# A boy sliding down an incline removes jacket how does this affect speed and momentum?

1. Apr 9, 2012

### Moose100

1. The problem statement, all variables and given/known data
A boy is sliding down a long icy hill on his sled. In order
to decrease his mass and increase his velocity, he drops
his heavy winter coat and heavy boots from (he sled while
he is moving. Will his strategy work?
2. Relevant equations
KE=1/2mv2
p=mv
mgh

3. The attempt at a solution

I thought that since he is decreasing his mass his velocity will go up. B/c in F=ma m and a are inversely related. I.e. if I drop mass a goes up which increases v?? Instead the answer (multiple choice) says that it won't work b/c his PE will go down.

How does PE and KE allow for his velocity to go down? How does this relate to momentum. I get that a reduction in energy will reduce but it's not clear how it specifically elates to velocity. Thanks!

2. Apr 9, 2012

### Brown Arrow

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

we have KE= 1/2 M* v^2 and P=M*v

KE= (1/2)(P^2)/M

3. Apr 9, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

Ok but the question is specifically concerned about speed.

4. Apr 10, 2012

### tal444

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

His potential energy will decrease as well, as PE = mgh. If he decreases his mass, his PE is decreased. Assuming no friction, PE = KE. If PE decreases, then it stands to reason that his KE will decrease, and thus his speed cannot possibly increase.

5. Apr 10, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

Ok that's what I thought. I guess what I was asking is what would that look like mathematically? Or is it more conceptual?
maybe Im being too picky

6. Apr 10, 2012

### gash789

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

Mathematically I would argue it something like:

The total energy of the system must be conserved, therefore

$\textrm{K.E} + \textrm{P.E}= \textrm{const.}$

$\Rightarrow \frac{1}{2}mv(x)^{2} + mgh(x)= \textrm{const.}$

The constant is arbitrary since we can define the potential as we like. If we define it such that the constant is zero at the point he looses weight then rearranging:

$\frac{1}{2}mv(x)^{2} + mgh(x)= 0$
$\Rightarrow v(x)^{2} = \frac{2mgh(x)}{m} =2gh(x)$

Hence the boys velocity is not dependent on his mass.

7. Apr 10, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

That's what I thought too. So why is it important to consider his mass?

8. Apr 10, 2012

### jhae2.718

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

If the total mechanical energy is independent of mass, and specific kinetic energy is v2/2, will changing his mass affect his speed? (This question is equivalent to the problem...)

9. Apr 10, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

The answer to the problem says that he loses PE to the objects he leaves behind.

So he loses PE but the speed doesn't change?

10. Apr 10, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

The kinematic equation that looks like KE but indep of mass

Last edited: Apr 10, 2012
11. Apr 10, 2012

### Moose100

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

v2=√(m1v1^2 +2m1gh1-2m2gh2)

Last edited: Apr 10, 2012
12. Apr 10, 2012

### jhae2.718

Re: A boy sliding down an incline removes jacket how does this affect speed and momen

Ok, I think I'm leading you down the wrong direction here. I used an expression derived assuming constant mass with quantities where mass isn't constant; I'm not quite sure why I went that way other than that it's a long day and I'm tired. I deleted the previous two posts I made under that assumption so as not to mislead future readers.
---

What happens is that when the boy throws away the coat and boots, the energy of those items leaves the system. The mechanical energy within the system is still conserved, but the total amount is reduced by the energy of the coat and boots which leaves (and goes to the surroundings).

So, the velocity is still independent of the mass and thus does not increase.

Last edited: Apr 10, 2012