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From: Tony M on 23 Apr 2010 08:49
A spaceship with a mass of 1000kg is initially at rest relative to an
external observer. The spaceship emits one photon with an energy of
1kg x c^2 as measured by the observer. We define a closed system
including the spaceship and the photon. Please provide the values for:
-invariant mass of the system
-total energy of the system
-velocity of the center of mass, and momentum of the system as
measured by the observer
-velocity of spaceship as measured by the observer
-rest mass of the spaceship (kg, minimum 4 decimals)
From: dlzc on 23 Apr 2010 10:38
Ooooooh. A *homework* problem.

On Apr 23, 5:49 am, Tony M <marc...(a)gmail.com> wrote:
> A spaceship with a mass of 1000kg is initially
> at rest relative to an external observer. The
> spaceship emits one photon with an energy of
> 1kg x c^2 as measured by the observer. We
> define a closed system including the spaceship
> and the photon. Please provide the values for:
> -invariant mass of the system

* A spaceship (and/or photon) with a mass of 1000kg

> -total energy of the system

* A spaceship with a mass of 1000kg * c^2 before, and

E^2 = (pc)^2 + (mc^2)^2 (after)

> -velocity of the center of mass, and momentum
> of the system as measured by the observer

* at rest relative to an external observer.

> -velocity of spaceship as measured by the observer

* "conservation of momentum"

> -rest mass of the spaceship (kg, minimum 4 decimals)

Now crack open your textbook. Two equations in two unknowns, it seems
to me.

David A. Smith
From: PD on 23 Apr 2010 12:55
On Apr 23, 7:49 am, Tony M <marc...(a)gmail.com> wrote:
> A spaceship with a mass of 1000kg is initially at rest relative to an
> external observer. The spaceship emits one photon with an energy of
> 1kg x c^2 as measured by the observer. We define a closed system
> including the spaceship and the photon. Please provide the values for:
> -invariant mass of the system
> -total energy of the system
> -velocity of the center of mass, and momentum of the system as
> measured by the observer
> -velocity of spaceship as measured by the observer
> -rest mass of the spaceship (kg, minimum 4 decimals)

We'll take c to be 3E8m/s exactly, just to make the calculations
simpler, rather than to generate precise numbers. The purpose here is
to show how the calculations work.
The system energy is 9E19 J, and the invariant mass of the system is
1000 kg.
The energy of the emitted photon is 9E16 J, and its momentum is 3E8
kg*m/s, and its rest mass is zero. The rocket's momentum is therefore
3E8 kg*m/s in the opposite direction. The momentum (and velocity) of
the center of mass is zero.
The total energy of the rocket is 8.991E19 J. It's rest mass after
emission of the photon is therefore given by m^2 = (E/c^2)^2 - (p/
c)^2, which yields m = 998.9995 kg.
The speed of the rocket is given by beta = (v/c) = pc/E = 0.0010, so
the rocket is traveling at 3E5 m/s in this frame.

You'll notice the sum of the rest masses does not add up to 1000 kg.

PD
From: Tony M on 23 Apr 2010 13:23
As PD above, please consider c = 3E8 m/s.
From: PD on 23 Apr 2010 13:44
On Apr 23, 12:23 pm, Tony M <marc...(a)gmail.com> wrote:
> As PD above, please consider c = 3E8 m/s.

And since I did all those calculations, what more do you need?
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