What Are the Steps to Conduct Elastic and Inelastic Collisions Using Photogates?

[kiddiegrade]

These are the instructions:

What to do:
1. Connect the two photogates to DIG 1 and DIG 2 ports of the LabQuest device. Connect this device to a computer and turn on the device.
2. Open Logger Pro 3.8.4 software. Click Folder icon/symbol. Open Probes & Sensors > Photogates > Two Gate Timing.
3. Place the two collision carts (each with a picket fence resting on top) in the linear track, such that the sticky portions or the attractive portions are at the end of the two carts are directly facing each other. Place one cart at the end of the track and the other one somewhere in the middle of the linear track.
4. Mount each photogate in an iron stand. Position them such that the one connected in DIG 1 is placed AFTER the cart at the end of the track while the other photogate is at the rightmost end of the second cart. Be sure that each chopper will pass through the photogate detectors once a collision is initiated. See Figure 1.
5. Set object lengths/distances 1 and 2, in the Photogate Distance dialog boxes, to be equal to 0.025 m. (The default object length for velocity calculation is 0.050 m. To change this value, right click on the Photogate Distance dialog box > open Parameter control options > change # of decimal places from 2 to 3 > set value to 0.025 m.)
6. Click Collect button in your screen to prepare the photogate. Give the cart placed at the end of the track a uniform velocity toward the (stationary) second cart. The two carts should collide and stick together, proceeding at a different uniform velocity. Record these velocities displayed in the dialog boxes as Velocity 1 and Velocity 2. Repeat this process 5 times and try to make the velocity of the cart you push as similar as possible with one another.
7. Cover the sticky portion at the end of one of the two carts using masking tape or if using magnets, make sure that the repelling sides are facing each other. Place one cart at the end of the track and the other one somewhere in the middle of the linear track.
8. Click Collect button in your screen to prepare the photogate. Give the cart placed at the end of the track a uniform velocity toward the (stationary) second cart. The two carts should collide and should not stick together, proceeding at different velocities. Record the initial velocity of the incident cart and the final velocity of the second cart. Repeat this process 5 times and try to make the velocity of the cart you push as similar as possible with one another.

The results are seen in the attached.

b.] attempt to the solution

IN table 2 (inelastic collision), I solved for the theoretical value using the formula:
mass1(initialvelocity1) = (mass1 + mass2)finalvelocity
where mass 1 = 0.4878kg and mass 2 = 0.507kg

In table 3 (elastic collision), I solved for the theoretical value using the formula:
mass1 (initial velocity1) = mass2 (final velocity2)
where mass 1 = 0.489kg and mass 2 = 0.5056kgQUestions:
1. If you were to get the percentage error, majority will be high? why is it so?
2. I was tasked to explain why the theoretical is higher/ lower than the actual or experimental value and I am having a hard time. because honestly, I don't know why.

I hope someone could help me with this. :(

 

[mfb]

In table 3 (elastic collision), I solved for the theoretical value using the formula:
mass1 (initial velocity1) = mass2 (final velocity2)
where mass 1 = 0.489kg and mass 2 = 0.5056kg

That is not right, the first cart can (and will!) have some momentum after the impact, too.

I can see some reasons why the measured velocity could be lower than the actual velocity, but no good reasons for the other direction.

Are you sure that you set the length of object 2 to its correct actual length? Did you measure it?
Did the two carts really stick together in experiment 1?
Did you measure the velocity of cart 1 at a position where you did not touch it any more?

Did you take a single car and let it pass through both gates to compare the velocities?

 

[kiddiegrade]

Our professor assisted us during the experiment. In experiment 2, we did not measure the velocity of the incident cart anymore and our prof gave us this equation. I think he was assuming that the incident cart will stop after the collision. (Does this make any difference?)

*Are you sure that you set the length of object 2 to its correct actual length? did you measure it?*
-What do you mean by this?

*Did the carts really stick together in experiment 1?*
-Yes I am, the did stuck together but the they both slowed down.

*Did you measure the velocity of cart 1 at a position where you did not touch it any more?*
-No we didn't? We pushed it and then it passed through the photogate sensor.. If, that's what you meant..

*did you take a single car and let it pass through both gates to compare the velocities?*
- In what experiment? Because in experiment 1, both carts passed through the second photogate sensor while in experiment two, only the initial velocity of cart 1 and final velocity of cart were recorded. (see attached photo of setup)

*What are these reasons? :)*

 

[mfb]

In experiment 2, we did not measure the velocity of the incident cart anymore and our prof gave us this equation.

Where do the numbers come from then?

I think he was assuming that the incident cart will stop after the collision. (Does this make any difference?)

This would require m1=m2. As the masses are similar, the difference is small.

*Are you sure that you set the length of object 2 to its correct actual length? did you measure it?*
-What do you mean by this?

In step 5, you are asked to adjust the length of the wagons in the software. As the software just measures the time, it calculates the velocity based on velocity=distance/time with the distance you inserted. If that value is wrong, the velocity measurement will be wrong, too.

*Did the carts really stick together in experiment 1?*
-Yes I am, the did stuck together but the they both slowed down.

That is one of the reasons why the velocity could be lower than predicted.

*Did you measure the velocity of cart 1 at a position where you did not touch it any more?*
-No we didn't? We pushed it and then it passed through the photogate sensor.. If, that's what you meant..

Okay. If you would have kept pushing while it is in the sensor, the velocity measurement would have been wrong.
The first sensor is very close to the starting point of the wagon, that has to be a very quick acceleration...

*did you take a single car and let it pass through both gates to compare the velocities?*
- In what experiment?

In a verification that the setup works.

*What are these reasons? :)*

That is your task :p. You mentioned one of them already.

 

[kiddiegrade]

clarification

*Where do the numbers come from then?*
- hahaha sorry. I meant we did not measure the velocity after pushing it. :) hahaha that is how the setup seemed like. the incident cart was a little bit farther in OUR setup. :)

*This would require m1=m2. As the masses are similar, the difference is small.*

Then are you saying the whole experiment is wrong because m1 is NOT EQUAL to m2?

one more thing, how come in the second experiment, the final velocity of the second cart was higher? isn't it suppose to slow down because it is greater in mass??

 

[mfb]

*This would require m1=m2. As the masses are similar, the difference is small.*

Then are you saying the whole experiment is wrong because m1 is NOT EQUAL to m2?

No, I am saying your formula is wrong. With similar masses, it gives a good approximation, but it is still wrong.

one more thing, how come in the second experiment, the final velocity of the second cart was higher? isn't it suppose to slow down because it is greater in mass??

"Slow down" is not related to the impact itself (where it certainly does not slow down!), so the mass difference has nothing to do with anything happening after the collision. It slows down, sure, but due to a different effect. Do you know what is responsible for this?

 

[kiddiegrade]

*No, I am saying your formula is wrong. With similar masses, it gives a good approximation, but it is still wrong.*

-I'm lost here! >.<

*"Slow down" is not related to the impact itself (where it certainly does not slow down!), so the mass difference has nothing to do with anything happening after the collision. It slows down, sure, but due to a different effect. Do you know what is responsible for this?*

Basing on Newton's law of inertia, "an object in motion will continue to move unless an external force acts on it", is the external force, gravity and friction responsible for this?

I am so sorry.. Our prof did not discuss this, we were just given the exercise.. I am so sorry. :(

 

[mfb]

Use quote tags to quote texts, please, they are clearer than stars:
[noparse]

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[/noparse] becomes

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*No, I am saying your formula is wrong. With similar masses, it gives a good approximation, but it is still wrong.*

-I'm lost here! >.<

Look up elastic collisions and formulas for that.

Basing on Newton's law of inertia, "an object in motion will continue to move unless an external force acts on it", is the external force, gravity and friction responsible for this?

Friction, exactly.

 

[kiddiegrade]

Use quote tags to quote texts, please, they are clearer than stars:

okay po! :) Now, I know!

yey! :) thank you so much.. it's almost clear na for me.. glad I have registered in this site! >.< thank you so much po, God bless you! :)