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

 

[nlightner]

Thank you for sharing your test results and homework problems. It's great to see that you are taking the time to review and understand the concepts in your physics class. Let's take a look at your solutions and see if we can clarify any misunderstandings.

1. Your solution for the first problem is correct, but let's take a closer look at the equations you used. In the conservation of momentum equation, you used the initial momentum of Train A (Pi) and the final momentum of the coupled trains (Pf). However, the initial momentum of Train B (0) was not included. The correct equation would be 5000*6.0= (5000+7500)*vf, which gives the same answer of 2.4 m/s. It's important to include all relevant variables in equations to ensure accurate solutions.

2. Your solution for the second problem is also correct, but let's clarify a few things. The archer's initial momentum is not 0, as you have assumed in your calculation. The correct equation would be Pi= (65 kg)*0 m/s + (250 g)*125 m/s. This would give a positive initial momentum of 31.25 kg*m/s. In order to find the archer's recoil speed, we would use the conservation of momentum equation, setting the initial momentum equal to the final momentum, and solving for the archer's velocity. This would give a recoil speed of 0.482 m/s, as you calculated.

3. Your solutions for part a and b are correct. In part c, you mentioned that KE is conserved under the condition of an elastic collision. This is correct, but it's important to note that KE is also conserved in a completely inelastic collision, where the two objects stick together after the collision. In part d, you mentioned that momentum will always be conserved in both elastic and inelastic collisions, which is correct. However, it's worth mentioning that in an inelastic collision, the total kinetic energy of the system is not conserved, but the total momentum is still conserved.

Overall, it seems like you have a good understanding of the concepts and equations involved in these problems. Keep up the good work, and don't hesitate to ask for clarification or assistance if you come across any difficulties in your studies.