Physics Of A Loop Using the Program "Tracker"

[njdcat]

Hi guys, currently trying to figure out part of my lab for Physics I. We used the program Tracker to gather information on a metal ball rolling down a metal track and through a loop. The origin was set at the bottom perpendicular to the top of the angled track where x and y = 0. Here is the data I gathered:

Obviously to calculate the KE and PE I have been using 1/2mv² and mgh. The ball weighs about 28.4 grams. However, I have been getting some pretty strange KE and PE numbers that don't follow the conservation of energy. I think what is tripping me up is that the ball at first rolls down an angled track and then enters circular motion. I also suspect that Tracker did not calculate the velocity correctly (those numbers seem odd to me). I am supposed to calculate the normal force acting on the ball at the bottom and top of the loop.

I at first calculated the acceleration using a=v²/r. I wanted to calculate the normal force at the bottom of the loop using F_norm=F_grav+F_net. I calculated F_grav using (m)(g) fairly easily. However, the acceleration numbers that I calculated to determine F_net just seem odd to me, which is why I suspect that my weird velocity numbers are incorrect, thereby throwing off my KE and PE calculations. Is it possible I am using the KE and PE equations incorrectly in terms of this problem or plugging in the numbers incorrectly? Physics is not my strong suit. Thanks for the help.

 

[berkeman]

Hi guys, currently trying to figure out part of my lab for Physics I. We used the program Tracker to gather information on a metal ball rolling down a metal track and through a loop. The origin was set at the bottom perpendicular to the top of the angled track where x and y = 0. Here is the data I gathered:
View attachment 214624

Obviously to calculate the KE and PE I have been using 1/2mv² and mgh. The ball weighs about 28.4 grams. However, I have been getting some pretty strange KE and PE numbers that don't follow the conservation of energy. I think what is tripping me up is that the ball at first rolls down an angled track and then enters circular motion. I also suspect that Tracker did not calculate the velocity correctly (those numbers seem odd to me). I am supposed to calculate the normal force acting on the ball at the bottom and top of the loop.

I at first calculated the acceleration using a=v²/r. I wanted to calculate the normal force at the bottom of the loop using F_norm=F_grav+F_net. I calculated F_grav using (m)(g) fairly easily. However, the acceleration numbers that I calculated to determine F_net just seem odd to me, which is why I suspect that my weird velocity numbers are incorrect, thereby throwing off my KE and PE calculations. Is it possible I am using the KE and PE equations incorrectly in terms of this problem or plugging in the numbers incorrectly? Physics is not my strong suit. Thanks for the help.

Welcome to the PF.

Do you have any pictures or scale diagrams of the experimental setup?

Also, the KE is not just 1/2m*v^2. There is another term you probably should be including...

 

[njdcat]

If there is another term, I am sorely ignorant as to what it may be. I can think of a few other variables related to the problem but I'm not sure which one would effect kinetic energy.

 

[berkeman]

View attachment 214627

If there is another term, I am sorely ignorant as to what it may be. I can think of a few other variables related to the problem but I'm not sure which one would effect kinetic energy.

Thanks, the picture helps.

As for the other energy term, here's a hint -- what would be different if the ramp and ball were frictionless?

 

[berkeman]

Also, can you show what formulas you are using in the Excel cells that are calculating things from previous columns?

 

[njdcat]

Well, I am aware that friction is affected the velocity of the ball. Should I also be calculating friction to obtain the kinetic energy? Our lab states to just use 1/2mv², so I wasn't too worried about friction.

The velocity is being measured through Tracker, but like I said, I don't believe that Tracker is calculating this velocity correctly. However, since our lab just stated to use the velocity from Tracker, I didn't think too much of it until I started calculating KE and PE. I was using 1/2mv² to calculate KE, but I realized that I was plugging in h instead of delta-h to calculate PE, so now my PE is much more concise.

 

[berkeman]

Well, I am aware that friction is affected the velocity of the ball. Should I also be calculating friction to obtain the kinetic energy? Our lab states to just use 1/2mv², so I wasn't too worried about friction.

The velocity is being measured through Tracker, but like I said, I don't believe that Tracker is calculating this velocity correctly. However, since our lab just stated to use the velocity from Tracker, I didn't think too much of it until I started calculating KE and PE. I was using 1/2mv² to calculate KE, but I realized that I was plugging in h instead of delta-h to calculate PE, so now my PE is much more concise.

Great, can you post your new numbers? Even with the correction I have in mind, your calculated numbers seemed way off at times.

The ball rotates when it rolls down the ramp. What is the total kinetic energy of a rolling ball? It's not just the energy from the motion of the center of mass...

 

[njdcat]

Great, can you post your new numbers? Even with the correction I have in mind, your calculated numbers seemed way off at times.

The ball rotates when it rolls down the ramp. What is the total kinetic energy of a rolling ball? It's not just the energy from the motion of the center of mass...

These are my new numbers for potential energy.

Should I be using the form of KE = 1/2Iω²?

 

[berkeman]

Should I be using the form of KE = 1/2Iω2?

The KE should include both the linear KE of the center of mass of the ball, and that rotational KE term. You would get the ω term from the linear speed of the center of mass and the radius of the ball.

 

[njdcat]

Alright, so would ω take the place of a variable in the linear KE equation, or is it just an added term to account for the rotational motion of the ball?

Also, I'm assuming to calculate for v, I would do something along the lines of KE_i + PE_i = KE_f + PE_f and solve that out? I think what truly trips me up is the ramp that the ball rolls down before it enters circular motion within the loop, but does this not matter because as a ball rolls it is always in circular motion compared to something like a box or roller coaster cart rolling down a ramp and entering circular motion?

 

[berkeman]

or is it just an added term to account for the rotational motion of the ball?

Yes.

I'm assuming to calculate for v

I thought v was given to you by the video tracker software, no? If not, it's just delta position / delta time for each of the positions acquired by the video tracker...

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/rolke.gif

 

[njdcat]

Yes.

I thought v was given to you by the video tracker software, no? If not, it's just delta position / delta time for each of the positions acquired by the video tracker...

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/rolke.gif
View attachment 214693

Velocity was given, but I am unsure whether it is truly calculating the correct velocity, as the numbers seemed high, so I will try it myself.

 

[berkeman]

Velocity was given, but I am unsure whether it is truly calculating the correct velocity, as the numbers seemed high, so I will try it myself.

Yeah, just add another column to the spreadsheet, so you can see the given velocity next to the velocity you calculate from the changes in position with time...

 

[njdcat]

Yeah, just add another column to the spreadsheet, so you can see the given velocity next to the velocity you calculate from the changes in position with time...

Here is my new data set. I actually had to redo tracking once more in Tracker due to scaling issues. I also discovered that Tracker provides data for kinetic energy and ω, so I used ω and the linear velocity tracker provided to determine that the ball's radius is about 0.035 meters (we weren't provided the radius in class). I calculated my own liner velocity using changes in position with time, and then calculated my own kinetic energy using 1/2mv² + 1/2mr²ω². The given and calculated velocities are fairly close in most regards, but the kinetic energy given in Tracker is very different at some points than the kinetic energy I calculated. The conservation of energy in the system is fairly decent, as we didn't really take into account things like friction or air resistance (those are questions for the lab write-up).

 

[berkeman]

The conservation of energy in the system is fairly decent

Is the column for "E" supposed to be the total Energy TE = KE + PE? The TE should be constant, to within experimental error (a few % hopefully). That E column is nowhere near constant...

ALSO -- How can ω be changing sign? The ball has the same sign of vector rotation along the path. It speeds up and slows down, but does not reverse it sense of rotation...