Lab 5 Conservation of Energy Lab Report PDF

Preview

Summary

phy 133 lab report. ...

Description

Veronica Uhuegbue Lab Section: PHY 133-L03 TA: Rugved Pund Partner: Zhaowei Qiu

Lab #5: Conservation of Energy Lab Report

Lab Performed: 3/11/19 Report Submitted: 3/23/19 Introduction: In this lab, we worked to verify the principle of conservation of energy. Ideally, the total

energy of a system should be conserved when changing from kinetic to potential energy. In this experiment, we observed the transfer of gravitational potential energy of a smaller mass and compared it to the kinetic energy made by a larger mass on an air track. The air track helped to minimize the effects of friction in the system, so we were able to conserve and measure energy in our experiment. The potential energy of our closed system was calculated by using PE=−mgx . The kinetic energy of both the 1 2 glider mass, M and the hanging mass, m was calculated by KE= (m+ M )v ❑ . The 2 goal was to measure a slope close to our expected value of -1 from our calculated values of KE vs PE.

Data and Calculations: Part 1: In this part, we measured D, the distance of some number of black-clear segments and divided by the number of segments N, to get d, the length of just one segment. Next, we weighed the mass of the glider, M and the 2 masses that’ll be hanging from the string, m for both parts 2 and 3. We also estimated an uncertainty for both measurements to be 0.1g, 0.0001kg. After recording the data received from the photogate for time and segment(x), the following equations were used in both parts 2 and 3 to calculate the data needed to get the slope of KE vs PE.

Part 2&3: D N σ d=σ D × N Fg=mg d=

σ Fg=g × σ m σ (M + m)=√ ❑ x ❑phys=x × d σ x ❑phys =x × σ d v ❑ phys=v × d σ v ❑ phys=v × σ d 2

σ v ❑ phys=2 v❑ phys ×σ v ❑phys PE=−Fg × x ❑ phys σ PE=PE √❑ 1 KE= ( M +m ) v ❑ 2phys 2 σ KE=KE √❑

Results:

Part 2:

The slope of this KE vs PE graph came out to be 0.922 when accounting for the uncertainty. This slope is somehow close to a +1 rather than a -1, even though this is clearly a negative slope. So therefore, our slope does not agree with the expected slope of -1.

Part 3:

The slope of the KE vs Pe graph comes out to be -0.9736, which is very close to our expected value of -1 when taking in account of the uncertainty, so therefore, our calculated slope falls within the range of the expected slope of -1.

Error Analysis: Possible sources of error can possibly originate from part 2 of this lab, especially since the calculated slope came out to such an odd number of 0.922, when in fact the slope is negative and its value should also be negative. Unevenness in the leveling of the air track could’ve been a source of this error. If proper precautions were not made in the first steps of setting up the air track, that could’ve altered the speed of the mass’ kinetic and potential energies and therefore change the slope of our graph. Another source of error could’ve stemmed from incorrect readings from the photogate. For example, when releasing the glider to pass through, it may not have been at complete rest, or we could’ve unintentionally added another force by pushing it. Also, when weighing the glider, we could’ve also included the weight of the string as well. All these errors may have not been accounted for in our error propagation. Even though they seem minuscule, they definitely could alter our results of the slope of Ke vs

PE to be larger or smaller than the expected value of -1.

Discussion: Deriving Conservation of Energyr

PE=U =∫ F ⋅dr ref

−dU F(x )= dx F(x )=−U ' (x )

Systematic Error: Massive PulleySince the pulley does have some mass, the speed at which the pulley rotates will increase, therefore the moment of inertia increases. So, both the kinetic and potential energy of the system increase and the slope will also increase, becoming a larger negative value.

Systematic Error: FrictionIf the pulley was in fact not frictionless, we would then have to account for it in our calculations to get the slope of our experiment. Additionally, friction would slow down the kinetic and potential energy of the system , therefore making the slope, a smaller negative value.

AccelerationSince both mass M and m are attached to the string, their acceleration should be the same. Since friction is negligible, the only force acting on the system is the force of gravity on mass m. the net force should also take in account the total mass of the system M+m and the acceleration. F❑net =mg , F❑net =( M =m)a By combining both equations together, we can solve for the acceleration of the system. m g a= M +m By simply rearranging the equation, we can also solve for g, the acceleration due to M+m ) gravity. g=a( m

Conclusion: In conclusion, we were able to effectively observe conservation of energy of an isolated system containing a glider M, and a pulley m. The slope of our calculated KE vs PE graph for the 0.02kg mass m, unfortunately was not close to the expected value of -1.

Rather, the slope came out to be 0.922. However, in part 3, with 0.04kg, the slope of our KE vs PE plot fell within the range of -1 because the value was -0.9736. Part 3 helps to prove that energy is truly conserved in an isolated system....