Conservation of EnergyObjectivesTo study an alternative to kinematic that doesn’t include vectorsReview Mechanical EnergyConfirm Conservation of Energy for a simple system.ResourcesLab demonstration video.All data is recorded in the Capstone file found in the assignment.IntroductionThis experiment is much like the previous lab: a cart will be launched up the track.The component of the force of gravity along the track will slow the cart, and eventually cause it to fall backward.This time, however, we will be interested in keeping track of the mechanical energy of the system, which is composed of the potential energy and the kinetic energy:E_mechanical=E_kinetic+E_potentialThe kinetic energy of an object of mass m and velocity v is E_kinetic=1/2 mv^2The potential energy of an object can have a variety of sources, and the equation of the potential energy depends on what the source is. For instance, an object attached to a spring has a potential energy associated with how compressed or stretched the spring is. This would have the form E_spring=1/2 k〖(Δx)〗^2, where k is a constant relating to how stiff the spring is, and Δx is how compressed or stretched the spring is.Most relevant for this lab is the potential energy due to gravity, which is given by E_gravity=mgh, where m is the mass of the object, g is the gravitational acceleration 9.802 m/s^2, and h is the height of the object. h is measured from some point of our choosing that we will call h=0. In this lab, we will call it the bottom of the trackIn this experiment, Capstone has kept track of the velocity and position of the Smart Car over time. This information will allow us to calculate the kinetic and potential energy at all points in time. Note that the position it keeps track of is the position along the track (labeled as x in the diagram), NOT the height.The theory is that mechanical energy is conserved in a closed system. That is, if the Smart Car were to only interact with the Earth through the gravitational force, and not interact with anything else, we would expect this mechanical energy to remain precisely the same throughout the car’s trip up and down the slope. While we expect the kinetic and potential energies to change, the sum of the two should not.Procedure 1, Trial 1Open Capstone and navigate to the tab that says “Procedure 1 Trial 1”In the image, find the angle of the track, using the angle tool.You will first need to click the “video analysis” tool to get access to the measurement tool icon . Clicking should produce a dropdown menu with the angle measurement tool.Measure the angle. See last week’s lab for tips about measuring the angle properly, I will deduct if you take an obviously poor measurement.Take a screenshot of your measured angleHitting may have caused your data in the plots to disappear. Reload the file in Capstone to get it back. Do NOT save the Capstone file, or you will be saving the version with the data cleared.To the right, you should have a position plot (the parabola) and a velocity plot (linear where position is parabolic). We will now extract position and velocity data:Upon clicking , choose the “Add multi-coordinates tool” option.Drag the tool to one of the first points at the beginning of the linear stretch of the velocity curve (see below). This is immediately after the car has been launched and is now traveling up the track. In Excel, create columns for both velocity and position, and then input the position and velocity from the multi-coordinate tool into the columns.Drag the tool (or create new one) to a new spot on the linear stretch and read off another pair of velocity and position values. Input into your Excel table. Repeat for a total of 5 points while the car is going up (positive velocity) and 5 points where it is going down (negative velocity). Make sure to only take points where the velocity looks linear.We have collected our data. Now, we will do some calculations to investigate the conservation of mechanical energy:Add a column in Excel and calculate the height above the 0 position. ( the Capstone data is for position “x” along the track, but you need the height at each point.)Look at the diagram in the intro and use trigonometry to figure out the heightInclude one sample calculationHave Excel carry out the height calculations for each row. Warning: Excel expects the arguments of trig functions (like sin, cos, etc) to be in radians. Use the conversion relationπ rads = 180^oAdd a column and calculate the Potential Energy of gravity of the system at each point. Look at the intro for the correct formula. The mass of the car in the first procedure is 249 g, as shown in the introduction page of the lab.Include one sample calculationHave Excel carry out the calculations for each rowAdd a column and calculate the kinetic energy at each point. Again, refer to the intro for the relevant formula.Include one sample calculationHave Excel carry out the calculations for each rowAdd a column and calculate the Mechanical Energy, which is the sum of kinetic and mechanical energy (see introduction)Include one sample calculationHave Excel carry out the calculations for each rowProcedure 1, Trial 2Repeat trial 1 with a more massive cart. The mass of the cart is now 504 gProcedure 2Repeat Procedure 1 with a different angle. Mass of the cart is now 249 gConclusionsComment on whether or not mechanical energy seems conserved in each trial. If the total mechanical energy does seem to change, is there a noticeable trend?When is the kinetic energy at its maximum and when is it at its minimum? When is the potential energy at its maximum and when is it at its minimum?

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