# Homework Help: Percentage of Original KE that is Convertible

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1. Sep 28, 2016

### Sunbodi

1. The problem statement, all variables and given/known data
A 18-kg child is sliding on an icy surface toward her mother at 3.0 m/s. Her 62-kg mother starts toward her at 2.0 m/s, intending to catch her.

2. Relevant equations

KEi= (1/2) (m1)(v1)^2 + (1/2) (m2)(v2)^2
KEconv= (1/2)μ(v12)^2
μ= (m1m2)/(m1+m2)
v12= |v2 - v1 |
3. The attempt at a solution
KEi= 205 kJ
μ= 13.95 kg
v12 = 1 m/s
KEconv= 6.975

6.975/205= .034
Percent would be 3.4%, not sure what I'm doing wrong.

2. Sep 28, 2016

### billy_joule

The problem statement appears incomplete, there's no question.

3. Sep 29, 2016

### haruspex

Is this supposed to be their relative velocity?

4. Sep 29, 2016

### jbriggs444

@Sunbodi has used the sadly common approach of putting the question into the thread title and the details in the body of the first post. This is, of course, improper. The body of the message should contain everything the reader need to understand it. This applies in Physics Forums just as in all other forms of communication.

In this case we are asked for the "Percentage of Original KE that is Convertible".

The KE that is not recoverable in the collision would be the KE corresponding to the combined mass of the mother and child moving at the velocity of their combined center of mass. It is not recoverable because conservation of momentum requires this motion to remain. The least KE the system can have (barring external forces) is with mother and daughter both motionless in their combined center-of-mass frame.

5. Sep 29, 2016

### Sunbodi

@jbriggs444 Thank you. It was a very stupid mistake of me to not add the question in the body of the message. It's my first thread and I created this account because of this stupid class that I'm in and this stupid stupid online site we're using to log our answers.

6. Sep 29, 2016

### Sunbodi

That's what I meant however because it's an inelastic collision I also attempted to find their combined velocity using the conservation of momentum equation. That velocity would end up being: 2.225 m/s. The final answer in that would end up being .168 and the percent would be 16.8%. I typed in .168 earlier and it didn't have a notification that I had a significant figure error so I'm a bit afraid of typing in 16.8 as I only have 3 attempts remaining.

7. Sep 29, 2016

### Sunbodi

I've solved the problem, it isn't 16.8% or 3.4% as those numbers are way too low and they'd make no sense at all. I made an error in calculating the relative velocity, if you need the actual solution and how I got there feel free to imbox me. Thanks to all of you kind souls who helped me solve this problem.