About Midterm Exam 2 • When and where – Thurs March 24 th 5:45-7:00 pm (after the break) – Rooms: Same as Exam I, See course webpage. – Your TA will give a brief review during the discussion session. • Coverage: Chapts 5 – 8 (4 chapters) • Format – Closed book, 20 multiple-choices questions (consult with practice exam) – 1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. – Bring a calculator (but no computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron. – Fill in your ID and section # ! • Special requests: – If different from Exam I, email me at [email protected]. edu – One alternative exam: 3:30pm – 4:45pm, Thurs Mar. 24, room TBA. Chapter 8 (cont.) Conservation of Linear Momentum Two dimensional collisions, varying mass and rocket propulsion 1
Transcript
About Midterm Exam 2• When and where
– Thurs March 24th 5:45-7:00 pm (after the break)
– Rooms: Same as Exam I, See course webpage.
– Your TA will give a brief review during the discussion session.
• Coverage: Chapts 5 – 8 (4 chapters)
• Format
– Closed book, 20 multiple-choices questions (consult with practice exam)
– 1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc.
– Bring a calculator (but no computer). Only basic calculation functionality
1. m1 collides with m2, completely inelastically. Both m2 and m1 then move together with a velocity Vf (before having risen significantly).
2. Both (m1 + m2) rise a height h, conserving mechanical energy E. (no non-conservative forces acting after collision)
Ex: Ballistic Pendulum
What is the initial velocity vli of the projectile? Known quantities: m1, m2, h
04/19/23 2Phys 201, Spring 2011
• Stage 1: Momentum is conserved Energy is not conserved
in x-direction:
Stage 2: Energy is conserved
Substituting for V gives:
Ex: Ballistic Pendulum
m1v1i = m1 + m2( )Vf
K +U conserved:12
m1 + m2( )Vf2 = m1 + m2( )gh⇒ Vf = 2gh
v1i = 1+m2
m1
⎛
⎝⎜⎞
⎠⎟2gh
04/19/23 3Phys 201, Spring 2011
Collisions or Explosions in Two Dimensions
y
x
before after
• Ptotal,x and Ptotal,y independently conserved
*Ptotal,x,before = Ptotal,x,after
*Ptotal,x,before = Ptotal,x,after
04/19/23 4Phys 201, Spring 2011
Explosions“before”M
A
Which of these is possible?
A (p appears conserved)
B (p not conserved in y direction)
both
B
“after”
04/19/23 5Phys 201, Spring 2011
Explosions“before”M
A
B
Which of these is possible?
A (p not conserved in y direction)
B
neither
“after”
04/19/23 6Phys 201, Spring 2011
• Assuming– Collision is elastic (KE is conserved)– No spin is imparted– Balls have the same mass– One ball starts out at rest
• Then the angle between the balls after the collision is 90o
ppf
ppi
FF PPf
before after
vvcm
Shooting Pool...
04/19/23 7Phys 201, Spring 2011
Shooting Pool• Elastic means conservation of kinetic energy
This is the Pythagorean formula for a right triangle
• Momentum conservation:
1
2m0v0
2 =p02
2m0
⎛
⎝⎜⎞
⎠⎟=
p12
2m1
+p22
2m2
if m0=m1=m2 , then
p02 =p1
2 + p22
Choose axes such that the initial momentum is in x direction, then
Initial:Px = p0
Py = 0
y
xθ
Φ
p1
p204/19/23
p0
p2
p1
Then we should have:
Θ + Φ = 900
Then cos θ = sin Φ and cos Φ = sin θ
8Phys 201, Spring 2011
• Tip: If you shoot a ball spotted on the “dot”, you have a good chance of scratching !
Shooting Pool...
04/19/23 9Phys 201, Spring 2011
04/19/23 10
• Suppose rain falls vertically into an open cart rolling with negligible friction along a straight horizontal track. As a result of the accumulating water, the speed of the cart 1. increases.
2. does not change.
3. decreases. • Mass is increasing - vertical impulse by
track - inelastic collision
• Mass is increasing and the horizontal momentum is fixed
• So the velocity must decrease! and so does kinetic energy (p2/2M)
Phys 201, Spring 2011
04/19/23
Continuously variable mass
• At t: M with v;
plus ΔM with u • At t+Δt: M+ΔM
with v+Δv.
Thus the impulse:
11Phys 201, Spring 2011
04/19/23
Continuously variable mass
In terms of the “relative velocity”
We arrive:
12Phys 201, Spring 2011
04/19/23
Rocket (jet) Propulsion• The operation of a rocket (jet) depends on the law of
conservation of momentum as applied to a system, where the system is the rocket plus its ejected fuel– This is different than propulsion on the earth where two objects exert
forces on each other• road on car• train on track
• The rocket is accelerated as a result of the thrust of the exhaust gases
• This represents the inverse of an inelastic collision– Momentum is conserved– Kinetic Energy is increased (like the explosion process, at the
