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.