velocity
 dx / dt 
 dr 
v
 dy / dt ;
dt
dz / dt 


p

m
v
;
momentum
impulse




dp  [dp] A  [dp]B  [dp]C ...
Force
 [dp ] A
FA 
dt
Weight


Fg  m g
Total Momentum

 

ptot  p1  p2  p3 ...
System’s Center Of Mass
Motion of COM

rCM



m1 r1  m2 r2  m3 r3 ...

M





M vCM  m1 v1  m2 v2  m3v3 ...  ptot
Internal versus external interactions.
No external interactions  ptot conserved
Inertial frames of reference:
Not accelerated (not rotating or any other kind of accel…)
C4R.1 A 56-kg canoeist sits at rest at the
back end of a 23-kg canoe. The canoe is at
rest in the still water of a lake with its front
end about 0.50 m from the dock. The
canoeist realizes that she has left the
paddle on the dock, so she carefully works
her way to the front of the 3.8-m canoe. Is
she likely to be able to reach the dock from
the front of the boat?
A.Yes;
B.No;
x=3.2 m
C.Mmmmmhhhh….. I don’t know.
Translation:
Given xi, L, mperson, mcanoe, calculate xf
What remains constant?
No external forces  Center of Mass fixed.
C5T.7 Two hockey pucks are sliding on a flat,
horizontal plane of frictionless ice. One puck has
twice the mass of the other. They approach each
other, collide, and stick together.
Initially the light puck is moving east at 3 m/s and
the heavy puck is moving west at 2 m/s. The final
velocity of the joined puck is:
A.Eastward;
B.Westward;
C.Zero;
D.Impossible to determine.
C5T.8 Two hockey pucks are sliding on a flat,
horizontal plane of frictionless ice. One puck has
twice the mass of the other. They approach each
other, collide, and stick together.
Initially the light puck is moving west at 4 m/s and
the heavy puck is moving south at 2 m/s. The final
velocity of the joined puck is:
A.Northeast;
B.Northwest;
C.Southeast;
D.Southwest;
E.Zero.
C5T.9 Two hockey pucks are sliding on a
flat, horizontal plane of frictionless ice. One
puck has twice the mass of the other. They
approach each other, collide, and stick
together.
Initially the light puck is moving south and
the final speed of the joined pucks is zero. The original
Velocity of the heavy puck must have been nortward:
A.True;
B.False;
C.I don’t know.
C5R.1 A small asteroid of mass 2.6×109 kg is discovered traveling
at a speed of 18 km/s on a direct heading for Starbase Alpha,
which is in deep space well outside the solar system. Lacking
weapons of sufficient power to destroy the asteroid, the frightened
starbase inhabitants decide to deflect it by hitting it with a remotecontrolled spaceship. The spaceship has an empty mass of
25,000 kg and a top speed of 85 km/s when its fuel is exhausted.
The asteroid has to be deflected so that by the time it reaches the
starbase, its center is 1800 m away from its original path. What is
the minimum distance before the asteroid’s projected impact that
the spaceship must reach the asteroid?
A.
B.
C.
D.
4×103 m;
4×105 m;
4×107 m;
4×109 m.
C5A.1 Consider a rocket in deep space whose
empty mass is 5200 kg that can carry 52,000 kg
of propellant. If the rocket engine can eject 1300
kg/s of propellant from its nozzle at a speed of
3300 m/s relative to the rocket, and if the rocket
starts at rest, what is its approx. final speed?
A.
B.
C.
D.
102 m/s;
104 m/s;
106 m;
108 m.