Did bad on my test but i think i get MOMENTUM

[zell_D]

Homework Statement

1. Train A 5000 kg couples with Train B 7500 kg. Train A is moving at 6.0 m/s before collision, while Train B was at rest. Find final Velocity of the coupled trains? Find initial KE and final KE? How much KE is lost, what fraction of the initial KE is lost?

2. 65.0 kg archer, standing on frictionless ice, shoots a 250 g arrow at a speed of 125 m/s. What is the archer's recoil speed?

3. If two objects collide and one is initially at rest, answer the following (ignore frictional effects)
a) possible for both of them to be at rest after collision?
b) possible for one of them to be at rest after collision?
c) under what conditions will KE be conserved?
d) under what conditions will momentum be conserved?

Homework Equations

P=mv
Conservation of momentum
KE=.5mv^2

The Attempt at a Solution

1. Pi= 5000*6.0=30000 J
Pf= (5000+7500)*vf
Pi=Pf
30000=12500vf
vf=2.4 m/s

KEi=.5(5000)(6.0^2)
=90000 J
KEf=.5(12500)(2.4^2)
=36000 J

90000-36000=54000 J lost

54000/90000=.6 = 3/5 of initial KE lost

2. Pi = Pf
0=m_archerv_archer+m_arrowv_arrow
v_archer=(m_arrowv_arrow)/-m_archer
v=(.250 * 125 m/s)/-65 kg = -.482 m/s

3. a) no, Pi=Pf, if final velocity = 0's, Pf=0. And that is not possible since initial velocity will generate a initial momentum, so Pi =/= Pf and this cannot happen in our system.
b) yes, assuming the two balls are identical. The moving ball will come to rest after collision with the other ball, the other ball will now be moving at the velocity the first ball was moving at. momentum was transferred
c) KE is conserved under the condition that the collision is an elastic collision
d) momentum will always be conserved, in both elastic and inelastic collisions. Given, however, that no external forces acts on the system, the total momentum remains constant.

 

[The Bob]

All seems fine to me.

2. Pi = Pf [...]
v=(.250 * 125 m/s)/-65 kg = -.482 m/s

Maybe just mention in your solution that the positive direction is the direction the arrow travels more explicitly but it is a small point.

The Bob