1. Test corrections due today. Today’s topics – Conservation of momentum
Announcements
Test corrections due today.
Today’s topics –
Conservation of momentum
Notion of impulse
Analysis of collisions
Elastic
Inelastic
11/22/2018
PHY Lecture 10

2. Generalization for a composite system:
Linear momentum: p = mv
Generalization for a composite system:
Conservation of momentum:
Energy may also be conserved (“elastic” collision)
or not conserve (“inelastic” collision)
11/22/2018
PHY Lecture 10

3. Snapshot of a collision:Pi
Impulse: Pf
11/22/2018
PHY Lecture 10

4. Example from HW:
Plot shows model of force exerted on ball hitting a wall as a function of time. Given information about pi and pf , you are asked to determine Fmax.
11/22/2018
PHY Lecture 10

5. Dp=(-mvf sin qf - mvi sin qi) i +(-mvf cos qf + mvi cos qi) j m vi qi
Notion of impulse:
FDt = Dp
Example:
Dp = mvf - mvi
Dp=(-mvf sin qf - mvi sin qi) i
+(-mvf cos qf + mvi cos qi) j m vi qi qf vf
-pi pf
11/22/2018
PHY Lecture 10

6. Dp=(-mvf sin qf - mvi sin qi) i +(-mvf cos qf + mvi cos qi) j Example:
Notion of impulse:
cause effect
Dp = mvf - mvi
Dp=(-mvf sin qf - mvi sin qi) i
+(-mvf cos qf + mvi cos qi) j
Example: m vi qi
Dp = pf - pi = F Dt qf vf
-pi pf
11/22/2018
PHY Lecture 10

7. Example: Suppose that you (mg= 500 N) jump down a distance of 1m, landing with stiff legs during a time Dt=0.1s. What is the average force exerted by the floor on your bones?
11/22/2018
PHY Lecture 10

8. 11/22/2018
PHY Lecture 10

9. Analysis of before and after a collision:
One dimensional case:
Conservation of momentum: m1v1i + m2v2i = m1v1f+m2v2f
If energy (kinetic) is conserved, then:
½ m1v1i2 + ½ m2v2i2 = ½ m1v1f2+ ½ m2v2f2
Extra credit: Show that
11/22/2018
PHY Lecture 10

10. More examples in one dimension:vi vf
before
totally inelastic collision
Conservation of momentum: m1vi = (m1+m2) vf
Energy lost:
11/22/2018
PHY Lecture 10

11. Elastic collision in 2-dimensions
Statement of conservation of momentum:
If mechanical (kinetic) energy is conserved, then:
 4 unknowns, 3 equations -- need more information
11/22/2018
PHY Lecture 10

12. Conservation of momentum Detector measures v2f , f
Example:
Conservation of momentum
Detector measures v2f , f
Note: energy is not conserved in this case.
11/22/2018
PHY Lecture 10

13. Elastic collision v1i q1 q2 Special case: m1 = m2 v1f v2f
q1 + q2 = 90o
11/22/2018
PHY Lecture 10

14. Suppose you are given h1, m1, m2 -- find h2 (assume elastic collision)
Other examples: h2
Suppose you are given h1, m1, m2 -- find h2 (assume elastic collision)
11/22/2018
PHY Lecture 10