Wednesday, May 25, 2011

Announcements:

• Estimated course grades to date are now posted on Blackboard.
• Let me know if my records do not agree with yours.

Assignments:

• HW9 is due at midnight tonight
• Read Chapter 10 and submit HW10 by midnight Friday
• Speeding Ticket Real-World Problem is due today.

Chapter 9:  Momentum and Collisions

Newton's Second Law (as Newton defined it):  F = dp/dt

Momentum (linear) is defined as:  p = mv

If no external forces act on a system, momentum is conserved (constant): pi = pf
A 2-dimensional collision can be analyzed along x and y axes.

Impulse = F*t = change in momentum

In an inelastic collision, momentum is conserved, but kinetic energy is not.
In an elastic collision, both momentum and kinetic energy are conserved.
Most collisions are partially elastic/inelastic.

Demo:  Momentum in one dimension - colliding carts

	m1	m2	v1i	v2i	p	v1f	v2f	KEi	KEf
elastic	m	m	0	v	mv	v	^0	0.5mv^2	0.5mv^2
elastic	m	m	v	-v	0	-v	v	mv^2	mv^2
elastic	m	2m	0	v	2mv	4v/3	v/3	mv^2	mv^2
elastic	m	2m	v	0	mv	-v/3	2v/3	0.5mv^2	0.5mv^2
inelastic	m	m	0	v	mv	v/2	v/2	0.5mv^2	0.25mv^2
inelastic	m	m	v	-v	0	0	0	mv^2	0
inelastic	m	2m	0	v	2mv	2v/3	2v/3	mv^2	0.66mv^2
inelastic	m	2m	v	0	mv	v/3	v/3	0.5mv^2	0.33mv^2

Problem:  If you are lazy and want to close a door by throwing a ball at it, should you throw a rubber ball or a ball of clay with the same mass?  Where should you aim?

Demos:

• Skateboard momentum
• Rocket balloon
• Egg in sheet/airbags
• Happy/sad balls
• Ballistic pendulum - Why not use KE = PE ?
• Newton's cradle
• AstroBlaster/2 ball bounce
• Ballistocardiograph (BCG)

Example Problem:  If you jump up in the air to a height, h, how much force does the ground exert on you when you land?  What do you need to know?

Solution:  You need to know the distance your body moves as you bend your knees:  x ~ 0.5 m
From conservation of energy, your speed just before touching the ground is:  v = sqrt(2gh).
From here, you can take two different approaches to solve this problem:

Conservation of energy:  work done by ground = change in kinetic energy
    F*x = 0.5mv²
    F = mv²/(2x)

Conservation of momentum:  impulse = change in momentum
    F*t = mv
    x = 0.5at²  and v² = 2ax, so t = 2x/v
    so  F = mv²/(2x)   - same as above for conserv. of energy

What is the maximum height a person can fall without suffering severe injury?
(see also problem 50 in chapter 5).
Human acceleration response data

Ponderable:  What would cause more damage:  a fast-pitch baseball, a speeding bullet, or an orbiting paint chip?  Is momentum or kinetic energy more relevant in answering this question?

Object	mass (g)	speed (m/s)	P (kg*m/s)	KE (J)
fast-pitch baseball	150	40	6	120
speeding bullet	5	400	2	400
orbiting paint chip	0.1	8000	0.8	3200

Responses to Minute Paper comments and questions from students last summer:

• I am very concerned about how to do well on the tests in this class. - Study as much as you can by solving suggested problems, answering conceptual questions, and practicing with previous exams or online quizzes.
• How do we get extra credit for original real-world problems? - See the instructions under real-world problems on the course syllabus.
• How much time is reasonable to spend on Mastering Physics? - These homework sets are intended to require about an hour and a half each.  Some problems can take a long time to solve if you get stuck, so I recommend not spending more than half an hour on any one problem.  I know that it is tempting to try to get 100% on every problem set, but you should budget your time wisely so that you do not spend too much time and energy on any one area.
• I get confused with signs and staying consistent throughout a problem. - You are not alone!  I have trouble with this too!
• What is the difference between momentum and impulse? - They are essentially the same, just different ways of conceptualizing the same value (one in terms of force and time, the other in terms of mass and motion).
• For Conceptual Exercise 9.14, why doesn't the triangle balance at M/2? - Because the mass (weight) is not distributed equally on both sides of the fulcrum.  The reasoning will become more clear when we study torques in Chapter 11.
• Is potential energy always positive? - No, not if the final height is lower than the initial height.
• Momentum is fun!  Is there a momentum meter? - I don't think so; perhaps you can invent one!