# Conservation Of Energy

The objective is to find the spring constant, and to find the potential energy of the system.

X1 X2 ΔPEg ΔPEs % of error.
04 .462 2.0678 2.967 43.49 %.
08 .431 1.7199 2.512 46.06 %.
12 .392 1.3328 1.950 46.31 %.
16 .351 .9359 1.367 46.06 %.
X1 X2 ΔPEg ΔPEs % of error.
215 .1301 .416 0.386 1.248 %.
255 .085 .833 0.772 7.323 %.
295 .055 1.176 1.158 1.531 %.
335 .019 1.568 1.548 1.276 %.
Calculations.
K=F/x.
2.9434N/.1025m= 28.71 N/m.
F=mg.
.30kg*9.8m/s2 = 2.9434N .
Percent error between ΔPEg and ΔPEs.
((2.967 - 2.0678)/2.0678)*100 = 43.49 %.
ΔPEg = mg(X2 - X1).
= (.5kg)(9.8m/s2)(.462m - .04m) = 2.0678J.
ΔPEs = ( ½)k(X22 - X22).
= ( ½)(28.008)(.4622 -.042) = 2.967J.
Standard Deviation.
√[(∑(k-kave)2/(n-1)].
=√[(∑(28.71-28.008)2+(28.54-28.008)2+ )/(4)].
=.4425N/m.
Question:.
Do the data indicate that the mechanical energy is conserved for this system?.
The data indicated for the mechanical energy is conserved for this system. This is not found from the high error between the change in spring potential and gravitational potential that was not conserved. The equation to find this relation is .
PEg = PEs.
.
Conclusion:.
The purpose of this lab was to find the spring constant. This was found through testing Hooke's law with hanging weights off of a spring, and measuring the distance the spring travels when it is released from a position other than the equilibrium point.
Another purpose of the lab was to study the effect of conservation of energy. By holding the mass above and below the equilibrium and measuring the distance that the mass travels when it is let go, we calculated if the energy is conserved. Equations for both gravitational and spring potential energy were used. The low percent error between the two values proves that the energy is conserved.
Most errors occur as random human errors. It was difficult to measure exactly how far the weights traveled when it was released.

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