Lab Report 3- Conservation of Energy PDF

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Lab Report 3...

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Julia Varricchio PHY 133 Section 31 Experiment 05: Conservation of Energy Experiment performed on: October 5, 2020 with F  aith Jarzembowski Report submitted: October 17, 2020

Introduction In this experiment, we tested the law of energy conservation . We used an airtrack attached to a massless, frictionless pulley in order to isolate our system. By isolating our system we can test the validity of the law of energy conservation. We do this by measuring the total energy of the system whic is the addition of potential energy and kinetic energy. The law of conservation of energy states that dEtotal/dt=0, so we expect that the slope of our total energy vs. time graph to be 0.

Theory The law of conservation of energy states that “energy can neither be created nor be destroyed. Although, it may be transformed from one form to another”. If the system is completely isolated the change in energy over time will be equal to 0. Total energy is equal to the addition of potential energy and kinetic energy. In other words although kinetic energy and potential energy may change in value they will still add up into a constant total energy. Also, if the system is isolated, this will prevent energy from being transformed into heat due to friction. If there is friction the total energy value will be altered and dEtotal/dt will not equal 0.

Procedure In the setup of the lab we levelled the airtrack and weighed the glider. We also had to setup the pulley by hooking a string to the glider and hanging the two masses to the other end of the string on the pulley. After the lab was setup, we performed the first part of the lab by hooking 20g to the bottom of the string and let the string pull the cart down the airtrack. The photogate software collected the time, position and velocity values of the cart in a graph of velocity vs time. We took

the 10 measurements of time, position, and velocity from the linear part of the graph. The second part of the experiment was similar to the first, however we attached 40g to the string.

Discussion Questions 1. Deriving Conservation of Energy

2. Systemic Error In our experiment we assumed that the airtrack and pulley were fricitionless, and massless. If our airtrack and pulley were not frictionless this would decrease our velocity. Friction is an opposable force to acceleration, which results in the decrease of velocity. If velocity is decreased than the value of kinetic energy will decrease, because of their direct relationship. In result, our energy vs time plot will be altered. Instead of the slope being constant, it will have decreasing slope. Likewise if the pulley is not massless, this would also alter the slope of the energy vs time plot. When a pulley is massless it does

not affect the acceleration of gravity on the glider. However, if the pulley has mass, it takes force of gravity to rotate the pulley. This causes the acceleration due to gravity to be lower on the glider, because it is split between rotating the pulley and pulling the weight of the pulley. This would decrease our measurement of total energy, by decreasing it. This would cause a negative slope for the total energy vs time graph.

Results

From the data collected we can see the relationship between total energy and time. Although there is a decrease for total energy in both graphs it is relatively small. This decrease can be due to friction, which would be an opposable force on the cart. This would slow down velocity and ultimately decrease total energy. We expected the slope to be 0 due to the law of conservation of energy, however in part A of our experiment the slope was -0.0242484 +/-0.000701488, and in part B of our experiment the slope was -0.0735412 +/-0.0020341. These slopes do not agree with our expected value of the slope, because they do not overlap.

Error Analysis

Although we calculated uncertainties in our measurements, there are other sources of error not included in our uncertainties. This includes friction and the mass of our pulley. Although we attempted to isolate our system from friction through the airtrack, frictions may have occurred through air resistance. The law of conservation of energy where dEtotal/dt=0 is only true when the system is isolated from friction and all mass is accounted for. Friction is an opposable force that would slow down the velocity of the cart. This would influence kinetic energy measurements hence altering total energy. Also, since the pulley is not massless this may also affect our measurements. It may slow down acceleration due to gravity, because force of acceleration is gonna be used to rotate the pulley. This would slow down our velocity and similarly to friction, it would alter the measurement of total energy.

Conclusion This experiment tested the law of conservation of energy. If our environment was truly isolated and our pulley was massless than dEtotal/dt=0. However, since our environment was not completely isolated from sources of error dEtotal/dt did not equal 0. Our value for dEtotal/dt when the string of the pulley had 20g attached to it was -0.0242484 +/-0.000701488, and for 40g it was -0.0735412 +/-0.0020341. To perform this experiment with more precision, we could use a massless pulley. This would ensure that the mass of the pulley would not affect the acceleration of the glider....