momentum and collisions-IO lab official

Momentum and Collisions

Introduction You may have learned that a moving object possesses kinetic energy. Momentum is another property of an object, related to its mass and velocity that is useful to describe its behavior. Momentum p is the product of the mass and velocity of an object.

p = m v (1)

You may have learned an external force produces a change in the momentum of an object. If we consider as our system two carts that undergo a collision, then any forces they exert on one another are internal to the system. In this experiment you will examine the momentum of two IO lab devices before and after collisions to see what effect, if any, these “internal forces” have on the momentum of a system.

Objectives: In this experiment, you will

1. Collect velocity-time data for two IO devices experiencing different types of collisions. 2. Compare the system momentum before and after collisions 3. Compare the kinetic energy of the system before and after collisions. 4. Examine force vs time graphs during all interactions.

Materials 1. Two IO lab devices with hardware kits. 2. Bumper Hoops and clay holders (Optional ) 2. (Alt) Use the Spring Washer system included with the IO Lab Hardware kits. 3. Laptop computer with IO lab software and logger pro. 4. Weight Sets 5. Books or ramps to guide devices 6. Velcro patches

Pre-Lab Question Consider a head-on collision between a cue ball and a billiard ball initially at rest. Sketch a velocity-time graph for each ball for the interval shortly before and after the collision. Justify your predictions for the final velocity of each ball.

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Set-up

Hardware Calibration.

If you have not used the io lab device on your computer you will need to complete the calibration process.

Calibration of accelerometer, gyroscope and magnetometer.

Click on the cog icon in the toolbar and select calibrations.

Fig 1: Calibration window to calibrate sensors. This will only need to be done once. Your calibration files are stored in the IO-Lab Workfiles folder. A video for calibrating the device can be found on YouTube here. Follow the instructions in the video

to calibrate both devices for this experiment.

Follow the onscreen instructions to calibrate Acc, Magn, and Gyro. Make sure that you click save after completing the process.

The final calibration you need to do is the force sensor. Once again, click on the cog icon and select Force. Follow the instructions given on the screen to calibrate the force sensor. Remember to click save after you have completed the steps. Once you are done, we can now connect the two devices to the software by a single USB device. Be sure to follow instructions given to configure your hardware and software correctly.

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Software window

You will need to setup the IO software so that you can see the force and position graphs for both devices. Click the Both button in the toolbar and then select Force and Wheel for both devices.

Fig 2: Software configuration to register both target and projectile. Be sure to note which remote is target and which is the projectile.


Fig 3. Graph tool bar and definitions. Notice that both position and acceleration are unchecked for the wheel. Make sure that you click reverse y axis for both the wheel and force sensor for the projectile remote.

One other point to note is that sometimes the force sensor can be a little “noisy”. This is, in part due to the motion of the device. To eliminate this noise, I suggest that you set the smoothing on the force sensor to 5 for each of the runs you make.

You are now ready to take data.

Final Setup points.

1. Be sure to weigh each of the IO devices without the dongle. 2. Be sure to set up your software to read both devices. You will be using the wheel and the force sensor for all of the activities of this lab. 3. Be sure to follow directions given by your instructor to have both devices being read by the software. 4. In all of the runs of this lab, friction will be an issue. Be sure that you are clear how to use the magnifying button on the graph tool bar to focus on the portion of the graph before and after collision.


Procedure

Elastic Collisions. 1. Attach the metal hoops to each of the IO lab devices. The hoops are flexible and will give a good elastic collision.

Fig 3a-IO devices with spring washer system.

Fig 3b-IO devices with hoops.

2. Position the target about 40 cm away from the projectile cart.

Practice gently launching the projectile cart into the target. The collision should be such that the distortion of the two hoops should be the same.

(Alternative: Using the spring and washer system included with the IO devices, you should practice

gently launching the projectile cart into the target cart in such a way that there is a smooth collision between the projectile and the target.)

3. Click record in the tool bar to start data collection. While running, re-zero the force and wheel sensor for both devices. (Note, don’t worry that time elapses, we will only use that portion of the graph that actually has data on it.). Once you have re zeroed both Force sensors, launch the projectile device towards the target. Fig 4 provides you with sample data. Your data will look similar.


Fig 4 a) Sample Force vs time graph for elastic collisions.

Fig 4 b) Sample Position, velocity and acceleration vs time graph. Note that this sample data was taken using the Washer Spring system. You will get similar results with the hoops.

4. Collect average force vs time and velocity vs time data for at least six elastic collisions, varying the mass of first the target and then the projectile. Note you do not need to worry about saving your data since the software will store each run in the IO lab work folder on your hard drive.

5. In this experiment, you are concerned with changes in momentum due to the collisions of the devices. Some slowing due to friction is inevitable. To minimize the effect of frictional losses in your analysis, you should select short intervals of the velocity vs time graph just before and just after the collision. You may select these sections on the graph by first clicking on the graph analysis tool then select the desired portion of the graph. The graph will display the average velocity (µ) and the standard deviation (σ), the position where the collision occurs and the acceleration. You will use the µ value for the velocity values.


5a) Drag over the portion of the projectiles velocity before the collision occurs. Place the µ value into the table as the initial velocity of the cart before the collision.

5b) Drag over the portion of the target’s velocity after the collision occurs. Place this µ value into the table as the final velocity of the target.

5c) Drag over the force vs time graph and for each cart record the average force, the change in time over which the collision occurs and the “a” value shown in the values chart.

Note that you will have to select the analysis tool bar for each of the graphs separately.


Inelastic collisions.

1. Attach two washers systems (one for each device) into the force sensor.

2. Cut two strips of Velcro one with felt and the other with the hooks. Place the hooked strip on the projectile cart and the felt strip on the target device.

3. Practice launching the projectile device into the target device so that when the Velcro strips come into contact the two devices come to a stop without bouncing. A collision that is too jarring will cause ringing in the force sensor and make your data difficult to interpret.

4. Position the projectile at least 40 cm from the target device. Click record in the tool bar to start data collection. While running, re zero the force and wheel sensor for both devices. Make sure that the y axis for the force sensor of the projectile device is reversed.

5. Collect data as before for at least three inelastic collisions, varying the velocity and mass of the both the target and projectile cart. Determine the velocity of the carts before and after the collision as you did in part 1. How will you record the velocity of the linked carts?


Evaluation of the Data

Elastic Collisions

1. We can use the tables below to help with your evaluation of the data before and after the collisions.

Table 1: Mass and Velocity Data

Table 2: Momentum Data for all runs.


Table 3: Average Force and Impulse data for elastic collisions.

2. How does the total momentum of the system after the collision compare with that before the collision? Do your results agree with your expectations? Explain.

1 3. Calculate the total kinetic energy E =

How do these quantities compare?

m v2 of the system before and after each collision. 2

4. Using the force vs time data, calculate the impulse on each device. Be sure to include the sign. How does the impulse match your “a” values? Are they the same?

5. How does the average force for the first device match the average force of the second device? Are the forces the same, should they be? Explain?


Inelastic Collisions

1. You can use the tables below to help you with your analysis of the momentum before and after the collision.

Table 4: Mass, initial and final velocity data for inelastic collisions.

Table 5: Initial and Final Momentum data for inelastic collisions.

Table 6: Average Force and Impulse data for elastic collisions.

2. How does the total momentum of the system after the collision compare to that before the collision? Is the agreement in these inelastic collisions as good as that in the elastic collisions? Try to account for any differences.

3. Calculate the total kinetic energy of the system both before and after each of the collisions. How do these quantities compare? Compare your findings with those of the others in your class.


4. We have used “elastic” to describe collisions in which the objects bounce, and “inelastic” to describe collisions in which the objects stick. Based on your comparison of the kinetic energy before and after collisions, provide a more conceptual definition of the descriptors.

5. Using the force vs time data, calculate the impulse on each device. Be sure to include the sign. How does the impulse match your “a” values? Are they the same?

6. How does the average force for the first device match the average force of the second device? Are the forces the same, should they be? Explain.

momentum and collisions-IO lab official

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