Physics lab report - one page, need it after 2 hours

activity-momentum-cap.docx

Home >Physics homework help >Physics lab report - one page, need it after 2 hours

Conservation of momentum

Objectives

In this activity we test one of the central consequences of Newton’s laws: conservation of momentum. We apply this law to a system of two colliding carts and analyze its validity for different types of collisions.

Background

Momentum is defined, for a single object, as the vector p=mv where m is the mass and v its velocity. But momentum and momentum conservation are concepts most useful in the case of composite systems. For a system with several objects, the total momentum is simply the vector sum of the individual momentum of the components:

In a process in which a constant external force acts on an object during an interval of time t, the total change in momentum is given by the impulse momentum theorem:

where J=F t is the impulse associated with the action of the force.

In a collision between two objects, A and B, the total momentum of the system is

If it is possible to neglect effects of friction between the objects and the environment, the net impulse during the collision is zero. The colliding objects exert force on each other, but by Newton’s third law, these forces are equal in magnitude and opposite in direction so that all these pairs of forces cancel out in the calculation of the total impulse. The result is that the total momentum should be conserved:

Writing this result in terms of the momentum for each object before and after the collision we obtain

As we will work with motion only along a line, we can simply use the x-component of these vectors. We will write pxAi for the initial momentum of the object A in the x-direction. The x-component of the previous equation can then be spelled out as

To prepare for this activity, review the application of the concept of momentum to collisions.

Procedure

A. Interface and Software setup

1. Check that interface is turned on, and that the stereo phone plugs of the two Motion Sensors are connected to the Digital Inputs 1, 2, and 3, 4 respectively. The yellow plugs must be connected to Digital Channels 1 and 3.

2. In Capstone open the file Act-momentum-CAP-file, available in the hard drive or in Blackboard.

3. Create a separate excel table with the following entries: masses of the carts, initial and final velocities of the carts, initial and final momentum of each cart. Add further columns to your spreadsheet as needed. Include columns for comparison of predicted and observed quantities.

B. Equipment setup

You will carry out collisions between two carts, and measure their positions by means of the motion sensors. In each collision you will give a starting push to one or two of the carts. Always start at about 10 cm away from the motion sensor, and do not let your hand interfere with the position measurement. After the collision it might be necessary to stop the carts so that they do not hit the motion sensors. Make sure that the rail is leveled.

We will consider three different types of collisions, and each will require different ends of the carts to collide. You will find carts with “plungers” and with magnets (marked M).

The collision types are:

1) Approximately elastic collision. Use carts with magnets to create a gentle collision between pairs of carts.

2). Totally inelastic collisions. In this case use the plunger side of the cart, but with the plunger fully contracted. In this way, on collision, the velcro pads will stick to each other.

3) Explosive collision. Use again the plunger side of the cart but set the plunger into one of its intermediate positions. On collision, the plunger (may) spring out. It may be necessary to try different initial conditions to observe the explosion.

C. Data collection

Determine the masses of the carts, and the mass of the black bar that will be used to change the mass of the carts.

Start with the elastic collision. Set the carts in their initial positions, press start, and push the carts towards each other. Stop the run after the carts are far away from each other. Analyze the graphs of position versus time for both carts, and determine their initial and final velocities from the graphs’ slopes near the collision point.

Make sure that you correctly translate the recorded slopes into velocities with respect to a selected system of reference. In particular, note that if your system of reference runs from left to right, one of the sensors will measure distances in the opposite direction. You will have to change the signs of the recorded velocities to adapt them to your system of reference.

The first figure on the left shows the results of recording the motion of the two carts. In this setup the top graph corresponds to a cart whose distance from the (left) sensor increases to the right. The bottom graph corresponds to a cart whose distance to the second (right) sensor increases to the left.

The slopes before the collision are determined as shown. The top cart moved to the right at a speed of .412 m/s. Its velocity points to the right and therefore vxAi=0.412 m/s. The bottom cart moved to the left with a speed of 0.422 m/s. Its initial velocity is vxBi= -0.422 m/s.

The slopes after the collision are determined as shown. The top cart moved to the left at a speed of 0.392 m/s. Its velocity points to the left and therefore vxAf= -0.392 m/s. The bottom cart moved to the right with a speed of 0.400 m/s. Its final velocity is vxBf=0.400 m/s.

$C:\Users\fsolis\Documents\Capstone labs\PHY111\Act 10 Momentum\Rawfigures.png$

$C:\Users\fsolis\Documents\Capstone labs\PHY111\Act 10 Momentum\BEfore.png$

$C:\Users\fsolis\Documents\Capstone labs\PHY111\Act 10 Momentum\After.png$

Repeat the experiment adding the mass bar to one of the carts.

Repeat the experiment (with two different mass distributions) using the inelastic collision settings. Make sure that the carts remain stuck after the collision.

Repeat the experiment (with two different mass distributions) using the explosive collision condition. Make sure that the plunger springs open during the collision.

D. Data analysis

Using the data collected, determine the degree of agreement of the experiment with the expected result. The key prediction is that the total final momentum is equal to the total initial momentum. As the initial momentum is often close to zero, to compare the initial and final momentum is not a good approach. Instead, determine and compare the magnitudes of the change in momentum for both carts. That is, we test, more precisely that the change pxA is equal to -pxB. Include columns for these quantities in your excel spreadsheet.

Brief report

1. For each of the runs, test the predictions of momentum conservation in the manner outlined above. Did you find that, within experimental error, momentum is conserved? State your results in the form of a percentage.

2. Carefully review the way in which the data collected was interpreted. In particular, for a set of graphs associated with one run, relate the graph features with events in the experiment, including the actual collision, but also the time during which the cars are being pushed towards each other. Sketch the graphs in your notebook and mark the relevant points.

3. Carefully review the way in which the data collected was interpreted. You should point out how the algebraic signs of specific momentum values were determined.

4. Discuss any relevant sources of error.

xBf

xAf

xBi

xAi

...

Ppp

=++

uuruur