Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's say
the mass acquires a velocity v, so the astronaut acquires velocity -v.

If I were asked, how much chemical energy does the astronaut lose... The
answer seems to me to be: mv^2 (sum of the final kinetic energies of both
the astronaut and the mass). There's no other source for the kinetic energy
to come from.

But if I were to use this idea of energy transfer (force through distance =
energy transferred) then, I'd get the result that the astronaut transferred
1/2(mv^2) to the rock (no problem).

But how does the astronaut gain his 1/2 (mv^2) of energy? There is only one
force acting on the astronaut. It comes from the rock. And this force
does -1/2(mv^2) of work. So how does the astronaut gain 1/2 (mv^2) of energy
when the only external force does negative work?

I know the energy comes from the chemical energy of the astronaut... What
troubles me is the failure to get this result through analyzing the
situation by energy transfer. How is the transfer of the chemical energy of
the astronaut to HIMSELF... expressed in the math?

Thanks for your help.

cool_cat wrote:
Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's say
the mass acquires a velocity v, so the astronaut acquires velocity -v.


Their momenta* will be equal and opposite, but not their velocities.

*with respect to the original reference frame where they were both
at rest.

If you push yourself off from the edge of a skating rink, how is the
chemical energy transferred to your motion?

-tg

wrote in message
ps.com...
If you push yourself off from the edge of a skating rink, how is the
chemical energy transferred to your motion?

-tg


Yes. This is what I'm asking. You push off the rink... some of your energy
is transferred to the rink(earth). This is the work you do on the rink. This
same work can be seen as negative work done by the rink on you.

The second process that takes place is that the chemical energy in your body
is converted to kinetic energy in your body. It is this second process that
I'm wondering about.

"Sam Wormley" wrote in message
news:u3wxe.111934$_o.106703@attbi_s71...
cool_cat wrote:
Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's
say the mass acquires a velocity v, so the astronaut acquires
velocity -v.


Their momenta* will be equal and opposite, but not their velocities.

*with respect to the original reference frame where they were both
at rest.

In my example I'm using equal masses... hence equal and opposite momenta =
the velocities are equal and opposite.

cool_cat wrote:

Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's say
the mass acquires a velocity v, so the astronaut acquires velocity -v.

Velocity is not conserved. Energy, linear and angular momenta are
conserved.

If I were asked, how much chemical energy does the astronaut lose... The
answer seems to me to be: mv^2 (sum of the final kinetic energies of both
the astronaut and the mass). There's no other source for the kinetic energy
to come from.

Why do you assume 100% biological-physical conversion efficiency?

But if I were to use this idea of energy transfer (force through distance =
energy transferred) then, I'd get the result that the astronaut transferred
1/2(mv^2) to the rock (no problem).

But how does the astronaut gain his 1/2 (mv^2) of energy? There is only one
force acting on the astronaut. It comes from the rock. And this force
does -1/2(mv^2) of work. So how does the astronaut gain 1/2 (mv^2) of energy
when the only external force does negative work?

Choose a center of mass reference frame.

I know the energy comes from the chemical energy of the astronaut... What
troubles me is the failure to get this result through analyzing the
situation by energy transfer. How is the transfer of the chemical energy of
the astronaut to HIMSELF... expressed in the math?

Thanks for your help.

Inertia. Conservation laws. Knowing what you are doing.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

"Uncle Al" wrote in message
...
cool_cat wrote:

Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's
say
the mass acquires a velocity v, so the astronaut acquires velocity -v.

Velocity is not conserved. Energy, linear and angular momenta are
conserved.


I know that. Please re-read my post. I'm assuming the masses are the same
for simplicity. Equal and opposite momenta and equal masses = equal and
opposite velocities.

If I were asked, how much chemical energy does the astronaut lose... The
answer seems to me to be: mv^2 (sum of the final kinetic energies of both
the astronaut and the mass). There's no other source for the kinetic
energy
to come from.

Why do you assume 100% biological-physical conversion efficiency?


Well, I was not really concerned with the lost energy. Ok. I'll rephrase
what I wrote... If I was asked how much chemical energy from the astronaut
goes into the kinetic energy of the two bodies the answer would be mv^2.

But if I were to use this idea of energy transfer (force through distance
=
energy transferred) then, I'd get the result that the astronaut
transferred
1/2(mv^2) to the rock (no problem).

But how does the astronaut gain his 1/2 (mv^2) of energy? There is only
one
force acting on the astronaut. It comes from the rock. And this force
does -1/2(mv^2) of work. So how does the astronaut gain 1/2 (mv^2) of
energy
when the only external force does negative work?

Choose a center of mass reference frame.


Thanks. I'll try this.

I know the energy comes from the chemical energy of the astronaut... What
troubles me is the failure to get this result through analyzing the
situation by energy transfer. How is the transfer of the chemical energy
of
the astronaut to HIMSELF... expressed in the math?

Thanks for your help.

Inertia. Conservation laws.

Yes, conservation of momentum and conservation of energy gives the result
that mv^2/2 of chemical energy goes into the astronaut's own body. I know
that already.

But my interest in this problem is to see the conversion of the astronaut's
chemical energy into his kinetic energy by just analyzing the forces acting
on him.

Knowing what you are doing.

What's with the attitude? Is there something wrong with asking physics
questions in a physics newsgroup? If I knew exactly what I was doing then I
wouldn't be here asking questions.

cool_cat wrote:
"Sam Wormley" wrote in message
news:u3wxe.111934$_o.106703@attbi_s71...

cool_cat wrote:

Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's
say the mass acquires a velocity v, so the astronaut acquires
velocity -v.


Their momenta* will be equal and opposite, but not their velocities.

*with respect to the original reference frame where they were both
at rest.


In my example I'm using equal masses... hence equal and opposite momenta =
the velocities are equal and opposite.



Bad example since the energy sources comes from the astronaut!

"Sam Wormley" wrote in message
news:YSzxe.113950$_o.53411@attbi_s71...
cool_cat wrote:
"Sam Wormley" wrote in message
news:u3wxe.111934$_o.106703@attbi_s71...

cool_cat wrote:

Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's
say the mass acquires a velocity v, so the astronaut acquires
velocity -v.


Their momenta* will be equal and opposite, but not their velocities.

*with respect to the original reference frame where they were both
at rest.


In my example I'm using equal masses... hence equal and opposite momenta
= the velocities are equal and opposite.

Bad example since the energy sources comes from the astronaut!

I don't follow. Why does that make it a bad example?

cool_cat wrote:
"Sam Wormley" wrote in message
news:YSzxe.113950$_o.53411@attbi_s71...

cool_cat wrote:

"Sam Wormley" wrote in message
news:u3wxe.111934$_o.106703@attbi_s71...


cool_cat wrote:


Something is bugging me... Consider a situation in space... an astronaut
mass m, and a rock m (no other objects anywhere). The astronaut exerts a
force F on the rock (let's say along the x axis) for some time t. Let's
say the mass acquires a velocity v, so the astronaut acquires
velocity -v.


Their momenta* will be equal and opposite, but not their velocities.

*with respect to the original reference frame where they were both
at rest.


In my example I'm using equal masses... hence equal and opposite momenta
= the velocities are equal and opposite.

Bad example since the energy sources comes from the astronaut!


I don't follow. Why does that make it a bad example?



The masses (rock and astronaut) cannot remain equal as the astronaut
exerts a F on the rock. The astronaut's mass will have to be reduced
and therefore her velocity will be greater than the rock's.