How Do You Calculate the Speed of a Bullet in a Pendulum Collision Problem?

[ritwik06]

Homework Statement

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

Homework Equations

Momentum remains conserved
Energy remains conserved

The Attempt at a Solution

I tried to solve this using two methods and thereby I got two different 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
$$v=\sqrt{360}$$

 

[ritwik06]

Please Explain this anomaly!
To different answers with the two probably correct applications. How is this possible?

 

[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.

 

[ritwik06]

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.

Thanks