Erica,+Allison,+Roshni

=Lab: Elastic Potential Energy= toc Members: Roshni Khatiwala, Allison Irwin, Erica Levine Date: March 7th, 2011 Class: Honors Physics Period 2

__PART 1: FINDING THE SPRING FORCE CONSTANT__

PURPOSE The purpose of this lab is to determine the spring force constant of the spring we are given.

HYPOTHESIS If we measure and graph the change in distance and the change in force of the spring as we add masses, then the slope of the graph will give us our spring force constant, which should be a relatively higher number than that of other groups' springs, because this one seems to be somewhat tighter.

MATERIALS Spring, mass hanger, spring stand, ruler, individual masses

SETUP

PROCEDURE 1. Set up the spring stand, with spring hanging on one side. Make sure that a ruler is positioned with the stand, close to the spring, so that the change in x distance can be easily measured. 2. Attach the mass hanger to the spring, and measure the change in distance. 3. Record mass and change in distance in Excel spreadsheet. 4. Repeat steps 1-3 for varying masses, plotting each set of data points on a Force-Distance graph (Hooke's Law tells us that force should be on the y-axis, and that the change in distance should be on the x-axis). 5. Once 5-6 sets of data points have been recorded, find the slope of the graph. This slope is the spring force constant.

DATA attachment:

GRAPH

SAMPLE CALCULATIONS PERCENT DIFFERENCE CONCLUSION The fit of our graph is linear due to the equation Fs=-kx where F is force, k is the spring constant, and x is the displacement from equilibrium. Using the slope of our position v. force graph, we determined that the spring force constant of our spring is 4.1566 N/m. This was 9.8% less than the class's average k value. First, this could be because our spring has been used less and therefore is less springy than the other groups'. However, this could also be due to error. Our main source of error in this experiment was probably our measurement. We were using the hook on then hanging mass to give us our x value and it may not have been accurate if we were looking at it at the wrong angle, etc.

__PART 2: DETERMINING THE RELATIONSHIP BETWEEN THE SPRING FORCE CONSTANT AND THE VELOCITY__

PURPOSE The purpose of this lab is to determine the relationship between the spring force constant of our spring, and the velocity of the cart we attached to the spring.

HYPOTHESIS If we increase the x value in the EPE = 1/2(kx^2) equation, then the velocity of the cart will increase as well, due to the EPE = KE equation.

MATERIALS Cart, spring, ramp, photogate timer, datastudio sensor

PROCEDURE 1. Attach the cart to the spring, and place on ramp. 2. Pull cart back at varying distances, and use datastudio to measure the time it takes for the flag on the cart to go through the photogate timer. 3. Use the distance and the time to find the velocity of the cart. 4. Create a Distance-Velocity graph

SETUP

DATA



GRAPH

SAMPLE CALCULATIONS

Theoretical Velocity: Experimental Velocity

PERCENT ERROR









CONCLUSION We assume that our main source of error was in pulling back the cart each time. While we tried to keep the x value both consistent and accurate, any slight deviation could have caused error. Even a few millimeters or a centimeter difference could have been the cause of this disparity. As seen by our percent error values, on general the error decreased the more we pulled the cart back, showing that the this small inaccuracy had a lesser effect overall. We determined that friction between the track and cart was minimal and most likely did not contribute to our error. As seen by the positive slope of our distance v. velocity graph, as we increased the (x) distance, the average velocity increased, proving our hypothesis correct. Our graph is again linear in correlation to the direct relation ship of the (x) and (v) variables in the equation EPE=kE --> 0.5kx^2 = 0.5mv^2.