CK-12-Physics - Intermediate

http://www.ck12.org Chapter 7. Momentum

FIGURE 7.12

Using Conservation of Momentum,pi=pfwe have:

0 = ( 0. 145 kg)

(

7. 00

m

s

)

+( 31. 555 kg)vg f

vg f=

(− 0. 145 kg)

(

7. 00 ms

)

31. 555 kg

=

− 1. 015 kg∗sm

31. 555 kg

=− 0. 03216 →− 0. 0322

m

s

→− 3. 22

cm

s

Notice that the solution is a negative number. This indicates that the girl is moving opposite the baseball. She’s
moving due east. The girl’s motion is, in principle, the same kind of motion that occurs when a spacecraft fires its
thrusters in outer space. The thrusters eject mass (exhaust gases) in one direction, and the spaceship is propelled
in the opposite direction, thus insuring that the momentum of the system is conserved. (The force on the exhaust
gases and the force on the spacecraft are a Newton’s Third Law pair of forces). Airplanes and jets use momentum
conservation as well but they do not rely on the exhaust gases as a spacecraft must. Instead, the propellers of an
airplane act to push air toward the back of the plane, thus pushing the plane forward. A jet does effectively the same
thing, only it uses its turbine to move the air backward. Though ejection of the exhaust in each case gives the airplane
and jet a bit of forward motion, this is not the primary cause of their forward motion as it is with a spacecraft. The
resulting motion that occurs due to mass ejection is often referred to as recoil.

A final comment on Example 7.3.4: It is clear that throwing one baseball did not give the girl an appreciable velocity.
Had she kept throwing balls, her velocity would continue to increase. Even so, considering the very small increase
in her velocity after throwing one ball, it seems clear that in order to increase her velocity appreciably, she would
need to throw many baseballs. This highlights the enormous fuel requirements for spacecraft. The recoil needed
for a spacecraft to leave earth is considerable. In fact, 90% of the mass of a spacecraft is fuel! It is an interesting
problem, though, beyond the scope of this book, to show that ejecting mass continuously rather than all at once (for
example, throwing one baseball at a time as opposed to all of them at once) will achieve a greater recoil velocity.

Check Your Understanding

1a. If a second baseball is thrown from the bag, and another computation is done in order to determine the girl’s
resulting velocity, what is the initial momentum of the system?

Answer:It depends!