Lab 10: Impulse Momentum You will have to try to find the simulation on the screen-short in the attach files to complete the Lab.
Virtual Lab: Impulse and Momentum
IntroductionThe momentum 
of a moving particle is defined as
Where 
is the mass of the particle and 
is its velocity.
The impulse 
of a force 
acting during a time interval 
is defined as
Where 
is the average force.
The JavaScript provided with this document simulates the elastic collision of two carts in one dimension, along a horizontal axis with a positive direction pointing to the right. It allows a user to change the initial velocities (
and 
) and the masses (
and 
) of the two colliding carts, and it shows the result as final velocities after of the collision (
and 
). It's also showing, with randomly built-in uncertainties, how the (virtually) measured interaction forces 
and 
change with time in a separate graph. Get familiar with running the simulation by changing the different available setting and controls while observing their effects.
1. Set the two masses to equal values (ex. 
kg) and run the simulation five times for different initial velocities.
2. Record the values of and in the data table below.
3. For each step, record the initial velocities and you chose, the final velocities and calculated by the JavaScript simulation, and estimate from the graph the areas between the curves and the horizontal axis, and then report them as 
and 
in the data table (
and 
). To facilitate a better view of the features of the graph, you can zoom in/out with the mouse wheel when the mouse pointer is in the graph area.
4. Calculate the changes in momentum 
and 
and write their values in the table.
5. Calculate the percentage differences 
and 
report them in the data table.
| Cart 1, | Cart 2, | |||||||||
|
[m/s] |
[m/s] |
[kg m/s] |
[N s] |
[%] |
[m/s] |
[m/s] |
[kg m/s] |
[N s] |
[%] | |
[kg]
[kg]
1. Set the two masses to unequal values (ex. 
kg and 
kg) and run again the simulation five times for different initial velocities.
2. Repeat all you did in steps 3 to 5 in part A.
Table 2.| Cart 1, | Cart 2, | |||||||||
|
[m/s] |
[m/s] |
[kg m/s] |
[N s] |
[%] |
[m/s] |
[m/s] |
[kg m/s] |
[N s] |
[%] | |
Questions
1. Show mathematically that a force applied on an object is related to the change in momentum like
.
(you might want to use the general form of the Newton's second Law 
)
2. Based on the data collected while using the JavaScript simulation, what can you conclude if you compare the changes in momentum 
and the values of impulse
for the two carts?
3. Looking at the values of initial and final velocities of both carts in Part A (equal masses), can you observe any systematic behavior of these quantities? Is there a similar trend in the values of initial and final velocities of both carts in Part B (unequal masses)?
4. Consider two masses in a closed system (constant total mass, no mass exchange with the surroundings). Show that Newton's third Law results in conservation of total momentum.
5. Why is the value of negative, while is positive, in all cases in Part A and Part B?
6. Consider a ball of 0.22 kg, initially at rest, is dropped from an initial height of 1.80 m. It rebounds back after colliding with the floor to a final height of 1.50 m. Determine the impulse on the ball delivered by the floor.
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