v=60 m/s

2nd method:
Momentum remains conserved
Energy remains conserved
Kinetic energy of the bullet =change in potential energy of the bullet bob system.
0.5*0.05*v^2=0.5*10*1.8
$$v=\sqrt{360}$$

2. Aug 26, 2008

### ritwik06

To different answers with the two probably correct applications. How is this possible?

3. Aug 26, 2008

### Dick

Kinetic energy isn't conserved. Overall energy is conserved, but the collision is inelastic. The bullet is stopped by the target. Some of the kinetic energy is lost to heat and other forms of energy. Momentum is ALWAYS conserved.

4. Aug 28, 2008

Thanks