1. Momentum Conservation

2. Law of Action Redefined
Newton originally framed the second law (acceleration) in terms of momentum, not velocity.
The rate of change in momentum is proportional to the net force and the change is in the same direction as the force
Final momentum: changed by the force
Rocket: has momentum
Initial momentum
Force: changes momentum

3. Momentum Change
If two forces are equal in magnitude, then the changes in momentum are equal in magnitude.
F12
pf1
pi2
pi1
pf2
F21

4. Internal Forces
When two bodies strike each other they exert a force on each other.
Considered together they are called a system.
The internal forces cancel out from the law of reaction.
Equal and opposite
The external forces remain.
F21
F12
Fg1
Fg2

5. Isolated System A system with no external forces is isolated.
Only internal forces that cancel out
The net change in momentum for all internal forces must be zero.
Total momentum in an isolated system is constant.
Zero change means constant value

6. Separation
A 732 kg satellite attached to a 325 kg booster rocket coast at 5.22 km/s.
Explosive bolts cause a separation in the direction of motion propelling the satellite at 6.69 km/s.
Find the momentum of the booster and the amount of energy in the explosion. V M v1 v2 m1 m1

7. Break Up Before the split, momentum is P = MV
M total mass
V initial velocity
After the split, the sum of momentum is conserved.
P = m1v1 + m2v2
Momentum is conserved.
Initial conditions:
M=732 kg+325 kg=1057 kg
V = 5.22 km/s = 5220 m/s
P = 5.52 x 106 kg m/s
Final satellite momentum:
m1 = 732 kg
v1 = 6.69 km/s
p1 = 4.90 x 106 kg m/s
Final booster momentum
p2 = 0.62 x 106 kg m/s
m2 = 325 kg
v2 = 1.91 km/s

8. Explosion Before the split, kinetic energy is Ki = (1/2)MV2
M total mass
V inital velocity
After the split, the explosion adds kinetic energy.
Kf = (1/2)m1v12 + (1/2)m2v22
The kinetic energy is not conserved, but energy is.
Initial conditions:
M = 1057 kg
V = 5.22 km/s = 5220 m/s
Ki = 14.4 GJ
Final energies:
K1 = 16.4 GJ
K2 = GJ
Kf = 17.0 GJ
Explosion energy:
KX = 2.6 GJ

9. Law of Reaction Redefined
The law of reaction can be defined in terms of momentum.
In an isolated system the total momentum is conserved.
total momentum of the rocket and gas stays the same
rocket
hot gas is forced out
rocket momentum increases
reaction force acts on the rocket

10. Thrust
If there is no external force the force to be applied must be proportional to the time rate of change in mass.
The mass changes by Dm
The velocity changes by Dv
The mass added or removed had a velocity u compared to the object
The force u(Dm/Dt) is the thrust

11. Water Force Thrust can be used to find the force of a stream of water.
A hose provides a flow of 4.4 kg/s at a speed of 20. m/s.
The momentum loss is
(20. m/s)(4.4 kg/s) = 88 N
The momentum loss is the force.

12. Heavy Water
Water is poured into a beaker from a height of 2 m at a rate of 4 g/s, into a beaker with a 100. g mass.
What does the scale read when the water is at 200. ml in the beaker (1 ml is 1 g)?
Answer: 302 g
There is extra momentum from the falling water.
This is about N or an equivalent mass of 2.4 g.