19-Sep-2016

Modeling Friction Forces
Jae Yoo
9/19/16
Partners: Sherry Ye, Chandler

Purpose
To apply Newton's laws throughout five different experiments in order to determine the coefficients of kinetic and static friction.

Part 1 Static Friction

A wooden block with the felt-side placed on the table and a string attached to the block. A weight is attached to the string which hangs over the table by a pulley.

We carefully add more weights and until the wooden block slips. Record the weight once it slips.
Try the same procedure with 4 more different weights of wooden blocks.

Once we got all the data we plot it in a data to find its slope to find coefficient of static friction.

We got our static friction as 0.2717

Part 2 Kinetic Friction

We used kinetic friction sensor to find the coefficient of kinetic friction as the picture shown above.
One pulled a wooden block with a constant speed and recorded data in logger pro.
We also tried this part with 5 different masses of wooden block.
Once all four graphs have been created in logger pro, we determined the mean force exerted on each stack of blocks and generated another graph to find the coefficient of kinetic friction.

After collecting all mean values, we graphed normal force vs friction force graph to find our coefficient of kinetic friction and our value was 0.2135

Part 3 Static Friction From A Sloped Surface

This time, we will be measuring static friction in different way, only by a wooden block. We began by placing the block on a horizontal track, slowly raising one end of the track until the block started to slip. We then measured and recorded the angle the track made with the horizontal.

The block started to slip at a degree of 28 and our calculated static friction was tan 28 = 0.531 which was way off from part 1


Part 4 Kinetic Friction From Sliding A Block Down An Incline

We measured the coefficient of kinetic friction by setting up a motion detecter at the top of a horizontal track steep enough so that a block will accelerate down the incline. We measured the angle of the incline and used a velocity vs. time graph to find the acceleration of the block. With this information we can use a free body diagram to again find µk. 

We got coeffiecient of kinetic friction as 0.21

Part 5 Predicting the Acceleration of a Two-Mass System

From this part, we took our coefficient of static friction and use it to derive an expression for what the acceleration of the block would be if we used a hanging mass heavy enough to accelerate the system. For the set up, we used is motion sensor, hanging weight, wooden block, pulley, and string just like part 1 but bigger hanging weight.



Our prediction for an acceleration was 1.591m/s^2 and logger pro's collected data acceleration was 1.556 which they came out very close to each other.

Conclusions
From this lab, we learned to how to find coefficient of both kinetic and static friction and how normal force and friction force are related. To tie up, we were being able to predict what the acceleration is going to be to use coefficient of kinetic friction in a given situation.

14-Sep-2016

Trajectories
Jae Yoo
9/14/16
partners: John Demontano, Shawn Mazzio

Purpose
To use the understanding of projectile motion to predict the impact point of a ball on an inclined board

Procedure
Set up as picture
Once the apparatus has been set up, we launched the steel ball from an identifiable point on the v-channel to see where it would land. We placed the carbon paper at the impact point on the floor and launched the ball five more times to get a more accurate distance of how far out from the tables edge the ball landed. We hung a plumb bob as well to get even more accuracy. After observing the marks on the carbon paper we used a meter stick to measure the distance from the edge of the table to the impact point.

Data
We measured the angel as 48 degree
and height of the point where ball free fall as 0.9638m and vertical travel distance as 0.6550m

Results/Analysis

After finding the launch velocity of the ball, we needed to find out where the ball would land on a different height. And the picture is about calculated result of the landing point at a new height.

Conclusion
The ball landed exactly where we expected it to land which was 75.21cm away from the initial point of the ramp. Our experiment was very successful although we had a little bit of uncertainly.

12-Sep-2016: Modeling the fall of an object falling with air resistance

Modeling the fall of an object falling with air resistance
Jae Yoo
9/12/16
partners: Sherry Ye, Chandler

Purpose
To determine the relationship between air resistance force and velocity. By gathering data of a falling coffee filters and graph the data we collect, we will find a relationship of Fresistance = Kv^n.

Procedure
As professor drops coffee filters with different mass, we collect data to see how velocity changes.


Data

mass of coffee filters


By plotting dots of each 1/15s of flame, we can find a path of coffee filters in very short amount of times.


Graphs of the plotted dots of each 1/15s of flame.






Pictures of Collected data of each coffee filters and when it makes a constant speed

Results/Analysis

Velocity and weight of each coffee filters
And the values of K and n from the linear fit of velocity vs weight graph
picture below is the linear fit graph


Conclusions
In this lab, we learned how to model a free fall object with an air resistance. We have concluded that Fresistance = 0.0006883 * V^1.366 and proved that there is an relationship between air resistance and velocity. We also measured our uncertainty due to errors of the experiment.

7-Sep-2016: Propagated uncertainty in measurements

Propagated uncertainty in measurements
Jae Yoo
9/7/16
partners: John Demontano, Shawn Mazzio

Purpose
We will be introduced to propagating uncertainties in the measurements we take for our data which leads to uncertainty in the final result. This simply means that we are going to find a range of values that will be with-in the accepted value. For instance, if we take a pen and weigh it on a scale. The scale is a cheap one so the range of uncertainty on the weight of the pen will be +/- the value on the display of the scale.

Procedure

We measure the weight and volume of two metal cylinders, Tn and Al.
We measure the weight with a scale and volume with the caliper
And we need to find their density. 

Data
Al was measured 52.0g with an uncertainty of +/-0.1g
Its length was 7.86+/- 0.01cm and diameter of base was 1.31+/- 0.01cm
Tn was measured 52.0g with an uncertainty of +/-0.1g
Its length was 2.07+/-0.01cm and diameter of base was 1.25+/-0.01cm

Result/Analysis


Conclusions
We concluded aluminum has density of 4.908+/-0.07752 g/cm^3
and tungsten has density of 20.47+/-0.582g/cm^3

7-Sep-2016: Non-Constant acceleration problem/Activity

Non-constant acceleration problem/Activity
Jae Yoo
9/7/16
partners: John Demontano, Shawn Mazzio

Purpose
To understand the convenience of how excel can calculate solutions from difficult and tedious problems

Procedure
A problem is given
A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a rocket mounted on the elephant's back generates a constant 8000 N thrust opposite the elephant's direction of motion.
The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the
m(t) = 1500 kg - 20 kg/s*t
Find how far the elephant goes before coming to rest

The given answer for the problem was at x = 248.7m when t = 19.69s


We are going to plug these equations into excel (we got them from the professor)

Data/Results/Analysis

The picture above is where we plugged all the given information into excel


This picture is where we found change of position becomes 0m for change of t is 0.1s


This picture is where we found change of position becomes 0m for change of t is 0.05s

Conclusions
1. Our t is between 19.6s and 19.7s and x is between 248.692m and 248.698m when change in t is 0.1s
And when change in t is 0.05, t is between 19.65s and 19.7s and x is between 248.697m and 248.698m
It was very close from the given answer of x = 248.7m when t = 19.69s

2. We can decide it is small enough for the time interval when we do not see much difference in results.

3. 
178.17m

31-Aug-2016: Free Fall Lab-determination of g and some statistics for analyzing data

Free Fall Lab
Jae Yoo
8/31/16
partners: John Demontano, Shawn Mazzio

Accomplishment
determination of g(and learning a bit about Excel) and some statistics for analyzing data

Theory/Introduction
In the absence of all other external forces except gravity, a falling body will accelerate at 9.8m/s^2

Apparatus/Procedure
1. Pull a piece of paper tape between the vertical wire and the vertical post of the device. Clip it with a weight to keep the paper "tight"
2. Turn the dial hooked up to the electromagnet up a bit
3. Hang the wooden cylinder with the metal ring around it
4. Turn on the power on the sparker thing
5. Hold down the spark button on the sparker box
6. Turn the electromagnet off so that the thing falls
7. Turn off power to the sparker thing
8. Tear off the paper strip


Data


The film of paper had dots generated by sparks that we measured with a ruler. Each dot was 1/60th of a second apart from one another. Dots gets more spread apart as we measure the distance between two dots.

Calculated results/graphs of data

We logged our time, distance, delta x, mid-interval time and mid-interval speed onto excel. With excel we are able to use the program to calculate and input the data in a timely manner. In the time column A3 we entered =A2+1/60 and then dragged the corresponding cells to have excel input the numbers for us. For distance the data was from the paper film we measured. Delta x the formula was =(B3-B2). Mid-interval time was =A2+1/120. Mid-interval speed was =C2/(1/60).
Velocity vs Time
Graphing our speed versus time, we highlighted our data from columns D and E. Selecting the XY scatter graph we were able to obtain what is showing on the left. Using excel to graph our data also allowed us to gain our slope by adding a trend-line in the options.
Mid-interval is the point between each of the 1/60th of a second.
Position vs Time
We obtained the position over time graph the same way as above. The difference is we highlighted our data from column A and B.

Analysis
We can find gravity from both the graphs by using two kinematic equations

we can apply first equations from velocity vs time graph to find g
or we can apply 3rd equation to find g from position vs time graph

Conclusions
We got g = 9.53m/s^2 and 9.58m/s^2 as the result from both data, y=952.89x+65.886 and y=479.18x^2+64.882x+0.0669
These are very close from the actual value of g=9.8m/s^2
There are some uncertainties during the lab and we will be dealing with it at part 2

Part 2- Uncertainty
There are two forms of error, random error and systematic error
Random error is scatter in data that you can't 'blame' on anything particular
Systematic error comes from assumptions we've made which are not true. We need better and more expensive equipment to solve the problem
Other error is human error, mistakes from human

Standard Deviation is a quantity calculated to indicate the extent of deviation for a group as a whole.
So we found Standard Deviation of the Mean of the class' data to find our uncertainty of g

As the result, we got 935.9+/-28.27 as our g
All of our g's are lower than the actual g
our average value is also lower than accepted value of g
Class's values of g is also lower than actual g
There are both systematic errors and random errors on our data

The lab was to find g and learning about uncertainty. There were errors occurred due to air resistance and friction forces. Key ideas for the lab was to know how to use excel and find g from the graph. we were supposed to get lower g value than the actual due to errors and be able to find the uncertainties from the errors.

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

Inertial Balance Lab

Jae Yoo
8/29/16
Partners : John Demontano, Shawn Mazzio

Accomplishment
We were trying to find a relationship between mass and period for an inertial balance.

Theory/Introduction
We often use spring scales and balances to measure mass. These measuring devices are calibrated to make use of the Earth's gravitational pull in order to determine mass, and would be useless for measuring mass without the presence of gravity. Mass measured in this manner is known as gravitational mass.
Mass, however, is a quantitative measure of an object's inertia, and is not dependent upon gravity. Therefore, the mass of an object remains constant, regardless of the presence or strength of a gravitational pull.
The Inertial Balance is a device that is used to measure inertial mass by comparing objects' resistances to changes in their motion.

Procedure

1. Use a C-clamp to secure the inertial balance to the tabletop. Put a thin piece of masking tape on the end of the inertial balance.
2. Set up a photogate so the when the balance is oscillating the tape completely passes through the beam of the photogate.
3. Set up the LabPro with a power adapter, USB cable, and plug adapter plugged into the DIG/SONIC1 input.
4. Open the Logger Pro application.
5. Record the period with no mass in the tray.
6. Add more mass 100g - 800g and record the period of each of them.

Data


Calculated results/Graphs



Analysis
From the equation T = A(m+Mtray)^n, we took natural log on both sides and got lnT = n*ln(m+Mtray)+lnA.
From this equation, lnT = n*ln(m+Mtray)+lnA, n is slope ln A is y-intercept on our graph.
We got n as 0.7139 and lnT as -5.392 from when Mtray was 335g.
And n as 0.6658 and lnT as -5.034 from when Mtray was 295g.

Conclusions
We used the original equation, T = A(m+Mtray)^n, to find unknown mass 'm' since we know all the other values.
We got 169.655g and 167.106g when the actual mass was 169g,
And 45.5949g and 46.4746g when the actual mass was 46g.
As the result, we got very close calculated values from the actual values.