Impulse and momentum lab answers

Virtual Lab: Impulse and Momentum

Introduction

The momentumof a moving particle is defined as

whereis the mass of the particle andis its velocity.

The impulseof a forceacting during a time interval is defined as

whereis the average force.

The JavaScript provided with this document simulates the elastic collision of two carts in one dimension, along an 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 forcesandchange with time in a separate graph. Get familiar with running the simulation by changing the different available setting and controls, and observe their effects.

Virtual Lab Procedure

Part A

1. Set the two masses to equal values (ex.kg) and run the simulation five times for different initial velocities.

2. Record the values ofand in the data table below.

3. For each step, record the initial velocitiesand you chose, the final velocitiesand calculated by the JavaScript simulation, and estimate from the graph the areas between the curves and the horizontal axis, and then report them asand 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.

Table 1.

Cart 1, [kg]

Cart 2, [kg]

[m/s]

[m/s]

[kg m/s]

[N s]

[%]

[m/s]

[m/s]

[kg m/s]

[N s]

[%]

Part B

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, [kg]

Cart 2, [kg]

[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 impulsefor 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 ofnegative, whileis 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.