Inelastic collision, kinetic energy

[lemonpie]

Homework Statement

A bullet of mass 10 g strikes a ballistic pendulum of mass 2.0 kg. The center of mass of the pendulum rises a vertical distance of 12 cm. Assuming that the bullet remains embedded in the pendulum, calculate the bullet's initial speed.

Homework Equations

p = mv, pi = pf, KEi + PEi = KEf + PEf

The Attempt at a Solution

m1 = 10 g = 0.01 kg, m2 = 2 kg, total mass M = 2.01 kg, h = 12 cm = 0.12 m

p1 = m1v1 = 0.01v1
p2 = Mv2 = 2.01v2

conservation of linear momentum pi = pf: 0.01v1 = 2.01v2

i would never have figured out how to use this otherwise -- i just don't know how people figure out to use equations from previous chapters (if someone has advice, please tell me), but apparently i apply conservation of mechanical energy:

KEi + PEi = KEf + PEf
0.5(2.01)vf^2 + 0 = 0 = (2.01)(9.8)(0.12)
1.005vf^2 = 2.36
vf = 1.53 m/s

pi = pf = 0.01v1 = 2.01v2
v1i = 201vf
v1i = 201(1.53) = 307.5 m/s

this is the correct answer, but i don't understand how to arrive at it. the part written in red is what confuses me. i would think initial KE means to use only the mass of the bullet, not the total, and also that when we figured out the velocity there, that would be the INITIAL velocity of the bullet, not the final velocity of bullet and pendulum.

 

[marlon]

When you apply the total energy conservation, you need to apply it on the total system : bullet + pendulum before and after impact, so :

1/2(m1+m2)v^2 - 0 = change in E_pot

The v is the velocity of the total system acquired because of the impact of the bullet. I wrote 0 because the final velocity of the total system is 0 (when the potential energy is at maximal value).

The fact that you need to work with the total system is also reflected in the fact that the center of mass is used to calculate the change in E_pot
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Conservation of linear momentum is applied on all objects individually before and after impact, so :

P_bullet + P_pendulum = P_(bullet+pendulum) ; where p_pendulum = 0 before impact.

marlon

 

[Doc Al]

this is the correct answer, but i don't understand how to arrive at it. the part written in red is what confuses me. i would think initial KE means to use only the mass of the bullet, not the total, and also that when we figured out the velocity there, that would be the INITIAL velocity of the bullet, not the final velocity of bullet and pendulum.

Realize that there are two "parts" to this problem:
(1) The collision itself. Momentum is conserved; energy is not. Vf refers to the speed of the system immediately after the collision.
(2) The rising of the pendulum that takes place after the collision. Here's where energy is conserved. The "initial" KE here means the KE at the start of the rising of the pendulum, just after the collision (speed = Vf). It does not mean the initial KE of the bullet before the collision (speed = Vi).

 

[lemonpie]

thanks. i realize now that i should have not assumed that energy would be conserved during the collision, since the two bodies stuck together. that helped me with the rest of the problem.