Chris,+Brett,+Ross,+Scott

=Lab: Law of Conservation of Energy 2= toc By: Bret Pontillo, Ross Dember, Chris Hallowell, and Scott Siegel Period 4 Due: 3/7/11

OBJECTIVE: What is the spring force constant? What is the relationship between EPE, KE, and GPE of a mass on an oscillating spring?

HYPOTHESIS: The further the spring is stretched out, the larger the velocity.

MATERIALS: 1. Frictionless Track 2. Cart 3. Spring 4. Data Studio Photogate Timer 5. Laptop 6. Excel Spreadsheet 7. Ring Stand 8. Various, Small Masses 9. Paper Flag (A marker easily read by the Data Studio Photogate Timer)

PROCEDURE FOR PART 1 (HOOKE'S LAW):

First, after we gathered all the necessary materials for the first part of the lab, we attached the spring given to us to a small ring stand, leaving the spring hanging. We then accounted for the hanging mass attached to the bottom of the weight, and figured out which position was going to act as "zero" for our experiment. Once that was determined, we added various, small masses to the hanging mass, at the bottom of the spring. We then measured the position of the bottom of the hanging mass, its displacement, and the amount of mass that was used to pull the spring down. We ran several trials of the previous procedure, finding the average displacement (or distance) for each weight. Lastly, we created a graph in Excel with the data recorded in our Excel Spreadsheet, including the weight and average displacement. We were able to hypothesize that the slope of this graph was the spring force constant.

PROCEDURE FOR PART 2 (LAW OF CONSERVATION OF ENERGY):

For the second part of our experiment, we laid a frictionless track on a flat surface, placed a cart (after we measured its mass) on the track, and attached a small, paper "flag" to the side of the cart (after we measured the width of the "flag"). Then, we attached the spring from the first part of our experiment to the cart and one end of the frictionless track. Next, we set up a Data Studio Photogate Timer to the track, in line with the paper flag, while the cart is at rest. Then, we opened Data Studio on our laptop, and connected the Photogate Timer to the laptop. After that, we measure the distance of the cart when it is at rest, assuming this as our "zero" position. Next, a member of our group pulled the cart back to a certain distance (centimeters), and released the cart, while at the same time recording the time the cart spent in the Photogate Timer using Data Studio. We then used this time to find the velocity of the cart for each of the trials. Lastly, we repeated the previous procedure several times, using varied distances. We used our Excel Spreadsheet to create a graph using the average velocities for the different trials and the various distances to form a conclusion on the relationship between the velocities and distances.

PICTURE OF SET-UP OF PART 2:



VIDEO OF PART 2: media type="file" key="Movie on 2011-03-03 at 11.32.mov" width="300" height="300"

DATA TABLE- PART 1:
 * We decided to use the position when .02 kg were on the spring as our original position. We then took measurements in comparison to that value.

GRAPH- PART 1: Using Hooke's Law, we can see that the slope of our graph is the "k" value of the spring. We can now use this value for Part 2 of our lab.

DATA STUDIO- PART 2:



DATA TABLE- PART 2:

GRAPH- PART 2:
 * As you can see, the distance the spring is pulled back is directly proportional to velocity.

CALCULATIONS- PART 2: First, we needed to find our experimental velocity. We will be doing the calculation below for the ".1 m" trial in the data table above. In order to find the velocity, used the distance of the paper that was passing through the photogate and the time that it took to pass through the gate.

We then needed to find the theoretical velocity using the Law of Conservation of Energy. Our "k" value came from Part 1 of our lab.

In order to find the percent error of the lab, we used the experimental and theoretical velocity of this trial.

CONCLUSION:

We were able to successfully prove our hypothesis using the law of conservation of energy. With no work being done (assuming the track was frictionless), we could determine that the only energy in the beginning was elastic potential energy, and the energy at the end was only kinetic. With most of the values accounted for, measuring velocity was simple, and our error showed that the error was not too great.

This lab had many possibilities for errors. First, our //k// value was solved for in a separate experiment, one of which required us to take into account inexact measurements, and sometimes, an oscillating spring. Furthermore, finding velocity, we had to place the photogate at a perfect distance, since putting it too far towards the side would allow the spring to fully coil back, lowering the velocity. Also, it is possible that using the spring too much could have "stretched" it out and made the final results more inaccurate.

Besides helping the class learn more about elastic potential energy, this lab had many real-life factors. For example, if someone wanted to sling shot an object, he or she could determine the final velocity of the projectile if the //k// value was known. Same thing for a trampoline and those awesome little toys that you push down on and pop up. Needless to say, understanding elastic potential energy and its relationship to kinetic energy has its benefits.