Nikki,+Alyssa,+Rebecca

Due: 3/7/11 Period 4
 * Elastic Potential Energy Lab**
 * By:** Alyssa Berger, Niki Kaiden, Rebecca Rabin

**Part 1:** Hooke's Law and finding the spring force constant

 * Hypothesis:** From the equation F=-kx, we believe that the slope of our graph will end up showing the "k" or spring force constant of this spring. In this equation, the displacement is on the x-axis and the force is on the y-axis, and therefore, if we did the experiment properly, the "k" value should be the slope of the graph.

Materials 1) Stand 2) Mass hanger 3) Ruler 4) Masses 5) Spring
 * Procedure**:

Set-Up and Methods 1) Attach the spring to the stand so that it is hanging. 2) Attach mass hanger to hanging end of the spring 3) Adjust ruler on the stand. Ideally, have the end of the spring on the 0 mark of the ruler but if not possible position it as close as can be. 4) Measure the distance the spring extends to on the ruler. 5) Add mass to the spring hanger 6) Measure the difference the spring extended to with mass and record. 7) Repeat steps 5 and 6 at least four more times, adding more mass each time.


 * Data** **Table**:

On our graph, the slope showed the value of the spring's force. Our group obtained 4.2558. The class average for the spring force constant was 3.819. The average of our results and the class average was equal to 4.0374.
 * Graph**:


 * Percent error between our spring force constant and the class average:**

**Part 2: D**etermine the relationship between the spring force constant and final velocity of the spring

 * Hypothesis:**
 * By increasing the horizontal distance (x), the final velocity of the car will increase thus creating a direct relationship between distance and velocity. **

Materials 1) Track 2) Stopper 3) Meter Stick 4) Same spring from Part 1 5) Photo Gate Timers 6) Cart
 * Procedure**:

Set-Up and Methods 1) Place the track on a flat surface 2) Attach the photo gate timer and timer to end of track 3) Attach a 1 cm paper flag to the end of your cart 4) Attach spring to cart and stopper so the flag attached to the cart goes through photo gate timer 5) Open Data Studio on your laptop 6) Record where the end of the cart is when the spring is not being extended. 7) Pull cart back and record difference in distance of the cart. 8) Let cart go and record information from Data Studios to calculate final velocity.


 * Sample data studio:**


 * Data Table:**

We graphed the experimental velocity versus the final distance, to ultimately receive a trend that they are directly proportional when using a spring. Our R squared value of .9996 shows that our results are very accurate!
 * Graph:**


 * Experimental Sample calculation trial 1:**
 * Theoretical Sample Calculation trial 1:**

Error Analysis:

Conclusion:

The data collected supports our original hypothesis. By discovering our proper "k" value, we determined that it was our spring was soft. This meant that it had the ability to stretch far, allowing us to increase the weight which would change the acceleration. We can determine the k value by the slope of the graph because it represents the spring force constant (k value). We know the slope of the line is the k value because the force equals the mass from the spring and x is the displacement, which would then only leave the k to be represented as the slope. There were several sources of error in our lab. In the first part where we were determining the exact k value, we could only obtain numbers with not that many sig figs and decimals. With such a precise and exact number as the k value of the spring, rounding and estimating limited the accuracy of our results throughout the entire lab. The error could be decreased by using more precise measuring tools for part one. In the second part, we made friction negligible however there was some amount of force due to friction that can change the value. If the photogate timer was not located exactly where the spring did not have any distance, the final velocity would be off.