c/The ion drive engine of
the NASA Deep Space 1 probe,
shown under construction (top)
and being tested in a vacuum
chamber (bottom) prior to its
October 1998 launch. Intended
mainly as a test vehicle for
new technologies, the craft
nevertheless also carried out a
scientific program that included
a rendezvous with a comet in
2004.(NASA)
being to the right. The initial momentum is (50 kg)(0 m/s)+(100
kg)(−5 m/s)=−500 kg·m/s, and the final momentum is (50 kg)(0
m/s)+(100 kg)(5 m/s)=500 kg·m/s. This is a change of 1000
kg·m/s, which is impossible if the two people constitute a closed
system.
One could argue that they’re not a closed system, since Lu might
be exchanging momentum with the floor, and Jen Yu might be
exchanging momentum with the seat of her chair. This is a rea-
sonable objection, but in the following section we’ll see that there
are physical reasons why, in this situation, the force of friction
would be relatively weak, and would not be able to transfer that
much momentum in a fraction of a second.
This example points to an intuitive interpretation of conserva-
tion of momentum, which is that interactions are always mutual.
That is, Jen Yu can’t change Lu’s momentum without having her
own momentum changed as well.
A cannon example 2
.A cannon of mass 1000 kg fires a 10-kg shell at a velocity of
200 m/s. At what speed does the cannon recoil?
.The law of conservation of momentum tells us that
pcannon,i+pshel l,i=pcannon,f+pshel l,f.
Choosing a coordinate system in which the cannon points in the
positive direction, the given information is
pcannon,i= 0
pshel l,i= 0
pshel l,f= 2000 kg·m/s.
We must havepcannon,f=−2000 kg·m/s, so the recoil velocity of
the cannon is 2 m/s.
Ion drive example 3
.The experimental solar-powered ion drive of the Deep Space
1 space probe expels its xenon gas exhaust at a speed of 30,000
m/s, ten times faster than the exhaust velocity for a typical chemical-
fuel rocket engine. Roughly how many times greater is the maxi-
mum speed this spacecraft can reach, compared with a chemical-
fueled probe with the same mass of fuel (“reaction mass”) avail-
able for pushing out the back as exhaust?
.Momentum equals mass multiplied by velocity. Both spacecraft
are assumed to have the same amount of reaction mass, and the
ion drive’s exhaust has a velocity ten times greater, so the mo-
mentum of its exhaust is ten times greater. Before the engine
starts firing, neither the probe nor the exhaust has any momen-
tum, so the total momentum of the system is zero. By conserva-
tion of momentum, the total momentum must also be zero after134 Chapter 3 Conservation of Momentum