Name: _______________________________
Date: ______ Per: ____
Momentum1: Keep it Constant
How Does a Collision Affect the Motion of Marbles?
1. Place five marbles, all identical in size and shape, in the center groove of a ruler. Launch a sixth
marble toward the five stationary marbles. Note any changes in the marbles’ motion.
2. Now launch two marbles at four stationary marbles. Then launch three marbles at three
stationary marbles, and so on. Note any changes in the marbles’ motion.
a) Launch two
marbles at four
stationary marbles
b) Launch three
marbles at three
stationary marbles
c) Launch four
marbles at two
stationary marbles
d) Launch five
marbles at one
stationary marble
3. Remove all but two marbles from the groove. Roll these two marbles at each other with equal
speeds. Note any changes in the marbles’ motion.
Analyze and Conclude
1. Observing: How did the approximate speed of the marbles before each collision compare to after
each collision?
2. Drawing Conclusions: What factors determine how the speed of the marbles changes in a
collision?
3. Predicting: What do you think would happen if three marbles rolling to the right and two marbles
rolling to the left with the same speed were to collide?
4. How do you change the velocity of a marble from moving to not moving?
2.1 Observe and Find a Pattern
Imagine observing the following experiments with two frictionless carts moving on a smooth track.
Complete the table that follows for each experiment. Consider your system of analysis to be both carts.
Experiment
Sketch the process before
the collision and after the
collision.
Write a table of knowns.
a) Cart A (200 g)
moving left at a
constant 0.70 m/s
speed hits
identical cart B
(200 g) that is
stationary. Cart
A stops and cart
B starts moving
at speed 0.70 m/s
to the left.
b) Cart A loaded
with blocks (total
mass of the cart
with blocks is
400 g) moving
left at 0.70 m/s
hits stationary
cart B (mass 200
g). After the
collision, both
carts move left,
cart B at speed
0.86 m/s and cart
A at speed 0.27
m/s.
Determine if anything is the same before
and after the collision for the system (i.e.,
is any quantity constant). Hint: think of
mass, speed, velocity, acceleration or some
combination of these quantities.
c) Cart A (200 g)
with a piece of
modeling clay
attached to the
front moves left
at 0.70 m/s.
Identical cart B
(200 g) moves
right at constant
speed 0.70 m/s.
The carts collide,
stick together
thanks to the
clay, and stop.
d) Repeat
experiment (c)
but this time cart
A is loaded (total
mass of the cart
with blocks is
400 g). After the
collision both
carts stick
together and
travel left at
speed 0.23 m/s.
e) After you come up with a physical quantity that is constant in each experiment, decide if the same
quantity is constant in all of the experiments. If not, revisit the experiments and find a physical
quantity that is constant.
Need Some Help?
Constant describes a quantity that does not change during a process. For example, the amount of money
in my pocket is constant from 6 am when I get up to 11 am when I go to lunch. The amount does not
change.
2.2 Test Your Idea: Homework
The following table has data about the collisions of two carts, including the masses of the carts, initial
velocities of the carts before the collision ( vi ), and the final velocities after the collision ( v f ). Determine
whether the same quantity is constant in these experiments as you found before.
Experiment
a)
Cart 1: mass = 2kg,
vi = +2.0 m/s,
vf = +1.0 m/s
Cart 2: mass = 2kg,
vi = 0 m/s,
vf = +1 m/s
b)
Cart 1: mass = 2kg,
vi =+2.0 m/s,
vf = 0 m/s
Cart 2: mass = 2kg,
vi = –2.0 m/s,
vf = 0 m/s
c)
Cart 1: mass = 4kg,
vi =+2.0 m/s,
vf =+0.5 m/s
Cart 2: mass = 2kg,
vi = –1.5 m/s,
vf =+1.5 m/s
d)
Cart 1: mass = 4kg,
vi =+2.0 m/s,
vf = 0 m/s
Cart 2: mass = 2kg,
vi = –2.0 m/s,
vf = +2.0 m/s
Sketch the process before and
after the collision. Clearly
identify your system.
Did the quantity remain
constant? Show your work.
e) Based on the experiments above, make a judgment about the quantity you identified in 2.1.
f) Why is mass x speed not appropriate for the constant quantity? Give an example from the
experiments above where mass x speed is not constant.
Did You Know?
The quantity you just identified is called momentum. Momentum is a fundamental physical quantity
that is possessed by all objects. The momentum p of an object is equal to the object's mass m times the
object's velocity v
r
p  mv .
Momentum is a vector quantity in the same direction as velocity. (It has the same sign as velocity on a
number line coordinate axis.)
g) What are the units for this new physical quantity?