Purpose: To observe the quantities that are conserved in two dimensional collisions where the objects recoil after the collision.

THEORY: In an elastic collision both kinetic energy and momentum are conserved. In the following equations; 1 and 2 designate the two objects colliding, unprimed variables indicates those before the collision and primed variables indicated after the collisions, p is momentum, KE is kinetic energy, M is mass, and V is velocity.

Conservation of momentum (a vector equation):

Conservation of kinetic energy (a scalar equation):

EQUIPMENT: Computer, and VideoPoint software.

PROCEDURE: There are several video files from which to chose. From the "PRU" subdirectory chose one of the following: For elastic collisions pru002, pru003, pru007, pru008, pru009, pru010, pru015, or pru018.

With the VideoPoint software mark the position of the object as it moves as demonstrated in the "Instructions for using VideoPoint". It will me necessary to collect data for each object in the collision. The velocities before and after the collision should be constant. The velocities can be calculated by dividing the distance traveled by the object by the time of travel. This data is available in VideoPoind by taking the differences between the final and initial readings both before and after the collision. Knowing the masses and velocities is enough information to finish the calculations. A step-by-step procedure for using VideoPoint is at the end of the experiment.

1. Calculate the initials and final velocities in the X and Y directions by dividing the distance traveled by the elapsed time..

2. Calculate the X-component and Y-component of the momentum of each object in the collision before and after the collision. Find the total momentum before and after the collision and find the percent error in agreement of these values.

3. Calculate the kinetic energy of each object in the collision before and after the collision. Find the total kinetic energy before and after the collision and find the percent error in agreement of these values.
 
 

QUESTIONS:

1. Where did the kinetic energy go in the inelastic collision if it was not conserved?

2. Look at the data and estimate the time it took for the collision to occur. Using the fact that the impulse is equal to the change in momentum, estimate the forces involved in the collision.

3. Was it approximately true that momentum was conserved in both the elastic and the inelastic collisions?

4. If one of the objects is intiially at rest, what is the angle between the directions of the two objects after the collision if they have equal masses?

5. In an elastic two-dimensional collision can the final velocities of the two particles be found by only knowing their initial velocities and masses?

STEP - BY - STEP Procedure for VideoPoint

Start VideoPoint.

Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.

In the "open" dialogue box do the following.

Select the drive letter of the CD drive in which VideoPoint is located.

Select movies folder and the appropriate folder under movies (here the "pasco" folder).

Under filename select the appropriate file to be loaded.

Press "OK".

The "Number of points" dialogue box will appear. Make sure "2" is selected and press "OK". The movie and software should now be loaded.

Record the masses listed in the first frame of the movie.

On the menu bar select "Movie" and "Full Screen" using the left mouse button.

Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on a point on one of the object and press the left mouse button. Repeat this process for the other object. The movie will advance one frame and the data is recorded. Repeat this process in the same order until all frames of the movie have been used. Be consistent and use the same point on the cart each time to record the data. Calibrate the movie.

Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.

The "Scale Movie" dialogue box appears. Select continue with the left mouse button.

Put the target cursor on the left end of the meter stick in the first movie frame and press left mouse button - repeat for the right end of the meter stick.

On the menu bar select "Movie" and "Normal Size".

Transfer the data

Observe the movie frame where the collision occurred and record the change in positions and elapsed time for the two frames immediately before and the two frames immediately after the collision

With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button and drag the

table to top of window.

Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seen.

p_x1 = M₁V₁ = ________ p_x2 = M₂V₂ = ___________

p_y1 = M₁V_y1 = ________ p_y2 = M₂V_y2 = ___________

p_x1` = M<sub>1</sub>Vx1` = __________ p_x2` = M<sub>2</sub>V<sub>x2</sub>` = __________

p_y1` = M<sub>1</sub>V<sub>y1</sub>` = __________ p_y2` = M<sub>2</sub>V<sub>y2</sub>` = __________

Total X-momentum before collision = p_x1 + p_x2 = _______________

% error _________

Total X-momentum after collision = p_x1` + p<sub>x2</sub>` = _______________

Total Y-momentum before collision = p_Y1 + p_Y2 = _______________

% error _________

Total Y-momentum after collision = p_x1` + p<sub>Y2</sub>` = _______________

Kinetic Energy {V₁ = (V_x1² + V_y1²)^.5 , V₂ = (V_x2² + V_y2²)^.5, V`<sub>1</sub> = (V`_x1² + V`<sub>y1</sub>²)<sup>.5</sup> , and V`₂ = (V`<sub>x2</sub>² + V`_y2²)^.5}

KE₁ = 1/2M₁V₁² = ___________ KE₂ = 1/2M₂V₂² = __________

KE₁` = 1/2M<sub>1</sub>V<sub>1</sub>`² = __________ KE₂` = 1/2M<sub>2</sub>V<sub>2</sub>`² = __________