1. 7.3 Conservation of Momentum
Internal and external forces can act on a system.
System
Environment
Internal forces = rider pushes on handlebars; handlebars push back on rider
External forces = tire exerts force on road; road exerts force against tire
Only external forces can change a system's momentum. Internal forces have no effect on a system's momentum.
Internal forces, like all forces, always occur in action-reaction pairs.
Because the forces in action-reaction pairs are equal and opposite - as required by Newton's Third Law - internal forces always sum to zero:
Because internal forces always cancel, the total force acting on a system is equal to the sum of the external forces acting on it:
We don't have to consider internal forces when calculating the total force on a system.

2. Momentum remains equal to zero until a nonzero total external force causes it to change.
If the total force is zero, Ftotal = 0, then the initial and final momenta must be the same, pf = pi. This is momentum conservation.
I = F t = pf - pi

3. Momentum conservation applies to all systems.
Momentum conservation results in recoil.

4. p. 247 37.) No, because conservation of momentum would be violated.
34.) the total momentum cannot change.
35.) They do not.
36.) Momentum is conserved for the system of the two skaters. Internal forces are those the two skaters exert on each other. External forces are weights and normal forces.
37.) No, because conservation of momentum would be violated.
38.) The momentum of the keys is not conserved because the external force of gravity continually increases their momentum. However, the momentum of the universe remains the same because both the Earth and the keys experience equal and opposite gravitational forces that change their momenta by the same amount but in opposite directions.

5. 7.4 Collisions Collisions
Collision = a situation where two objects free from external forces strike one another.
Collisions
Elastic collision
Inelastic collision
Momentum is conserved
Momentum is conserved
KE is conserved
KE is not conserved
Some of the initial KE is converted to sound, heat, and deformation
Objects rebound off each other
Completely inelastic collision
Most of the initial KE is converted to sound, heat, and deformation
Colliding objects stick together

6. ptotal = ptotal mv = 2mvf 1/2 v = vf KEinitial = 1/2 m v2
Completely Inelastic Collisions: Same mass
Momentum:
Car 1
Car 2
p1 = mv p2 = 0
ptotal = mv + 0 = mv
p1 = mvf p2 = mvf
ptotal = mvf + mvf = 2mvf
ptotal = ptotal
mv = 2mvf
1/2 v = vf
Kinetic Energy:
KEinitial = 1/2 m v2
KEfinal = 1/2 (2m) (1/2 v)2 = 1/4 m v2 = 1/2 KEinitial

7. Completely Inelastic Collisions: Different masses
pi = pf
Completely Inelastic Collisions: Two Dimensions
p. 253
(Both the x and the y components of momentum are conserved separately. Here x is chosen arbitrarily.)

8. pf = pi KEf = KEi Elastic Collisions p. 256
Elastic collisions conserve energy and momentum.
pf = pi
KEf = KEi
Remember that since we are using velocities, not speeds, the objects can reverse directions, so their velocities can be positive or negative.
p. 256
49.) If no external forces act on the system, then the total momentum cannot change.
50.) they are equal
51.) It is converted to other forms of energy.
52.) a completely inelastic collision
53.) The total external force (such as friction, gravity, normal forces, etc.) must be zero.
54.) No; the collision could be partially inelastic