# Lab Report: Proving that energy is conserved within a system

This Is defined by Hooker’s Law shown below. F ? -xx The law of conservation of energy is that energy cannot be created or destroyed, it can only be changed from one form to another. This means that the total amount of energy in an isolated system is constant over time. This means that the only thing that can happen to energy in a closed system is that it can change from one form to another. In this experiment energy changes from elastic potential energy to kinetic energy to gravitational potential energy. Some energy is also lost due to friction which creates heat and sound during the experiment.
Initial = Final Eek + Pep gravitational I + Pep spring + E thermal I = Kef+ Pep gravitational f + Pep bring f + E thermal f + Neon- conservative This equation clearly shows the energy transfer during the experiment Including the energy lost In non-conservative forms such as heat and sound. Basic energy formulae were also used In this experiment In order to calculate energy as it changes form. Eek- move Pep gravitational MGM very important as it is used a wide variety of physical applications. It is especially relevant and applicable in situations which there is little to no friction, such as in astrophysics.
Energy and applied forces can be calculated in order to accurately determine values seen in the equations above. Method: The equipment was set up as indicated in figurer . The track was placed at such a gradient where the cart would not reach the top of the track or come to close to the censor after pushed by the compressed spring. It should also be noted that the gradient of the slope remained constant throughout both experiments. The readings were zeroed and data was then collected by the censors and graphed on the program Logger Pro.

Figure 1: Experimental setup For the first experiment, the cart was released from different heights on the ramp ND measurements of the force and compression of the spring were taken in order to be able to calculate the spring constant. For the second experiment the spring on the cart was compressed and the cart is placed then released using a hard object such as a ruler. The spring then pushed the cart up the track and the censors took the reading of the force, displacement, velocity and acceleration needed in order to calculate the energy as it changed form in the system.
Results: Measurements for finding the spring constant of the spring x = displacement of spring from equilibrium position. F = force applied by the spring on the cart. K = the spring constant of the spring. Table 1 : Measured displacement of the spring and force applied by the spring and the calculated spring constant results. The uncertainties for the displacement and the force were chosen because of the accuracy of the censors and the ruler respectively. The uncertainty of the spring constant was calculated by halving the range of the results.
Measurements for finding the total energy during the second experiment Value Symbol Result Initial Compression of Spring 0. 033 В± 0. 001 m SF 0. 018В±0. 001 m Velocity as cart leaves spring I 0. 75В±0. 05 runs-l Velocity Just before collision if 0. 69 В± 0. 05 runs-l Max distance traveled Adam 0. 661 В± 0. 005 m Position at random point DRP 0. 198В±0. 005 m Velocity at random point Table 2: Velocity and distance measurements taken by the censors in order to prove conservation of energy. The uncertainties for the each of the results were chosen because of the accuracy of the censors respectively.
Analysis: Finding the spring constant of the spring To find the spring constant we use Hooker’s Law (F = -xx). The negative sign shows that the spring is being compressed and can be ignored in this case. For the first value: x = 0. 010В±0. 001 m and 5. 7 В± 0. 3 = 570 ram-I This process was then repeated for each data value and then the average of the results was found to be 598 Nm-l. The uncertainty for the spring constant was calculated by halving the range of the values which was found to be В± 28. 5 Nm-l . This gives the final value for the spring constant of the spring to be 598 В± 28. 5 Nm-l .
Conservation of Energy Graph 1, 2,3: These graphs shows the carts velocity and position and well as the force exerted in the spring by the cart as it moves up and down the slanted track. Using he results found in Table 2, the elastic potential energy, gravitational potential energy and kinetic energy can be calculated at six points during the experiment. These points are; before the spring is released, Just after the cart loses contact, at the during the first collision, and at some point between the release and collision points above. Before the spring is released all the energy is stored as elastic potential energy in the spring.
This can be easily calculated using the spring constant and the displacement of the spring. K = experimentally measured spring constant = 598 Nm-l . = initial compression of the spring = 0. 33 m Just after the cart loses contact with the spring, we can assume that all of the elastic potential energy has been converted into purely kinetic energy. Kinetic energy can be calculated using the mass and velocity of the cart. M = mass of cart = 0. 521 keg v = velocity as cart leaves spring = 0. 75 ms-l At the top of the slope the cart has stopped as the energy has been converted into purely gravitational potential energy.
This can be calculated using the mass and height of the cart as well as gravity. G = acceleration due to gravity = 9. 81 ms-2 = maximum height = 0. 036 m The maximum height of the cart was found by first calculating the angle of the slop using trigonometry. = 3. 130 This angle was then used with the maximum distance traveled value to calculate the maximum height. Just before the spring hits the bottom again the energy is again kinetic. This can again be calculated using the mass and velocity of the cart. At a chosen point part way up the slope the total energy will be the kinetic energy at that point plus the potential energy at the point.

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