Lab 13: Magnetic Potential Energy Lab

Introduction: In this lab we will be looking in the potential energy found in the magnets of the cart and the wall. This lab will test out whether or not the conservation of energy applies to the system.  The challenge for this lab is to find an equation for magnetic PE will help us better understand the concept.

Setup:
                                         

The setup for this lab will involve a frictionless cart with a strong magnet on one end approaches a fixed magnet of the same polarity. when the cart is at the position of closest approach to the fixed magnet, the carts KE  is momentarily zero and all of the energy in the system is stored in the magnetic field as magnetic potential energy, then rebounds back. whatever is stored as PE will be converted back as KE. 

Purpose: As stated in the intro, the purpose of this lab is to find the equation and the distance between the cart and the magnet attached to the wall. We do this in order to pinpoint the exact moment the magnets interact before repulsing each other. When the art is at the position of the closest approach to the fixed magnet the carts kinetic energy is zero and the energy is stored in the system.

 These picture you see here are the diagram what we will be looking for and provide a more visual representation f what i described above. 

Data

The pictures you see right here are the graphical representation of of the experiment we just conducted. In the first picture the graph is that of the first trial with all the initial conditions intact. There the sensor pick up a velocity of 0.544 m/s and when we took the integral of the graph and got a energy reading of 0.4359 N*s, the second trial we added a 200 g mass to the cart which in turn gave us a higher energy reading of .5786 N*s, but lower velocity of .528 m/s. this is expected as the more the mass a particle has, lower the velocity and higher the energy it will. The third trial has a different setup from that of trials 1 and 2. For trial 3 we had the track setup at an incline with varying increments of theta with it. The cart would then be sent down the incline we recorded the separation distance between the cart on the incline and the magnet at the end. The data table above the graph, is the varying  heights and degree levels we used for the experiment. After the trials conducted we have found the separation distance before KE is transferred to the magnets as GPE  is approx. 2.35 cm. with a height of 3.4 cm at 6.5°. The lab also asked us to find an equation to relate the transfer of energy between two particles. We used an improper integration and what found to be our equation is 4.35* 10^-5 * r^-1.449.

Conclusion: After running the trials we managed to find our equation  and separation distance. There were however sources of uncertainty sand error that may play into effect of the data and equation we found for thelab. One source of uncertainty was the timing cart, as we did had some accounts of miss--timing when we let the cart roll down the track. Another source of certainty  may be the level of the track, we did have problem leveling the track for the second part of the experiment. This leveling had an impact to the cart's velocity which also explains the velocity readings in our graphs above. 

Lab 11: Work-Kinetic Energy Theorem Activity

Introduction: In this lab we will be inspecting closely to the concept of work-kinetic energy theorem by conducting four different experiments. First experiment is "Work done by a constant force", in this experiment we will be using a cart with a mass and force sensor and a counter weight attached to a string. The second experiment is "work done by a non constant force, using night the same track setup done in experiment 1. however instead of the tension cable and hanging mass, we will be using a spring force attached to the end of the of track. The third experiment is "Kinetic Energy And The Work-Kinetic Energy Principle", This experiment involves another cart track setup, but this time we will have the spring on the cart while it is heading towards the motion sensor. Finally we will do experiment four which is more of a analytic experiment than a involved one, this involves watching a video titled "Work KE theorem cart and machine for Phys 1.mp4. We will be watching and stopping the video at key points to analyse the force vs position for the machine stretching the rubber band in the video. As we watch the video we will be recording all measurements, that we will use for the final part of the experiment, calculating the final speed and using it to plot a force vs distance graph of the rubber band and the machine pulling it.

Setup:

This setup for EXPT 1  is mass pulley system, with a cart on the track and a hanging mass attached to the rear end of the car. In front of the track there is a motion detector and on top of it is force sensor. These two sensors are used to collect data used for the analysis in this experiment.

For EXPT 2 and EXPT 3, the setup will change from that of expt 1. This setup will involves a spring force. This setup will allow us to test both non-constant forces and the work- kinetic energy principle. For EXPT 2

Lab 10: Work and power

Introduction: In this lab we will be testing out the relationship between work and power in a unique involved way. This involves using a rope, a pulley system and some people to output power to the rope. We will do the experiment outside and test out the the relationship between work and power .

Setup:

This the mass-pulley system we will be using for the experiment. Here we will be lifting a known mass by a measured distance. (We'll be pulling on a rope that goes over a pulley to a backpack containing a known mass. You'll lift the mass by pulling on the rope). The second experiment of the experiment is walking up the stairs and recording the time it takes to reach up the stairs, while calculating our power output. The last experiment is now running up the stairs, timing and calculating power output, same steps s part two.

Purpose:The purpose of this lab is to observe and apply the concept of work and power. The experiment that we performed apply a certain type of work that if we were able to convert that work into power we have something to keep energized. After the experiments were completed we took the data we collected and calculated the amount we generated from each experiment.

Data/Conclusion:

The data here is the calculations we did for each experiment. For the first experiment the calculations shown here demonstrates the amount of power generated pulling the hanging mass to the top, the second and third experiments show the same purpose of generating power of going up the stairs but through different speeds (i.e. walking and running). Below the data calculations are the questions asked in the lab handout. These questions will test our knowledge of how muh we know how to do work and power problems.

Conclusion:

In these photos above, are the calculations for the problems in the lab handout, for part a our analysis for the neglected KE in calculation for total work, it shows that our percent error was around -0.189% which it is almost to the point negligible error (would not alter) our results in any way. 

Part b, we have calculated the total steps it would take to generate the same power as a microwave oven does,  and we found it takes us on average 602 steps go up and down the stairs to generate the same power as a microwave oven. For part c, we would need to take 26 flights of stairs of stairs to generate to the same amount of power as the microwave for six minutes to cook two potatoes. Finally part d, we managed to calculate the data shown in the lab for the three questions. part a the person would need to generate about 3.1 KJ/s to generate heat for a 10 min. shower. As for question 2 it would take 40 people to generate the amount of energy needed to power the shower. 

3-04-2017. Lab 9: Lab-Centripetal acceleration and angular speed.

Introduction: For this lab we will be testing the concept of centripetal force using a tripod and a motor attached to a board and some string with a hanging mass. To give a rundown of what the concept we are study is, centripetal force is the force that makes a body follow a curved path. Its direction is always curved to the motion of the body and it is fixated to a fixed point of the center of curvature.

Setup:

Here is a picture of what the apparatus we are using looks like. The apparatus is a horizontal rod mounted to a vertical rod all mounted to a motorized tripod. At the end of the horizontal rod we have a some string attached with a rubber stopper at the end. Outside the assembled apparatus is a ring stand with a horizontal piece of paper sticking out.

Purpose: The purpose of the trials is to find the relationship between centripetal force and its angular frequency when it rotates. The drawing of the experiment above is the diagram when will use for our calculations when determining our data. To find our ⍵, we need to measure our height from the rod attached to the tripod, the length of the string, the radius of the rod, and the height of the attached mass from the string. Once we find the dimensions of the apparatus, we can find our 𝛳 by taking the difference of the two heights using the result for our adjacent side to our angle and using the length of the string, we can use a cosine function to find 𝛳, and then using it to find ⍵.

Data:

31-03-2017: Lab 8 Centripetal acceleration with a motor

Introduction: In this lab we will be looking viewing a demonstration of an experiment using a wireless force sensor mounted onto the large rotating disk with one axis pointing toward the center of the disk. During the trials we will view the whole system rotating as the instructor makes certain modifications to the setup.

Purpose: The reason for this demonstration to determine the relationship between centripetal force and angular speed of the rotating disk. To put more simply, we need see how the rate of acceleration relates to the frequency of the disk’s rotation. In order to accurately determine the relationship, we are going to conduct 11 trials with varying measurements made to the setup. The first varying measurement marking a starting point on the disk. We do this to keep track of the number of time the disk’s rotations passes through the photogate, enable us to determine the period (time it takes to complete x number of rotations) of the disk. Second is the force sensor reading, this measurement is taken to determine the amount force it exerts when rotating on the system. To measure accurately, we attached a mass to a string and place it on the center of the disk, with the force sensor faced flat onto the disk. As the disk is spinning the sensor will record the force of the mass attached to the string while it is rotating. The final measurement we take is the distance of the mass from the center of the rotating disk, for this measurement, we look at the disk’s radius, using the string for the mass-force measurement, we record the length of the string from the center to the edge of the disk, and for each trial we increase the radius as we go on.

 Setup:

1.       Place the wireless force sensor on the disk. Zero  the force sensor with the disk rotating,.

2.       Adjust the voltage the on the power supply, turn on the scooter motor, and let the disk come up to a constant speed record the force sensor reading.

3.       Collect the period and the force data for:

. a variety of rotational masses at a fixed speed (look at the effect of changing m)

. the same mass at a fixed speed but different radii (look at the changing r)

. the same mass at a constant radius but a variety of rotational speeds (by varying the voltage from the power supply feeding the motor)—(look at the effect of changing omega).

Data Shift 

Force vs. Mass: 

The data shown here, was the reading we got from the sensor attached to the rotating disk. As you can see, the amount of force increases as we increase the the rotating speed of disk. With

the amount of force increasing , it also increased its angular velocity and acceleration as well. The statistics you see on the left shows the it's both linear and angular velocity and acceleration, it is under the min and max with the third trial having a maximum velocity angular velocity of 20.62, a minimum velocity of 9.192 m/s and a acceleration of 3.198 m/s^2.


Conclusion: After completing the trials we can conclude that our hypothesis was prove correct in regards to the relationship between force and centripetal acceleration. The amount force generated in the trials with the disk attached motor relates to centripetal acceleration. The faster the velocity and acceleration is the higher the force is generated.

18-03-2017. Lab 5: Trajectories

Introduction: for this lab we will be further our understanding of projectile motion. To do so we will using an apparatus (as shown below) to demonstrate the concept in full view. To use our understanding of projectile motion to predict the impact point of a ball on an inclined board.

Procedure: To commence the experiment, we we must set up the apparatus , where we will launch the ball from a readily, identifiable, and repeatable point. near the top of the inclined ramp. Next to record our impact point, we will use carbon paper and tape it to a regular piece of paper, so when the ball lands on the impact point, the carbon paper records where it lands. We will do this five times to verify our predictions, and if they are correct, they will virtually land the same place each time.

Data/Calculations:                                            
                                                                       

This calculation above is used to find the how far it lands from the table's edge when it is being launched. To use this, we must first find the time t  using the height and angle measured before commencing the experiment. Once find x we can determine the launch speed of the ball as shown in the calculations above. When calculated, we found our  launch speed to be 15.1 cm/s and landing edge to be 20.2 cm.

Continuing our calculations from above, using our results from the calculations of v_0 and x we can use them to calculate the theoretical value of our landing distance from the apparatus. When calculated, we expect the ball to be found the 24.4 cm from the landing site of  the apparatus. When performing the experiment however we found the ball to land 26.3+/- 0.32 m from the apparatus, almost 2 cm  from our predicted impact point. Performing the experiment a number of time shows the ball landing between 2-4 cm from the theoretical impact point. Indicating a source of error in the experiment.

Conclusions: After completing the experiment, we were able to demonstrate the concept of projectile motion. In write-up, we indicated that we encountered a source of error in the experiment. One of the source may be the measurement of our height from the apparatus.

14-3-2017. Lab 3: Non-Constant acceleration problem/activity

Introduction: In this activity we will explore the concept of non-constant acceleration by applying it in a problem.
Problem: 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 1500-kg 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/) so that the m(t) = 1500 kg - 20 kg/s*t.
The objective of the problem is to find how far the elephant goes before coming to rest. Now there two ways we can find the distance of the elephant, an analytical approach and a numerical approach.

Analytical approach: This method involves using the Newton's 2nd law giving us the acceleration of the elephant + rocket system as a function of time. a(t) = Fnet / m(t). Next we can integrate the acceleration from 0 to t to find 🔼v and then derive an equation for v(t). Then we can integrate the acceleration from 0 to t to find 🔼x and then derive an equation for x(t), were we can use integration by parts. Once all the integration is all done and we can add all the elements to find the distance the elephant travels until the rocket runs out of fuel.

Numerical approach: As we can see from above, the analytical approach is time consuming. It turns out we can do it faster by using the numerical approach.

Conclusions:
1. When doing it numerically it was faster and more simple to use then the analytical approach, the former method allowed us to retain most of the original data, while the latter method allowed forced to us alter our data to fit the parameters of the problem, as when we did the numerical approach using Excel, our values for 🔼v and 🔼x were inconsistent with each other.

13-03-2017 Free Fall Lab

Introduction: For this lab we will be looking at the determination of g by using an apparatus to study of the basic laws of motion, demonstrating a free falling body.

Purpose: The purpose of this experiment is to examine the absence of all other external forces except gravity.

This is the apparatus used in the experiment. To us the apparatus we must first pull a piece of paper between the vertical wire ad the vertical post of the device. Second turn the dial hooked up to the electromagnet up a bit. Third hang the wooden cylinder with the metal ring around the electromagnet. Fourth turn on the power on the sparker thing. Fifth hold down the spark button on the box. Sixth turn the electromagnet off, so the thing falls. Seventh turn off the power to the sparker thing. Finally tear off the paper strip and set up the spark paper,to obtained the data for the next portion of the lab.

Data

This data shown above shows us the value for g for the object that falls on the apparatus and statistical data for our experiment. As we can see the avg value for our g constant is 962.852 m/s^2. 

Lab 1: Finding a relationship between and period for an internal balance. 8-Mar-2017

• Purpose: In this lab we are trying to highlight the relationship between mass and period for inertial balance. To do this we need to measure the period of oscillation for a bunch of different masses, that we can use to develop a mathematical model of the relationship between period and added mass. 

   This is the inertial pendulum that we will use to find the relationship between mass and period. This device allows us to record oscillations that occur during movement. The pendulum has a metal tray attached to two springy pieces of metal. So when we give the metal a pus, it will vibrate back and forth. this is how we will record our oscillations.

To obtain the data for this lab, we first must record the oscillations from the pendulum, using a motion sensor. First we start with no mass to test the sensor reading then we start adding the masses from 0 to 800, and record the time it takes to complete one oscillation on LoggerPro.

This is graph that  details the parameters of the experiment. Where we used the motion sensor to determine the period and distance the oscillations traveled.

During the day of the lab, we measured the oscillations that took place on the spring pendulum, then took the raw data the you above, and came up with an equation to find the unknown mass. After that we were able to conclude that that are range of masses for this experiment were between 275<m<325.