Worksheet for Exploration 8.1: Understanding Conservation
Laws
Observe the animation to see if you can discover any conservation laws.
You should determine whether your laws hold for the left half of the
animation, the right half animation, or the entire animation. Properties
that you might want to consider are number of particles, color, and sum of
the particle speeds. Restart.
The animation will run for 100 seconds.
i.
For animation 1 play the simulation, then restart and record speeds before and after collisions while
stepping through several collisions. You may start stepping through at any time, you do not need
to catch the first collision.
Speed 1 Speed 2 Speed 3 Speed 4 Speed 5 Sum
col1
2
3
4
5
6
ii.
What conservation law can you come up with for animation 1?
iii.
Do again for animation 2.
Speed 1 Speed 2 Speed 3 Speed 4 Speed 5 Sum
col1
2
3
4
5
6
iv. Describe interactions that you may have observed between objects in animation 2.
Worksheet for Exploration 8.2: An Elastic Collision
The animation shows an elastic collision between two
masses (position given in centimeters and time given in
seconds).
a.
Set the initial velocity of the blue ball to zero. For the three conditions of the relative masses of
the blue and red balls shown in the table, PREDICT what value (or values) of the initial velocity of
the red ball will result in...
i. Fill out the table (predictions).
1.
2.
3.
both balls moving to the right after the collision.
the red ball stopping after hitting the blue ball.
the red ball moving to the left after the collision and the blue ball moving to the right after the
collision.
Enter the range of initial
velocity values for red
ball that results in...
1
2
3
mred = mblue
mred = 2*mblue
mred = 0.5*mblue
AFTER you have made your predictions, test them using the animation. Were you correct? If not, explain.
b.
Now set the initial velocity of the blue ball to -20 cm/s, the initial velocity of the red ball to 5 cm/s,
and the masses equal. PREDICT the direction each ball be traveling after impact. AFTER you
have made your prediction, try it. Were you correct? If not, explain.
Predicted direction Red______________
Predicted direction Blue______________
Measured direction Red______________
Measured direction Blue______________
c.
Set the initial velocity of the blue mass to -10 cm/s and the red mass to half the mass of the blue
ball. PREDICT the velocity the red mass must have in order to completely stop the blue mass
when they collide. Now try it, were you correct? If not, explain.
i.
ii.
d.
Vred=_______
Check your conservation laws and make sure momentum and kinetic energy are conserved for
this elastic collision. Assume the mass of the blue ball is 1.00 kg.
Set the initial velocity of the blue mass to -10 cm/s and the red mass to twice the mass of the blue
ball. PREDICT the velocity the red mass must have in order to completely stop the blue mass
when they collide. Now try it, were you correct? If not, explain.
Vred=_______
Worksheet for Exploration 8.3: An Inelastic Collision with
Unknown Masses
The initial velocities of the two carts in the animation can be changed by
entering new values into the text fields (position is given in meters and time
is given in seconds). As the carts approach one another they stick
together. Restart.
Repeat the animation using varying velocities as you answer the following
questions. Right-click on the graph to make a copy that can be expanded for
better resolution.
NOTE: This is a completely, or perfectly inelastic collision!
a.
Run the animation using 2 m/s and -2 m/s for the velocities of the left and right carts, respectively.
What is the change in velocity of the left cart? The right cart? What is the ratio of these changes?
i.
vgreen i=_______
vred i=_______
ii.
vred f=_______
Careful calculating the change in velocity for each cart. Direction and signs matter!
∆vgreen=_______
∆v green
∆v red
b.
vgreen f=_______
∆vred=_______
= _______
Simulate collisions using other values of equal but opposite velocities. How does this effect the
changes in the velocities? The ratio of the changes?
vgreen i=_______
vgreen f=_______
vred i=_______
vred f=_______
∆vgreen=_______
∆vred=_______
∆v green
∆v red
= _______
c.
Run the animation using 1 m/s and -2 m/s for the velocities of the left and right carts, respectively.
What is the change in velocity of the left cart? The right cart? What is the ratio of these changes?
i. First measure.
vgreen i=_______
vgreen f=_______
vred i=_______
vred f=_______
∆vgreen=_______
∆vred=_______
∆v green
∆v red
ii.
= _______
Now use conservation of momentum to predict the ratio of the change in velocities. Your
expression should be in terms of the masses only.
d.
Is the ratio of the changes in the velocities always the same?
e.
What is the mass ratio of the carts?
Worksheet for Exploration 8.4: Elastic and Inelastic Collisions
and ∆p
Enter in a new value and click the "set values and play" button to register
your values and run the animation (position is given in meters and time is
given in seconds). We have set limits on the values you can choose:
0.5 kg < m1 < 2 kg,
0 m/s < v1 < 4 m/s,
m/s.
and
-4 m/s < v2< 0
The bar graph gives an instantaneous reading of each cart's energy and the check box changes the collision
type from perfectly elastic to perfectly inelastic. Restart.
Answer the following questions for both the elastic and inelastic collisions.
For elastic collisions:
a.
Vary the mass and velocities, is ∆p1 = -∆p2?
i. Measure v1 final and v2 final to determine the change in momentum for each cart.
b.
Why should this be the case?
c.
Is the energy of the system constant (kinetic)? If not, where is it going?
i. Calculate the total kinetic energy before the collision and after.
For inelastic collisions:
d.
Vary the mass and velocities, is ∆p1 = -∆p2?
i. Again measure velocities and calculate the change in momentum for each cart.
e.
Why should this be the case?
f.
Is the energy of the system constant? If not, where is it going?
Worksheet for Exploration 8.5: Two and Three Ball Collisions
If you drop a rubber ball and it hits the ground at 5 m/s
it bounces back at almost the same speed (position
is given in meters and time is given in seconds).
But what happens if you drop two balls stacked one
upon another? A common lecture demonstration has
a professor dropping a light ball and a heavy ball at the same time. The light ball is directly above the heavy
ball so that the heavy ball hits the ground first, bounces back, and then hits the light ball which is still on its
way down. Restart.
This animation uses two balls with a mass to mass ratio of 1:10. We consider motion on a horizontal air
track so we can ignore the effect of gravity so as to make the physics as clear as possible. The balls move
at constant speed to the left before hitting the wall and assume all collisions are elastic.
a.
Predict the velocities of the balls after the first set of collisions. That is, when both balls are moving
to the right.
i. Measure the velocity of each ball just before the collision occurs.
vred i=_______
ii.
Predict the final velocities using results from conservation laws.
vred f=_______
iii.
vgreen i=_______
vgreen f=_______
Measure the velocities after the collision.
vred f=_______
vgreen f=_______
b.
Predict the velocities if you use three balls with mass ratios of 1:10:100.
i. You already have the results of the red/green ball collision above. With the same results for
red and green, the green ball then hits the blue ball. What are the velocities of each ball
immediately after the next collision occurs (green to blue)?
vred later=_______
vgreen later=_______
vblue later=_______
ii.
Now measure each velocity
vred later=_______
vgreen later=_______
vblue later=_______
As a side note, you should notice that the subscript names have been changed from initial, to final,
and then “later” so that different names apply to different numbers (within the same problem).
c.
Now run the animations. Were you correct? If not, explain why.
i.
You should check to ensure that momentum is conserved through each of the ball to ball
collisions in this simulation. However, as a ball hits the edge of the box you may notice it
bounces back. What has happened to conservation of momentum in this instance? Discuss.
Worksheet for Exploration 8.6: An Explosive Collision
The system's total kinetic energy is increased in a 1200 J explosion in the
animation (position is given in meters and time is given in seconds).
Restart.
Use a mass ratio of 1:2 for the following (a,b,c,d). (The initial loadup
conditions).
a.
Draw energy diagrams for the system before and after the explosion.
b.
What percentage of the explosion's energy is converted to kinetic energy?
%Energy Converted=_________
c.
What percentage of the explosion's energy (the initial 1200J) is recoverable?
d.
Is the process shown in the simulation reversible?
Vary the mass of the left cart from 0.1 kg to 1.0 kg for the following questions.
e.
Does the larger or the smaller mass receive the most energy?
i. Using conservation of momentum only, predict the ratio of the smaller masses Kinetic energy
to that of the larger mass.
ii.
How does this compare with your measurements.
f.
Does the larger or the smaller mass receive the most momentum?
g.
Does the ratio of the two masses have any effect on the total resulting kinetic energy?
h.
Does the ratio of the two masses have any effect on the recoverable energy?
Worksheet for Exploration 8.7: A Bouncing Ball
The animation represents the seemingly simple example
of a ball hitting the ground and bouncing back (position is
given in meters and time is given in seconds). The
graph can show velocity vs. time or acceleration vs. time
and can be zoomed in to see the collision with the ground.
Also shown are three bar graphs representing the different
types of energy associated with the ball: the kinetic energy
(orange), the gravitational potential energy (blue), and the
elastic potential energy (green). Restart.
a.
b.
There are 3 important time intervals during the animation. What are they? Briefly describe what is
happening during these intervals.
i. Interval 1, time range & discuss
ii.
Interval 2, time range & discuss
iii.
Interval 3, time range & discuss
Draw energy diagrams, that is, find the values and plot a bar graph, for the kinetic energy of the ball
(vs. time).
c.
Draw the graph of momentum vs. time. Describe what is happening to the momentum during the
three important time intervals. If the momentum of the ball is changing, describe why.
d.
Draw the graph of the net force vs. time. Describe what is happening to the net force on the ball
during the three important time intervals. If the net force of the ball is changing, describe why.