Lab #9:
BOARD MEETING GAMMA
Collision Elasticity & Relativity
Physics 203: Prof. Daniel A. Martens Yaverbaum, Prof. Max S. Bean
John Jay College of Criminal Justice, the CUNY
Consider the following scenario (Two Pool Balls):
Answer ALL questions on paper with your groups; THEN POST RESPONSES to the STARRED QUESTIONS
ON YOUR WHITE BOARDS.
I. Perfectly INELASTIC—ONE-DIMENSIONAL.
For this preliminary problem, make the UNREALISTIC ASSUMPTION that the two balls have glue all over their
surfaces so that they STICK TOGETHER upon colliding.
Assume that the NUMBERS written on their balls on their MASSES (in grams) and that any velocity that you are
given or that you calculate is constant (there is no acceleration except during the tiny time interval of collision itself.)
Assume that the balls rolls toward each other with equal and opposite constant velocities—along an x-axis that
might require you to tilt your head a bit.
In the reference frame (perspective) of the LAB (pool hall):
The 10-ball approaches with an initial velocity of +200 cm/s.
The 13-ball approaches with an initial velocity of -200 cm/s.
Answer the following questions from the reference frame (perspective) of the LAB:
A. AFTER THE COLLISION, at what velocity will the 10 & 13 combination travel?
B. BEFORE THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
C. BEFORE THE COLLISION, what is the momentum of the CENTER OF MASS of this 2-ball system?
D. AFTER THE COLLISION, what is the momentum of the CENTER OF MASS of this 2-ball system?
E. AFTER THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
F. *** In ONE COMPLETE SENTENCE OF ENGLISH, Justify any relationship you do or do not find between answers (B)
and (E).
G. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 10-ball?
H. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 13-ball?
I.
*** AS A RESULT OF THE COLLISION, How much momentum does the 10-ball lose?
J. *** AS A RESULT OF THE COLLISION, How much momentum does the 13-ball gain?
K. AFTER THE COLLISION, how much momentum does the 10<>13 combination have?
Answer the following questions from the reference frame (perspective)
of the CENTER OF MASS:
L. BEFORE THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
M. AFTER THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
N. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 10-ball?
O. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 13-ball?
P. *** AS A RESULT OF THE COLLISION, How much momentum does the 10-ball lose?
Q. *** AS A RESULT OF THE COLLISION, How much momentum does the 13-ball gain?
R. In one complete sentence of English, would the relationship between your answers to N and O be different for
different types of collisions?
S. AFTER THE COLLISION, how much momentum does the 10<>13 combination have?
II. Perfectly ELASTIC—ONE-DIMENSIONAL.
For this preliminary problem, make the VERY (but not perfectly) REALISTIC ASSUMPTION that the surfaces of the
two balls act like extremely high-K Hooke’s Law springs so the that collide PERFECTLY ELASTICALLY.
Assume that the NUMBERS written on their balls on their MASSES (in grams) and that any velocity that you are
given or that you calculate is constant (there is no acceleration except during the tiny time interval of collision itself.)
Assume that the balls rolls toward each other with equal and opposite constant velocities—along an x-axis that
might require you to tilt your head a bit.
In the reference frame (perspective) of the LAB (pool hall):
The 10-ball approaches with an initial velocity of +200 cm/s.
The 13-ball approaches with an initial velocity of -200 cm/s.
Answer the following questions from the reference frame (perspective) of the LAB:
A. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 10-ball?
B. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 13-ball?
C. BEFORE THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
D. BEFORE THE COLLISION, what is the momentum of the CENTER OF MASS of this 2-ball system?
E. AFTER THE COLLISION, what is the momentum of the CENTER OF MASS of this 2-ball system?
F. AFTER THE COLLISION, what is the velocity of the CENTER OF MASS of this 2-ball system?
G. AS A RESULT OF THE COLLISION, should the 13-ball gain more, less or the same momentum as the the 10-ball
loses?
-Answer the following questions from the reference frame (perspective)
of the CENTER OF MASS:
H. *** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 10-ball?
I.
*** BEFORE THE COLLISION, what is the LINEAR MOMENTUM of the 13-ball?
J. AFTER THE COLLISION, what is the velocity of the 10-ball?
K. AFTER THE COLLISION, what is the velocity of the 13-ball?
L. ***AS A RESULT OF THE COLLISION, How much momentum does the 10-ball lose?
M. ***AS A RESULT OF THE COLLISION, How much momentum does the 13-ball gain?
N. AFTER THE COLLISION, what is the LINEAR MOMENTUM of the 10-ball?
O. AFTER THE COLLISION, what is the LINEAR MOMENTUM of the 13-ball?
Answer the following questions from the reference frame (perspective) of the LAB:
A. *** AFTER THE COLLISION, what is the velocity of the 10-ball?
B. *** AFTER THE COLLISION, what is the velocity of the 13-ball?
Why do objects simply reverse direction (without changing speed) in a
perfectly elastic collision—
when observed from the Center of Mass Reference Frame?!