1. 6 Linear Momentum & Collisions
Motion and its conservation
Impulse-Momentum Theorem
Homework:
6, 9, 13, 21, 40, 63, 72, 87.

2. Conserved Quantities Energy – has __________________
Motion – has only _______________
How does Nature conserve motion?
Speed?
Velocity?
Mass x Velocity?

3. Motion and Its Conservation
Not Conserved
Not Conserved
Not Conserved
Conserved
Conserved
stops
smooth and level
rough

4. Momentum Momentum = mv Symbol: p , P . SI Unit: kg·m/s
Ex. 1000kg car moves at 8m/s.
mv = (1000kg)(8m/s) = ______________ kg·m/s

5. Impulse impulse = Ft force x time = change in momentum
SI Unit: N·s = kg·m/s
Ex. A 4000N force acts for 0.010s.
impulse = Ft = ______________= 40 N·s

6. Impulse and Momentum Impulse = Ft = ______________________
consequence of Newton’s 2nd law that Ft = change in momentum
F = ma
Ft = mat
Ft = (m)(at)
Ft = (m)(Dv)
_____________________

7. Impulse Example
A braking force of 4000N acts for 0.75s on a 1000kg car moving at 5.0m/s.
impulse = Ft = (-4000N)(0.75s) = N·s
mDv = Ft = kg·m/s
Dv = (-3000 kg·m/s)/1000kg = -3m/s
vf = vi + Dv
= ____________

8. Collisions “Brief” interaction between objects
Objects share the collision force (N3L)
One object gets +Ft, the other gets –Ft.
As a whole, they receive no impulse, thus no change in total momentum of this system (due to the collision)

10. Conservation of Momentum (i.e. Motion):
Initial Momentum (Motion):
Final Momentum (Motion):
(Since )

11. Collisions elastic: total KE _________________
inelastic: total KE ________________
complete inelastic: objects move at _____________________ after collision, total KE decreases

12. Conservation of Linear Momentum

13. 2 objects (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final
Each car has mass 1000kg
(1000)(10) + (1000)(0) = (1000)v + (1000)v
10,000 = 2000v v = 5 m/s

14. When does Conservation of Momentum occur?
Answer: When Fnet = 0 (e.g. level frictionless surface)
or _______________________________

15. Conservation of Momentum may occur when KE is lost
Ex: Mass m, Speed v, hits & sticks to another mass m, speed = 0. Final speed of each object is v/2.
K-initial = ½(m)(v)2 + 0 = ½mv2.
K-final = ___________________________
______ the original KE converted to heat, sound, etc.

16. 2 dimensional p conservation

17. Example: m1 = 0.010kg, m2 = 1.0kg, v1i = 200m/s.
Calculate vf (mom. cons.), Then calculate h (using energy).

18. Summary momentum = mass x velocity Ft = change-in-momentum
Momentum is conserved when net external forces are negligible
Momentum conservation may occur for elastic & inelastic collisions