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. 

Non Constant Acceleration Sept 7

Non-Constant Acceleration Lab (Elephant)

Carlos H., Dahlia T., Ariel D.

Sept 7, 2016

1.So in this lab we will the difference in working out a problem analytically and numerically using excel.

2. So we are given a problem involving an elephant with a rocket booster . The elephant has an initial velocity going down the slope. The rocket booster turns on in the opposite direction stopping the elephant. We need to find how far it will go before coming to rest. First analytically (analyze as the professor has done it for us ) then in excel where it would be easy to change numbers (mass, Vo, etc.). Hence- an important note to the reason why this problem is tougher is because the acceleration isn't constant nor the mass as the rocket fuel burns off as it produces its thrust. 

Elephant Problem Photo

3. We looked and analyzed the solution in an analytical approach . Since numbers weren't constant there had to be an integral approach which was very hard and long. Although in this case possible the professor said sometimes it would be extremely hard to get an answer. Ultimately the solution was found . Now we would try on our own (in our groups) to solve and set up a table where we could solve for this numerically piece by piece. Finding the average acceleration for the time interval then the change in velocity followed by the speed at the end of the interval then the average speed at the end of the time interval lastly finding the position change, we would be able o find the position the elephant would be at.

Analytical Approach

Numerical Approach

4. To find the final value for distance we put the time to increase every .1 seconds ( we belived the accuracy would be good enough ) and look for when the velocity became zero. It is good to keep in mind the the velocity would eventually become negative as the thrust would push the elephant back still after the velocity became zero. Here is a picture of the lab when we found the velocity to become zero. 

5. In conclusion sometimes problems are tough to solve analytically. Although I'm sure after this lab we should know how to approach or understand how the analytical solution would be, the numerical approach with excel gives us many advantages. Advantages where we could easily change the inputs to find different outputs. Cheers. 

29-Aug-2016: Finding a relationship between mass and period for an inertial balance

Lab Group

Carlos Hernandez

Ariel De Leon    

Dhalia 

 Finding a relationship between mass and period for an inertial balance. 

2.This experiment should allow us to understand how mass affects the period . Or how we can find the mass based of the period an object has.

3.  So we know there is a relationship between mass and period. My initial theory and thoughts to what would link them is the following. The period of something swinging is dependent on the mass and earths gravitational pull on it. If something has a greater mass it would slow down the period.

4. We first used a floppy metal piece that attaches to the table called an inertial balance. Using logger pro and a period detector device we manged to start the experiment. We first put weights on the metal piece (knowing the mass) to create a function.  We did this for a couple of masses to perfect the function. After this process we got a graph whose function looks like Y=mx+b. We know that the formula that relates mass and period is T= A(m+Mtray)^n. using algebra we managed to make it look like a y=mx+b function and it looked like the following: lnT=nln(m+Mtray)+lnA. Now after changing and adding a few features in logger pro , we were ready to measure the period of an object with an unknown mass. I will explain the the graphs and how we solved for the masses in step 7. step 5 will contain photos of date we compiled and lab equipment. while step 6 will contain photos of my calculations.

5)

6) 

7) So the graphs in step 5 are graphs of of the periodic movements of  two unknown objects whose masses we would try to find. The steps for doing this we first had to get an upper bound and lower bound of certainty for our original graph. our lower bound for Mtray was 280 and upperbound was 320. Anything below or above that would be to uncertain. Using only the period of the known objects we would plug that in to our power law equation . We ofcoarse solved for the mass twice , one with the lower bound date and the other with the upper bound data. One key feature is that the "B" in y=mx+b is actually a LnA. so to get the B or in other terms the A of the power law, we have to solve for A. We did this for both unknown objects. For unknown object 1 the 2 masses we got were 229g, and 240g. The mass of the object was actually 251. We were in a 10% margin of error which in my eyes isnt too bad. My beliefs for the uncertainty might include; human error, the object not being uniform, the object placed further or closer to the edge in respect to our weights trials. Our known object 2 was around the same margin of error and the same procedures were done. 

8) Overall I believe the lab was a success we learned how to use the power law equation for period and mass . It was also a great help understanding graphs which I believe will be useful in this coarse. I talked about uncertainty in step 7. Although I did no calculations on  it as I still don't have it clear how to do it. Thank you.