A secondary experiment was also conducted to prove conservation of energy. A spring on the cart was compressed and then released, pushing the cart up the slanted track. Force, position and velocity were all measured in order to be able to calculate the energy of the cart in each of the six significant positions on the track. These values were then compared in order to prove that energy is conserved, Introduction: The force need to compress a spring is directly proportional to the distance the spring is compressed relative to the equilibrium position. 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 i * Pep gravitational i* Pep spring E thermal i = Kef Pep gravitational f
Pep spring f * E thermal f 4- 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= lymph Pep gravitational MGM Pep spring %ex. Et Mac Fed The law of conservation of energy is 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 ores 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 amp and 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 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. Spring on the cart. Bring constant of the spring. Force applied by the k = the Table l: Measured displacement of the spring and force applied by the spring and the calculated spring constant results. The uncertainties tort 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 Initial Compression of Spring 0. 033 0. 001 m Spring compression during collision 0. 018 В± m Velocity as cart leaves spring 0. 75В±0. 05 ms-l Velocity just before collision 0. 69 05 ms-l Max distance traveled Adam 0. 661 В± m Position at random point 0. 198 005 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 oeuvre 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 and F=5. 3 = =570 Nm-l 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 I, 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 the results found in Table 2, the elastic potential energy, gravitational attention 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 top of the slop, just before it hits the spring again, at the maximum compression 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. 21 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. M = mass Of cart = 0. 521 keg due to gravity = g. Mums-2 = acceleration 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. The uncertainties above were calculated from the uncertainties of the original aloes. They were then submitted into the equation and then converted back to an absolute uncertainty. Discussion During the first experiment, the force applied to the spring and spring displacement could be accurately measured.
This means the spring Of the spring used to push the cart could be determined and used in the energy calculations. This value baas 598 28. 5 Nor;l. Although energy is always conserved, throughout the experiment the experimentally measured values of energy at each stage deferred significantly. The values of energy ranged from an initial elastic potential energy of 0. 33 0. 7 J through to 0. 29 0. 013 J as the cart lost contact with the spring. As the cart reached a maximum height its energy dropped to its lowest value of 0. 184 0. 03 J.
The cart was then recorded to have gained energy again as it was calculated to have 0. 316 0. 1 Jon a chosen point as the cart traveled back down the slope. Finally the cart was calculated to have 0. 248 0. 05 J just before it reached the bottom to the slope. This shows that although the total energy remains similar, energy is not conserved in this system, This is because energy is converted into not just the energy torts discussed. Energy is converted into heat and sound energy due to friction, Energy is also used in the rotation of the wheels.