19-April-2017: Lab 15: Collisions in two dimensions

Lab 15: Collisions in two dimensions

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: April 19, 2017

Purpose of the lab: 
Look at a two-dimensional collision between a steel ball and another steel/aluminum ball and determine if momentum and energy are conserved.

Set up:
A iphone 5 with camera, two same steel balls, and a aluminum
we put our phone above the table, then capture two video.
First one is steel ball collision with steel ball, second one is steel with aluminum.

Measured data:
The mass of the steel ball: 0.071 kg
The mass of the aluminum ball: 0.01 kg
The length of the glass table: 58.6 cm

For the first one, we used steel with steel collision. we added three point series and set the origin on the collision point.

Then we use steel and aluminum

Analysis:
First collision graph:

Conservation of momentum:
momentum before collision: m*vx1 = 0.033, m*vy1 = -2.84*10^-4
momentum after collision: m*vx2+m*vx3 = 0.028, m*vy2+m*vy3= -7.1*10^-3
KE before collision: 0.5*m*(vx1^2+vy1^2)=0.0077J
KE after collision: 0.5*m*((vx2+vx3)^2+(vy2+vy3)^2)=0.0059
For first collision, there is some errors that makes the initial result and final result are not very close.

Second collision graph:

Conservation of momentum:
momentum before collision: m1*vxi=0.054, m1*vyi=-0.0038
momentum after collision: m1*vxf+m2*vx2=0.0535, m1*vyf+m2*vy2=-0.0061
KE before collision: 0.5*m1*(vxi^2+vyi^2)=0.02J
KE after collision: 0.5*m1*(vxf^2+vyf^2)+0.5*m2*(vx2^2+vy2^2)=0.0195J
For the second collision, the result is much more closer, which means this one has less errors.

Conclusion:
In this lab, we wanted to find out the conservation of kinetic energy and momentum. However, there are many errors in this lab. Our video is captured by a 30 fps iphone 5, so when we were adding points for the graph, it's very hard to add points on the correct place. Then our velocity have errors too.

19-April-2017: Lab 14: Impulse-Momentum activity

Lab 14: Impulse-Momentum activity

Author: Tian Cih Jiao

Lab Partner: Weisheng Zhang, Kitarou

Date: Apri 19, 2017

Purpose of the lab: Observe/verify the impulse momentum theorem

Theory/Introduction:

EXPT 1: Observing Collision Forces That Change With Time

First, we replace one end of force senor by a rubber stopper. Then we give a push to the cart so that it has a V0, after the collision, it has a Vf.

According to impulse-momentum theorem, change in momentum of the cart = net impulse.

So m * (Vf - V0) = The integral of F(t)

We can calculate the integral through the graph draw by the force sensor.

EXPT 2: Larger Momentum Change

Add some hundreds of grams of mass on the cart and do the same process in Part 1.

EXPT 3: Inelastic Collision

Replace the spring with a plasticine so that the cart will stop after collision. 

Apparatus/Experimental procedure:

Left is spring, right is plasticine






Measured data:
The mass of the cart is measured to be 0.64 kg originally (1.14 kg if a 500-gram mass is installed onto the cart).

EXPT 1 Graph:


EXPT 2 Graph:


EXPT 3 Graph:


Analysis:
EXPT 1: Integral is 0.7022, which is Impulse. It should be equal to change in momentum. Change in momentum = 0.64 * delta v = 0.64 * 1.124 = 0.71936
EXPT 2: Integral is 0.9844, Change in momentum = 1.14 * 0.844 = 0.96102
EXPT 3: Integral = 0.3328, Change in momentum = 0.64 * 0.508 = 0.3253

Conclusion:
From the lab result, we can get that the Impulse-momentum theorem applies to elastic collision but not to inelastic collision.

17-April-2017: Lab 13: Magnetic Potential Energy Lab

Lab 13: Magnetic Potential Energy Lab

Author: Tian Cih Jiao

Lab Partner: Weisheng Zhang, Kitarou

Date: April 17, 2017

Purpose of the lab: The purpose of this lab is to verify that conservation of energy applies to the system we set

up (cart-magnets system).

Theory/Introduction:

For this lab, we use the conservation of energy to find out the magnetic potential energy.

First, we used a track with different slope and get several data for the graph.

Apparatus/Experimental procedure:

Apparatus: cart, two strong magnets of the same polarity, air track glider, some books to change the slope, aluminum reflector installed on the cart for detection of motion, motion detector, Logger Pro.

Procedure: 

First, we need to find out the function for F(r). We change the slope to get a equilibrium position, where the magnetic repulsion force = the gravitational force component parallel to the track. This component is mgsin(x), where x is the angle of the raised track.We changed the slope so that we get enough data, then we can powerfit to find out the graph.

After we find the formula of F(r), we can now prove the validity of conservation of energy theorem is this setup. 

We turned air track power off, put the cart on the air track, close to the magnet. Run the motion detector. Determine the relationship between the distance the motion detector reads and the separation distance between the magnets.

After that, start the cart at the far end of the track. Start the detector and give the cart a gentle push. Record the data before, during and after the collision. Plot a graph showing PE, KE, and total energy of the system as a function of time.

Measured data:

The mass of the cart is measured to be 340 grams (0.34 kilograms).

To figure out the formula of F(r), five sets of data are collected.

x = 1.6 degrees r = 30.9 mm mgsin(x) = 0.34 * 9.8 * sin(1.6) = 0.093N

x = 3.8 degrees r = 22.3 mm mgsin(x) = 0.34 * 9.8 * sin(3.8) = 0.221N

x = 5.8 degrees r = 18.1 mm mgsin(x) = 0.34 * 9.8 * sin(5.8) = 0.337N

x = 7.5 degrees r = 16.1 mm mgsin(x) = 0.34 * 9.8 * sin(7.5) = 0.432N

x = 9.2 degrees r = 14.5 mm mgsin(x) = 0.34 * 9.8 * sin(9.2) = 0.533N

Kinetic Energy = 1/2 * m * velocity^2
The formula of Umag (magnetic potential energy) is derived from F(r), one of us calculated it on paper by hand.

Separated Distance =  0.342m = measured distance (which is 14 mm) + adjustment value

Graph for F(r) :

According to graph 1, F(r) = 159.3 * r^(-2.13). The integral is calculated to be -4.076. Therefore, U(r) = -(-4.076) = 4.076 J.

Analysis:

The sum of Umag, magnetic potential energy (in light green) and Kinetic Energy (KE) equals total energy (in blue).

According to graph 2, total energy (in blue) maintains a steady level in spite of the little zigzag (close to being a constant), which means that conservation of energy theorem applies to this setup reasonably enough.

Conclusion: According to our data (figure and graph), conservation of energy theorem applies to our setup as well (cart and magnets). 

Possible sources of error:

The phone we used to measure the angle of the incline is not calibrated (which may result in inaccurateness).

The assumption of zero friction on the air track (which leads to larger magnetic PE)

10-April-2017: Lab 11: Physics 4A Work-Kinetic Energy Theorem Activity

 Lab 11: Physics 4A Work-Kinetic Energy Theorem Activity

Author: Tiancih Jiao

Lab Partner: Harvey Thai, Jesus Gonzalez

Purpose of the lab: Measure work done by forces and figure out how kinetic energy and the work-kinetic energy principle works in real life.

Theory/Introduction:

KE= 0.5* m * v^2

W = delta (KE) = KEf - KEi

In this experiment, we have 4 parts. The first is to hang a mass with a string to the force sensor on the cart. The second part is to use a spring to hang on the force senor, and pull the cart to 0.6 m position. The third part is when the cart pull to the 0.6 m position, release it and record the data. The last part is to watch a video and find the work done by the force.

Summary of apparatus/experimental procedure:

Summary of apparatus/experimental procedure:

1. Set up the track, cart, motion detector, force probe, pulley, cart stop and hanging mass.

Plug the force sensor, and zero it. Put a 500-g mass hanging on the force senor and calibrate it to 4.9 N.

measure the mass and put the mass in User Parameters.

Level the tract to reduce the errors.

hang a 50-g mass and release to get the graph.

2. Set up the ramp, cart, motion detector, force probe, and spring.

make sure spring is unstretched. move the cart slowly to 0.6 m position. Sketch the graph.

3.Move the cart to 0.6 m position, then release the cart and graph.

Find the change in KE of cart after release. then find the work.

4. When we have the distance and the time, we can calculate the final speed and the KE of the cart.

Measured data:

M cart = 500 g

User parameters : m = 1 kg

For the first graph, we get the integral is 0.1788, and the KE is 0.160, which is very close to each other.

And then we change the area larger, we get integral is 0.3002, and the KE is 0.277.

For the next part, we get integral is 0.02471, and the KE is 0.023.

So we get that the area of the force graph is close to the KE calculated by the KE  equation.

Conclusion:

From the result of the experiment, we can get that the integral of force is pretty close to the KE. The level and the mass measure would be the error of this experiment.

05-April-2017: Lab 10: Activity - Work and power

Lab 10: Activity - Work and power

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Purpose of the lab:

Purpose of this lab is to calculation work and power based on real-life scenarios.

Theory/Introduction:

The first scenario is to lift a known mass up by a measured distance. We are doing this lab outside, where we lift a 5-kg backpack from the first floor to the second floor (top of the balcony). We measure the height of the floor, record the time needed to lift the backpack by pulling the rope. We calculate the power by calculating the work (gravity of the backpack times the height of the balcony) and dividing it by time.

We calculate the power output of someone walking/running up the stairs by using the height and the time of the process.

We measured the height of each stairs and then multiply it to the number of stairs to get the total height.

Measured data:

To get an accurate data of height, we measured three times for a single stair, then we get 6.3, 6.5 and 6.9. We calculated the average of them and get 6.6 inch. And there are 26 stairs. So the total height is 4.37m.

And the time is 11.2 s.

For the walking/running stairs part, we got 12.93 seconds for walking and 5.27 seconds for running.

Analysis:

This is the calculation of how we calculate the power output for lifting a backpack.

This is the calculation of how we calculate the power output for walking/running up the stairs.

Conclusion:
a) Let the speed is constant during walking and running. Then the angle of the slide is 40 degree. Then people travelled is h/sin(40).
Walking average speed = (h/sin(40)) / t(walk) = (4.37m/sin(40)) / 12.93s = 0.526 m/s
Kinetic energy (walking) = 0.5 * Mperson * v^2 = 0.5 * 88 kg * (0.526m/s)^2 = 12.17J
Running average speed = (h/sin(40)) / t(run) = (4.37m/sin(40)) / 5.27s = 1.29 m/s
Kinetic energy (running) = 0.5 * Mperson * v^2 = 0.5 * 88 kg * (1.29m/s)^2 = 73.22J
b) Pmicrowave / Pwalking = 1100/291.47 = 3.77 flights (walk) 
    Pmicrowave / Prunning = 1100/715.12 = 1.54 flights (run)
c) Pmicrowave * time (in seconds) / Work = 1100 * 360 / 3768.686 = 105.08 flights
d)
(1) 12.5 MJ * 10^6 J/MJ / (10min * 60 s/min) = 20833.3 watts.
(2) 20833.3 watts / 100 watts per person = 209 people 9(can't be 208, must be larger than 208)
(3) 12.5 MJ * 10^6 J/MJ / 100 (J/S) = 125000 second

04-April-2017: Lab 9: Centripetal force with a motor

Lab 9: Centripetal force with a motor

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Purpose of the lab:

The purpose of this lab is to find out the relationship between theta and omega. The experiment setup follows the photo

Theory/Introduction:

get h by the things showed below, when it hit the paper.

cos(θ) = (H-h)/L. then, θ= arccos((H-h)/L).

we will timer 10 rotation for how much time, then ω= 2*PI/(t/10)

Summary of apparatus/experimental procedure:

The following things are what we use in this lab.

Actual apparatus

 This is to measure the height, when it hit, it's the height.

Measured data:

H = 1.98 m +/- 0.01m

L = 1.6m +/- 0.01m

h = 0.81m +/- 0.01m

R = 0.8m +/- 0.01m

t1= 28.05s

t2 = 22.98s

t3 = 21.37s

t4 = 17.27s

t5 = 14.73s

t6 = 12.41s

Analysis:

And we use the table following to get more accurate results.

Conclusions:

θ is related to ω, and it increase with it.
and there are some errors in this lab.

31-March-2017: Lab 8: Demonstration - Centripetal Acceleration vs. angular frequency

Lab 8: Demonstration - Centripetal Acceleration vs. angular frequency

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: March 31, 2017

Purpose of the lab: To determine the relationship between centripetal force and angular speed

Theory/Introduction: 

To establish a relationship between centripetal force and angular speed, we first look into the function of position in terms of time. We get the function of velocity by doing the first derivative and the function of acceleration by doing the second derivative. By plugging the first equation into the acceleration one, we get a = -w^2 * r(vector), F = mwr^2.

Summary of apparatus/experimental procedure:

In this lab, we controlled many variables (mass, radius, and power) to see the change of Force.

Measured data:

Analysis: 

Controlled mass, we get this graph. The slope is 0.2224 which is very close to the mass of object which is 0.2 kg.

Controlled radius, then w should be constant, but it isn't, and mass should be vary.

r = 0.47m, slope = 0.4636.

r and w are constant, mass vary.

rw^2 = 0.004193, the slope = 0.004287

Mass and radius are constant, w vary.

mr = 0.078, slope = 0.08829

Mass and w are constant, r vary.

mw^2 = 0.0338, slope = 0.02936.

Conclusion:

Friction between the motor and the disk is one of the possible sources of error.

28-March-2017: Lab 7: Modeling Friction Forces

Lab 7: Modeling Friction Forces

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: March 13, 2017

Purpose of the lab:

There are five different experiments involving friction. The purpose of the lab is to measure both the kinetic and static coefficients, make predictions on accelerations and compare them to experimental values.

Theory/Introduction:

(1)   Static friction: The original plan was to hang a cup of water and to keep adding water drops to it. However, the system is set up in way where the block is connected to a hanging mass with a string. Instead of adding water drops to the cup, we add to the hanging mass by 5 grams at a time. We stop adding mass to it until the block starts to slide. Record data and do calculations.

(2)   Kinetic friction: This part of the lab requires a calibrated and zeroed force sensor. By connecting the force sensor and the block using a tied string, we pull it horizontally at a constant speed and record the data. We repeat the same processes for different masses (a set of five) to have a better idea of the average of the coefficient of kinetic friction.

(3)   Static friction from a sloped surface: For this part of the lab, we slowly raise one end of the surface until the block starts to slide. Measure that data and determine the coefficient of static friction.

(4)   Kinetic friction from sliding a block down an incline: Different from the last part, we give a pretty small force to make it move at a certain acceleration. Record that data and determine the coefficient of kinetic friction.

(5)   Predicting the acceleration of a two-mass system: Based on the calculated results in previous parts, we can establish a model for the case where a hanging mass sufficiently heavy is connected to the block to accelerate the system. Compare the theoretically predicted values to our experimental results.

Summary of apparatus/experimental procedure:

This lab set up : 

LabPro, Force sensor, block, hanging masses, string, wooden surface

Measured data:

Part 1:

Part 2:

Part 3:

We use app to measure that the angle is 34 degree.

Part 4:

The angle of the incline is 

Part 5:

The model we establish for the system of the hanging mass for accelerating the block is:

Analysis:

Part 1:

The slope = coefficient of static friction.

Part 2:

The slope = coefficient of kinetic friction.

so it is smaller than static friction.

Part 3: Then we use the slipping angle to get the following equation.

Part 4:
The block slides along the surface at an angle of 21 degrees above horizontal.

We apply linear fit to the velocity v.s. time graph (y = mx + c). As shown in the graph, the slope of the graph (m) is the acceleration, which is 0.249 m/s^2.

Following is one of us calculation, using acceleration, angle and mass of the block to get coefficient of static friction.

Part 5:
Since we have established our own model, we can predict the minimum amount of mass needed to accelerate the system.

As the calculation shows, the minimum mass is 0.045 kg.

Conclusions:

From the lab, we know that coefficient of static friction is larger than that of kinetic friction.
And there is still some errors like different surface.