Aaron Lin
Period 3
Honors Physics 1
3/16/2004
Spring Lab
Objective:1) Find the K value for a certain spring.
2) To study the conservation of energy.
Theory: In order to find the K value for a certain spring, the spring equation F=kx is used. Since we need k, we divide each side by the x value to obtain F/x=k. This represents the Force divided by the distance being equivalent to the spring constant k. Since we have multiple data sets, a graph was naturally the best option. Each data set was plotted and a line of best fit drawn. The slope was then found and this represented the k value (since force is on the y-axis and distance is on the x-axis). For the second part of the lab, we wanted to confirm this k value with another method, using the conservation of energy. Since the potential energies at the two extremes of the spring are equal (one being gravity, the other being the spring), we can set them equal represented by the equation max=kx^2/2. Using a mass and a spring, x, Ug and Us are obtained, which makes the calculation of the spring constant k possible. A simple percent error was then calculated to confirm.
Diagram:
Data and Calculations:
Part 1
Trial # / Mass(kg) / X(m) / K(N/m) [graph] / F(N) / Stretch(m)1 / .05 / 0.02 / 19.83 / .49 / 0.02
2 / .1 / 0.045 / 19.83 / .98 / 0.045
3 / .15 / 0.062 / 19.83 / 1.47 / 0.062
4 / .2 / 0.09 / 19.83 / 1.96 / 0.09
5 / .25 / 0.12 / 19.83 / 2.45 / 0.12
F = kx
F/x=k
Line of best fit: y=19.83x+0.13
Slope (k) = 19.83
Part 2
Trial# / Mass(kg) / X1(m) / X2(m) / X3(m) / Xavg(m) / K(N/m) / % error1 / .05 / .049 / .038 / .048 / .045 / 21.78 / 9.83
2 / .01 / .079 / .1 / .091 / .090 / 21.78 / 9.83
3 / .15 / .130 / .147 / .110 / .129 / 22.79 / 14.93
Ug=Us
Mad=1/2kx^2
(.05)(9.8)(.045)=(1/2)(x)(.045)^2
x=21.78
% error
(experimental-actual)/actual*100
(21.78-19.83)/ 19.83*100 = 9.83%
Conclusion: In this lab, we first found the spring constant k by obtaining trial sets of mass and distance. This data was used in a graph to obtain the spring constant using an implementation of the equation f=kx, where the slope represents k. Using this as our true value, we set out to study the conservation of energy. Using Ug=Us, since the potential energies of both extremes of the spring are equal, we found k for three trials. The experimental values were then compared with the actual ones obtained in the first part of the lab. The percent errors were not dramatically high, but were not very low either. For two trials, the percent error was 9.83, and for the last trial it was 14.92. For this part of the lab, visual accuracy was key to obtaining accurate data. We needed to observe and record exactly how far the mass went down to when released. This is the sole source of error for this lab. Since the spring moves fast and is relatively hard to observe, a decent percent error is expected.