Lab 16 Angular Acceleration Carlos Hernandez

Angular Acceleration 

Name: Carlos Hernandez

Partners: Dahlia Tran.

Date: October 31 and Novemebr 2 of the year 2016

Theory: We want to apply some known torque to a system and measure/understand its relationship to angular acceleration. Different trials will be done changing stuff to the system to understand the virtues that compose angular acceleration. 

Lab Constraints: In this Lab we will be doing different trials. to the right of the picture above, one may appreciate that there are three disks that will be subject to rotational motion using a air valve that makes the disks move the disks have a string attached a that goes over and out the table like so ^ and a mass is attached to the string hanging off the table. And logger pro to measure the angular velocity over time.

Procedure: Now that we have all that we need we will turn on the air valve and let the cylinders move. For the first experiment we used a hanging mass of only .025 Kg with the torque pulley on the top being small and the Disk that will rotate will be only the top. (At this point both the bottom and the top are steel ). We do this for 6 trials with the mass changing, as well as witch disk moves and of what material (steel or aluminium) and the torque pulley being either small or large,(the large doubling the small in diameter). Below will be a picture of the six experiments and there corresponding constraints.  

Logger Pro Procedure: In the photo above one may see that there are values for angular acceleration down , up and average. 

Experiment 8: Conservation of Linear and Angular Momentum

Expiriment 8 (Lab 20)

Conservation of Linear and Angular Momentum

Name: Carlos Hernandez

Partners: Dahlia, Bmaya, Luis

Purpose: 

Lab 19 - Conservation of Energy/Conservation of angular momentum

Lab 19

Conservation of Energy/ Conservation of angular momentum

Name: Carlos Hernandez

Partners: Dahlia, Luis, Bmaya

Purpose: Using Conservation of Energy and Conservation of Angular momentum, we are to predict how high a meter stick(rod) will go, being pivoted from one end and having an inelastic collision with some clay at the bottom most point. The experiment will be compared to a video capture that will help find the clay's height above the ground via logger pro. 

Lab 18- A lab Problem- Moment of Inertia and Frictional Torque

Lab 18

A Lab Problem - Moment of Inertial and Frictional Torque

Name: Carlos Hernandez

Partners: Bmaya, Mohammed 

Purpose: Find the frictional torque of a large metal disk and its shaft to predict the time of decent of a cart through a 1 meter ramp attached to the disk by a string. 

Lab 17 Finding the moment of inertia of a uniform triangle

LAB 17

Finding the moment of inertia of a uniform triangle 

Name: Carlos Hernandez

Partners: Bmaya, Mohammed

Purpose: The Purpose of this lab was to determine the moment of inertia of a right triangular thin plate around its center of mass, for two perpendicular orientations of the triangle. 

Background Info and Approach: To be clear, our physics utensils that are needed to do the lab include, comprehension of torque and the parallel axis theorem. The Parallel axis theorem was used on a notebook problem to find the moment of inertia around a triangle from the center of mass. 

Procedure: What we would like to reach at the end of the lab is a comparison of the inertia of a triangle between our experimental data(through our apparatuses) and our formula for the triangle which we have previously found to be 1/18*M*B^2. The set up to retrieve our experimental data is almost exactly the same as Lab 16. A photo of it below. 

-The main and only difference of this set p is the ability to put the triangle as shown above, directly on the center of mass. 

We will collect data 3 times. The first without the triangle, the second as shown above with the longest side going up with its 90 degrees, and the third time with the longer side now parallel to the table. Below will be the data collected with the 3 experiments. 

 The same process was used to get the omega. Finding the slope of the graph. Both going up and down and averaging them





After having our omega values, the first step was to calculate the value for inertia for all 3 trials. Later on the Inertia of the system with the triangles will be subtracted from the system without a triangle, to find the inertia of just the triangle and that's what we will use to compare. Below is a photo of the calculation of the systems inertia for all 3 cases.

Now we are able to compare. For the experimental we will subtract the triangle system inertia by the solo system. And that shall give us the inertia of the triangle. That was done for both of the triangles positions. Then we compared it to the inertia by the formula 1/18MB^2 Derived by the parallel axis theorem. Below is the work and values for each triangle and both experimentally and through the Inertia formula. 

As one might see the values are actually very very close.

Triangle long side parallel to the ground : Exp-.00053 , IFormula-.00056

Triangle short side parallel to the ground : Exp- .00023, IFormula-.00024

Conclusion: Hurray! The Experiment is a success, the numbers are at around 5% error, I believe there are very few places to blame for error as there is very few places for humans to manipulate the actual system. A place for error might be that the system is completely friction-less or the other is the calculation of omega, we did average out that calculation. Nonetheless, Our comparisons were great and our understanding of inertia is ever more clear. Cheers. 

Lab 15 Carlos Hernandez

Collisions in two dimensions

Name: Carlos Hernandez

Partners: Dhalia Tran, Ariel Tran

Date: 10-17-30

1. In this lab we wanted to see a collision where the objects did together and see if energy was conserved. 

2. I did not come the 2nd day of this lab as I injured my back. So all I did was was capture the video of the 2 marbles colliding and putting it into loggerpro, and tracing the path of the balls frame by frame. I understand it is my responsibility to finish the labs on another day and take full responsibility. Cheers. 

Lab 14(not named in lab book) Carlos H. Ballistic Pendulum

Ballistic Pendulum

Name: Carlos Hernandez

Lap Partners: Dhalia Tran, Ariel De Leon

Date: 10-12-16

1. In this lab we will find the velocity of a ball firing into a ball going up a theta.

2. In this lab we utilized a ball . A pendulum mechanism which when firing a ball into the block will go up an angle theta. the ball stays inside which will make it into a inelastic collision. A slow motion video will be posted below on how the mechanism works.

3. We did 3 trials of shooting the ball. Getting 3 thetas and using the average. The mass of the block was 84g and the ball was 8g both with a +-.1 in uncertainty

L up in the work is the length of the string, being 21 cm. When plugging in the data our V initial for the ball come out to be around 6m/s 

After this we decided to do the second of the lab for fun which is if the ball is shot from the table how far away will it land. we measured the height of the table, distance inside the table where the ball will be shooting from and with simple kinematics ( Y direction to see when it hits the floor then use the time to find the x distance) the distance away from the table would be 2.44m and the total distance traveled by the ball would be 2.7 m work will be posted below. 

In conclusion, in this lab we use  the conservation of momentum and the conservation of energy to find the velocity initial of the ball, and therefore use a few measurements to find the distance the ball would travel. This ballistic pendulum lab was great to show how momentum and energy are conserved. Cheers. 

Lab 13 Carlos H. (Magnetic Potential Energy Lab)

Magnetic Potential Energy 

Name: Carlos Hernandez

Lab Partners: Ariel De Leon, Dhalia Tran

Date: 10-10-16 & 10-12-16

1. In this lab we will be analyzing and looking at the conservation of energy with magnetic potential energy.

2. In this lab we utilized a track which blows air, a cart mounted on the track which with the air makes it have virtually no friction(negligible). a magnet at the end of the track, caliper, meter stick, books, to help balance the track to a level surface,  a strong arm to lift the track for the experiment, and a photo to measure angles. 

3. We raised the track like so at an angle theta, we used a phone to measure the angle theta and with a caliper measured the distance separated by the magnet. We raised the track and took data 8 different times , a photo with the data is placed below.

After collecting out data we then put graphed in logger pro the force of the magnets by the distance of separation, we then put a power fit on the graph to get a fitting function where A is multipled by r raised to B

This concluded the first day of the experiment, on the second day we now used a motion detector, measuring a distance from the motion detector to the cart and the cart to the end of the track to get our distance that needs to be subtracted from our distance measured by the motion detector. Our separation ended up being .3621 +- .1 (from the ruler) After this we made a collection of data with the cart slowly (constantly) moving towards the magnet and moving back. With this data we are able to calculate or Kinetic energy and Gravitational energy given from the previous part of the lab.

After inputting our U-mag and KE information into logger pro we managed to see what the total energy of the system was . Surprisingly the experiment went well and the data collected looked great. The total energy did not go up (which would be crazy!) and tried to remain constant. The slight decrease to my thought might be due to some slight friction on the cart nevertheless we see how conversation of energy remains through all forms of energy and try it out through a magnetic lab which is great. Cheers.

Lab 12 Carlos H. Conservation of Energy-Mass-Spring System

Conservation of Energy-Mass & Spring System

Name: Carlos Hernandez

Partners: Dhalia Tran, Ariel De Leon

Date: 10-5-2016

1. The essence of this lab is to look, analyze, and understand the energy in a vertically- oscillating mass-spring system where the mass of the spring is non-negligible( has to be taken into account). (the reason this lab has the text centered is because there is a glitch that doesn't let me write from left to right.)

In this lab the utensils that were used where; a spring, mass , motion detector, a paper to make the motion detector read the position better and Logger Pro. the information retrieved is the following , Mass of Spring = .065 kg, Mass Hanging On Spring = .45, Height in the Bottom = 1.23 m. 

After making out spring oscillate up in down in a smooth motion we managed to get this beautiful sinusoidal graph which is essential to help us get the spring constant which was k= 16

In this problem we needed to integrate the sum of all the Gravitational potential energy by getting a small piece of dm of the spring, and dh, and the integration was from a y from the bottom to dm. Another thing that was solved for was an expression for Kinetic Energy for the spring.The elastic potential energy equation that was used was .5*K*X. So the total energy for the system was 1. Gravitational of the handing mass and spring, 2. KE of the hanging mass and spring, 3. And Elastic Energy. The work for the calculated equations is below. 

All the equations for energy were input into logger pro and are below. 

The sum of all these energy throughout the entire position should remain relatively constant, I believe if there is much error it would be in measurements or calculations, I was pretty happy with the graph we got for the motion and feel like there isn't much more places where error could be at. In this lab we see and experiment with the Conservation of Energy extensively and feel like at first it was quite difficult to understand but looking back, was very helpful and makes perfect sense. Cheers  

Lab 11 Carlos H. Work-Kinetic Energy Theorem

Work-Kinetic Energy Theorem Activity 

By: Carlos Hernandez

Partners: Ariel De Leon

Date: 10-5-2016

1. For this lab we will see how kinetic energy is related to work, using a spring. 

2. 

The tools utilized in this lap where; a cart, track, spring, force detector, motion detector, and a small piece of cardboard to make it easier for the motion detector to read the position. The premise of the set of the cart shown above is to after balancing out the force detector, measure the position of the card and the force by the connection to the spring.

In the top part of the graph the force was graphed by the position we selected the part of the graph that would be most useful to us as the beginning and the ending part of the graph would make our calculations faulty(I'm not sure if that is a word). After excluding the outer parts we integrated graph which gives us the work done in that period. Below we inputted values and graphed kinetic energy. The kinetic energy we got was 1.942 J while the work done was 2.379 J. this means there is about a 29% error in between the values. We did feel this percentage was fairly high so we redid the experiment as there was an uncomfortable feeling for the high percentage. 

In this trial our work turned out to be 1.996 N while the Kinetic energy in the graph below was 1.659 which gives us a error between the values of  about 27%, the percentage was still high but we believe that there might have bee error by the sudden jolt on the cart when letting it go after stretching the string and such. And the end on the lab we still manage to see how the area under the graph for force by distance gives us the work done where we can see the kinetic energy of the system, cheers. 

Lab 9 Carlos Hernandez Centripetal Force

Centripetal Force With A Motor

Name: Carlos Hernandez

Lab Partners: Dhalia Tran, Ariel De Leon

Date: 10-3-2016

1. Our job for this lab is to understand and show the relationship between Angle Theta and The angular velocity (w).

2. So for this experiment we have a system that looks exactly like the above, the middle top part rotates causing the string to rotate as well . The angle and height little h are all dependent on the angular velocity, the first thing we do is find a few key measurements that we will need for this experiment. Here is a photo of what was measured as well as a photo of the system at work.

The photo to the right was edited to show the strings "motion" and a circle was put to show where the end of the string is traveling.

In the work from the picture above we solved for omega (w) using the diagram on top, a free body diagram and omega related equations. After having our equation from above and the data collected stated in the beginning , we were ready to place our data in excel. 

The Data was input including the 2 different ways of solving for omega(t),using the (2*pi)/time and the omega(h) using the equation solved for in the previous photo.  Once we had our two omegas, we plotted them vs each other homing to get something close to a slope of 1/1 which we did, thus proving that either way we can solve for omega. I was actually surprised by how great the plot came to be considering the various ways there could have been error in measurement.

The lab was a success and the equation derived worked like a charm and shows that we can solve for omega using theta and the height of different positions which is definitely very useful. The error was very minimal but most likely due to measurement error, or time keeping error.    

Lab 8 Carlos Hernandez

Demonstration--Centripetal Acceleration vs. Angular Frequency

By: Carlos Hernandez

Lab Partners: Dahlia Tran, Ariel De Leon

Date: September 28, 2016

1. We want to show and understand how Ac=(V^2)/R is related to w=V/R where Ac is Centripetal Acceleration and w is angular speed. Therefore we want to know and understand how the Centripetal force is m*R*w^2

2.  We all know and understand how The Force of an object is equal to the mass multiplied by the acceleration . Now we Know the Acceleration for Centripetal force is the equation stated above now we want to understand this, this lab will be done documenting data that the professor gets from the rotating table, there is a block attached to the center of the center by a string from this mechanism we will know the following information, mass of the block(we change it throughout the experiment), Radius in cm, Volts inputted to the system, Time in sec, and the Force gotten by the Force detector attached to the block and the string. The professor did this experiment several times like so; 4 times with the mass of 200g , the radius of those 4 times being, 19cm, 28.5 cm, 40 cm, and 54 cm. the volts for those for times was fixed at 6.1 , and of coarse the time and Force changed for each scenario, a photo with all this data will be below. After those 4 trials the mass stayed the same for the following next 3 trials as will as the radius at 54 cm but the volt input were changed to 6.6 , 7.0 and 7.7. after these 3 trials there was 1 trial done with the mass at 100g, radius 50cm, and volts 7.7, and one last trial with the mass at 50 g  radius 54.

Free fall Lab Carlos Hernandez 9-7-2016

(This lab was already posted but I accidentally put it on a different blog. Now that I understand how blogger works a bit more I am re-posting it where all my other blogs are at just to have it in the same place as the others. Thank you)

Free Fall Lab

Carlos Hernandez , Dhalia Tran, Ariel De Leon

September 5 and 7, 2016

2). This lab consists of two parts, the first of which involves using a spark generator and tape to find the acceleration of gravity. It also will get us thinking on our margin of error and why, that is where part two comes in. In part two of the lab we will begin to think about, understand, and solve for errors and uncertainty. 

3 ). So in this lab like stated above we will be solving for, verifying for, gravity. Using a spark generator and a tape, about 1.5m long, we will be able to pinpoint the exact position and time that a magnet (of unknown mass, it isnt needed) takes to fall . The spark generator will shoot electricity between the magnet and the metal rod where in between is the tape which will end up marked with small dots where there electricity struck every 1/60th of a second. Once we had our data on tape strip we began to measure the distance between each dot. Obviously it increased with time as it was accelerating downward to to G. We then input our values of our change in distance and the mid interval time which were of coarse both known. After finding our Value for G , As a class we got every groups value for G . Thee were a total of 7 different G values. The prof. gave us an explanation on what  dev from the mean is . Using this simple understanding we found out how off were we from the average. The average of G was 956 which probably isn't too good of a reference of  an average but the concept was understood. We then began to work with the standard deviation. Which is a formula very similar to uncertainty. With this . We understood how  deviations work and averages come into play in 

4) Besides all the stuff stated above , there is something very important that has been learned in this lab and that is understanding LABS. Labs aren't always perfect and one needs to always put into account why data might be faulty or off. The problem isn't the lab , it would  become a problem if we don't state it or understand what outside "forces" might affect the data. Cheers, below will be pictures of instruments used for the lab and the excel graphs as well as other stuff. 

Modeling Frictional Forces 9-21

Modeling Frictional Forces

Carlos H. Dhalia T. Ariel D

9-21-16

This lab was broken up into  4 parts . What this lab will cover is friction of static and kinetic. We will be doing different types of experiments to measure fricution

The stuff that will be used in this lab include, 4 blocks a flat surface , in this case we used a cut up door I believe it was, a pulley, weights , motion detector, and force sensor. 

Part 1 For the first part we attached a block to the string which went to a pulley and down to some mass. We found the breaking points of mass for 1 blockc, 2 blocks , 3 blocks and 4 blocks. (each block has different mass and the mass was appropriately added on). 

Trial 1 Mass 180g, mass on pulley 90g

Trial 2 Mass 320g, mass on pulley 180g

Trial 3 Mass 496g, mass on pulley 265g

Trial 4 Mass 629g, mass on pulley 330g 

After simple Calculation our static friction coefficient came out to .5

Part 2 of the lab was working with kinetic Friction. We again worked with the same blocks and found the coefficient of kinetic friction by pulling on the block with a force sensor at a constant acceleration.  (The force sensor was properly calibrated at 0 when at a horizontal position.) 

Masses on Trials are the same as part 1 of the lab

Trial 1-  .58 N 

Trial 2- .85N

Trial 3- 1.35N

Trial 4 -1.48N

The calculated kinetic friction was .2616

 Part 3 We found static friction from lifting the service until breaking point. we only did this with one mass which was of 180g. Although the mass doesnt matter because when we solved for the Static friction coefficient the mass cancels out along with gravity leaving a tan of our angle which we measured to be 21.8 degrees. The coefficient of static friction came out to be .4 a picture of our work will be below

Work part 2 and 3

Part 4 

For this part we will raise the surface a tad bit more to where the block slides down contently. We measured it to 25.5 degrees and the mass of the block was 180g we attached  a motion detector ad for it to acelerate at .939m/s down . After our calculation that will be posted below we fount the kinetic to be .37

Conclusion - This lab helped us learn and understand how to find the values for the coefficients of friction in different ways and using different tools. This also helped us understand how friction is linked with forces, angles , mass , tension etc. Cheers 

Propagated uncertainty in measurements Sept 7

Propagated uncertainty in measurements

Carlos H., Dhalia T., Ariel D.

9-7-16

In this lab we will be finding and putting to the test our skills on propagated uncertainty, the test objects will be 2 cylinders.

First we were given an explanation on how to use a caliper and use it for maximum accuracy. Once we learned. We choose 2 metal cylinders. We measured its Diameter, length, and mass for both of them. Ofcoarse measuring objects have their tolerance levels . The caliper measured to a +- .01 while the mass scale measured to a +- .1. We then used the Density equation which can be seen in the picture above , above the metals. Once plugging in our numbers we will start to solve for the uncertainty as we knew how. We solved for the partial derivatives and solved for the 3 variables. we squared them , added them and square rooted the result. The result gave us the uncertainty . solving for the equation gave us our density . Here is the work and how we solved for the uncertainty. 

In conclusion this lab helped us understand how to find uncertainty when measuring objects, and the importance of taking uncertainty into account. Cheers

Trajectories lab 9-21-16

Trajectories lab

Carlos H., Dhalia T., Ariel D.

9-14-16

2. So in this lab we will understand how trajectories work with a problem hand on. Many times we get use to book problems and fail to get our "hands dirty" with real experiments. This lab will help us understand angles ,distance, speed, slope and anything that goes into trajectories.

3. In this lab we will be utilizing a small round object in this case a marble, as well as a ramp that  we could put in a slope for the ball to travel in. Carbon paper. So that we can know exactly where the ball lands by the markings on paper cased by the bounce and a measuring stick. 

4. We first lifted the ramp at a slope that would cause the ball to go at a reasonable distance from the table. Next we placed the paper where we would see the ball landed. After getting data of where the ball landed we started to get to work in calculations .

first we found the distance find times and got the average distance to be more accurate. The distance was 66.36cm from the table in the x axis with an uncertainty, also calculated, that came to be + - .33. The height from the ground to the table(the point where the ball left the table) was 95 cm with a +- .1 for the uncertainty . With this we were able to find with what velocity it left the table being 150.7 cm/s and the uncertainty being the most tedious to solve for being +- .75. 

Now for the second part of the lab or the most interesting part we put a slope from the table to ground. Now we were to predict where the ball would hit on the slope. With our phones we got the angle to be 48.6 degrees on the slope and managed to solve for the distance into the slope where the ball would hit. 

As seen on the photo by our calculations the ball should hit somewhere around 79.5cm . After putting a carbon paper on the slope to test we dropped the ball 5 times . The ball hit at 81 cm, 80.5m, 81.2cm 81.8cm, and 81.9 cm .

I am actually a little surprised with how close our calculations came to be. Surprised in a good way and it left our group feeling like the lab was a success . Trajectories after this lab became a lot more clear and easy to understand after doing this real world problem . Cheers 

Modeling the fall of an object falling with air resistance Sept 12, 14 2016

Modeling the fall of an object falling with air resistance 

Carlos H., Dhalia T., Ariel D.

Sept 12, 14

2. In this lab the goal is to find the relationship between the force of air resistance and speed. 

3. The way this lab will go is by using some features of Logger pro. First the professor found the mass of a group of coffee filters then we could easily find out the mass of each individually. We will capture video of 5 different trials of dropping the coffee filters. Starting with 1 ending with 5. The point is to eventually import the video to logger pro and find the terminal velocity for the coffee filters. 

4. In this lab we utilized the coffee filters the laptop front Camera to record the fall and a yard stick. The yard stick was used as a point of reference to let logger pro what the distance of something is. After recording the video of the 5 trials used a tool where we can plot the data from the video into logger pro. Once we got that data we imported it to excel (manually). We put the tie intervals to ever .1s, as when we plotted dots following the coffee filters on the way down, the frames where changing every .1 sec. the mass of each coffee filter which ended up being .0008947 a constant we were able to get being .00373 N-s/m and n being 1.929. These figures where plugged into the equation (m*g*k*^n)/m to find the acceleration. Once all this was complete we filled down the t, a, change in V, and V columns down. The key to finding the relationship of air resistance and speed was finding the terminal speed. So we ended up looking until the speed remained about constant to the thousandths place.  

In conclusion this lab helps us relate the force of air resistance to its terminal velocity. Thinking into a force diagram type of scenario, when the speed of an object increases, the force pushing or accelerating an object must increase as well to keep it accelerating. If the acceleration is constant the object will eventually find a terminal velocity. The faster something goes the more the air resistance force pushes back.