Proof of the conservation of momentum and kinetic energy

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1 Experiment 04 Proof of the conservation of momentum and kinetic energy By Christian Redeker

2 Contents 1.) Hypothesis ) Diagram ) Method ) Apparatus ) Procedure ) Errors ) Systematic errors ) Reading errors ) Random errors ) Results ) Conclusion/Evaluation ) Bibliography ) Note ) Figures

3 1.) Hypothesis The principles of conversation of momentum and conservation of energy are two of the fundamental statements in physics. This experiment aims to deliver an experimental proof of both of them by creating a linear collision. Before it is gone deeper in the actual theoretical procedure of the experiment it is necessary to have a look into the basic theories behind both of those two principles. Therefore the mathematical proof of those two principles is shown in the following paragraphs: The law of conservation of momentum states the following: Given a system of two masses say m 1 and m 2 with velocities and, the total momentum of the system is defined as the vector sum of the individual momenta: Where P is momentum, m is mass and v is velocity. Before it is gone deeper into the actual proof of momentum conservation the term momentum must be defined. Momentum (p) can said to be a measure of the amount of motion involved in a movement. It is defined as the mass (m) of a body times the velocity (v) with which the body moves. In mathematical terms it is therefore as expressed as in the following equation: As it is stated in the equation both velocity and momentum are vectors. The direction of the momentum is always the same direction in which the body moves (i.e. the directionis equal to the direction of the velocity of the body). Thereby the unit of momentum is kgms -1. In terms of momentum, Newton s second law of mechanics can be stated as: Where F is the net force and t is the time. This can mathematically be proven if the mass involved in the movement is considered as being constant. This proof is shown in the following: 3

4 Where a is the acceleration. Newton s first law of mechanic is the foundation of the conservation laws. It states the following: If a body A exerts a force on body B, then body B exerts an equal but opposite force on body A 4. To actually proof the conservation of momentum it is look at a simple elastic collision as an example. An elastic collision is in contrast to an inelastic collision, a collision which conserves kinetic energy as well as linear momentum 5. This type of collision appears virtually never in nature; therefore it is a rather idealised model. In an inelastic collision kinetic energy is converted into several other forms of energy like thermal or sound energy. Everyday collisions are most accurately described by the model of an inelastic collision. However, the conservation laws are not violated by the model of an inelastic collision because the energy involved in the movement does not disappear; it is merely converted into other forms of energy. However, to prove the conservation laws in the simplest way, a collision is considered as being elastic. Therefore it is looked at a very simple example of an elastic collision. In this example a body A of the mass m a which moves with velocity u a collides with a body B of the mass m b which moves with the velocity u b. While the masses of the bodies stay the same before and after the collision, the velocities of both bodies change due to the collision. Body A moves with the velocity of v a and body B moves with a velocity of v b after the collision. The described situation is visualised in figure 1. Figure 1: Schematic drawing of the movement of body A and B before and after the collision As shown above, Newton s second law of mechanics can be written in the following form: 4

5 In this case Δp is the change in momentum of body A. Hence the difference between the momentum of body A after the collision and before the collision is assumed to be Δp. Therefore the following can be said about the force which is exerted by body A on body B during the collision: Due to Newton s third law of mechanics body B will exert an equal but opposite force 6 on body A. Therefore F is defined by the difference between the momentum after the collision and the momentum before the collision of body B divided by the time period. This definition is mathematically expressed in the following equation: Because the time period is the same in both force defining equations, it can be said that the momentum difference of body A and the negative momentum difference of body B after and before the collision are equal to each other. This is expressed by the following equation: If this mathematical term is rearranged, it delivers the mathematically proof of the conservation of momentum. The rearrangement is shown in the following equation: Therefore the momentum before the collision ( ) is equal to the momentum after the collision ( ). Therefore the law of conservation of momentum is proved. From this result, the proof of the conservation of kinetic energy can be obtained. Kinetic energy (E (kin) ) in terms of momentum is defined as the momentum squared divided by two times the mass of the body involved. This is mathematically expressed by the following equation: When the mass is assumed to be constant, the only size that can change the amount of kinetic energy is the momentum. As it was shown above, the momentum before and after the 5

6 collision is the same. Therefore the kinetic energy involved in a collision before and after the collision must also be the same. While this is the theory, the theorems have also to be proven by an experiment. In this experiment it is tried to carry out an elastic collision between two trolleys. Both trolleys are designed to be almost friction free. Thereby one trolley is accelerated and after a short time period collides with a second trolleys. On the colliding sides of the trolleys plasticene is fixed, so that both trolleys stick together and move as one body after the collision. To determine the momentum respectively the kinetic energy of the movement before and after the collision, masses and speeds of the in the movement involved bodies has to be determined due to the defining formula of momentum and kinetic energy. Speed is defined as distance per time; therefore a time period with a corresponding distance has to be measured. In this experiment those two values are determined by using a ticker tape timer. Therefore a ticker tape, a very long and thin strip of paper, is fixed at the back of the accelerating trolley. Afterwards it is tailored through a hole in the ticker tape timer. The ticker tape timer is connected to the national grid. In the hole of the ticker tape timer is a device which makes points on the ticker tape every time a complete wave has passed through the ticker tape timer (i.e. every 1/50 s due to the frequency of the national grid being 50 Hz). When the accelerating trolley is released and accelerates, the ticker tape moves with the same velocity as the trolley, through the hole in the ticker tape timer, because it is fixed at the trolley. Thereby the ticker tape timer continues to make a point on the ticker tape each 1/50 s. At a higher velocity the points are further away from each other than at a lower velocity. After the collision, the mass of the moving body changes because then trolley 1 and trolley 2 move with as one body. Therefore the speed of the movement is decelerated due to the collision. Therefore the points on the ticker tape are nearer to each other after the collision than before the collision. The expected appearance of the recordings on the ticker tape is shown in figure 2. Figure 2: Expected appearance of the recordings on the ticker tape after the experiment With the help of those recordings the speed and afterwards the momentum respectively the kinetic energy before and after the collision can be determined. How this is done is shown in chapter 5. The theory of conservation of momentum and kinetic energy described above was designed for an elastic collision. However, as stated above elastic collisions do virtually not occur in nature. With the equipment which is used in the experiment it is not possible to simulate a 6

7 perfect elastic collision. Therefore the energy involved in the collision is expected to be partially converted into other forms of energy (see chapter 7. Conclusion). Therefore the sum of kinetic energy of both trolleys before and after the collision is not expected to be exactly the same. Because the sum of kinetic energy of both bodies involved in the collision is not expected to be same before and after the collision, the sum of the velocities of both bodies before and after the collision, and therefore the momentum before and after the collision, is not expected to be perfectly equal as well. Both, the kinetic energy and the momentum after the collision should therefore be slightly less than before the collision. However, the kinetic energy respectively momentum before and after the collision is not expected to differ to a very large extent. 2.) Diagram Figure 3: The set-up of the experiment to prove the law of conservation of momentum and kinetic energy 3.) Method 3.1) Apparatus Two trolleys, ticker tape timer, ticker tape, power unit, plasticene, masses, 2 cables, tape, scale 3.2) Procedure The principle set-up of the experiment is shown in figure 2. Firstly, the power unit was connected to the national grid and with two cables to the ticker tape timer. The masses of trolley 1 and trolley 2 were measured with a scale. A ticker tape of roughly one metre length was fixed with tape at the back of trolley 1, so that it was not in contact with the wheel, so that it did not impede the movement of the trolley. A piece of plasticene was fixed on each of the colliding sides of the trolleys, so that they would stick together after the collision. Trolley 7

8 1 had a built in spring to drive the trolley with a sharp impulse force. The plunger was pushed and lifted up to fix with the groove. The position of the end of the plunger was arranged so that it was in contact with the ticker tape timer, so that when the plunger was released caused the trolley to move forward. On the top of the trolley was a pin, which, when pushed caused the plunger to release. Thereby the ticker tape timer was pressed down by one of the performers in order to give enough resistance against the releasing plunger. Before the plunger was released, trolley 2 was placed nine centimetres away from trolley 1 with the side on which the plasticene had been fixed frontal to the small side of trolley 2. When the plunger was released, trolley 1 accelerated and collided with trolley 2, so that both trolley moved as one body after the collision. After a while both trolleys came to rest. Afterwards the recordings of the ticker tape timer were analysed. The speed and the distance covered before and after the collision of trolley 1 respectively trolley 1 plus trolley 2 had to be determined. The recordings of the ticker tape timer could be split into the movement before and after the collision, due to the distance of the points on the ticker tape. The speed of the combined trolleys must be less than the speed of only one trolley; therefore the points on the ticker tape got nearer to each other at the moment the collision had occurred. The points and the distance before and after the collision were counted in eleven point units. With those data the speed before and after the collision could be determined as shown in chapter 5. The procedure was repeated with a higher initial velocity of trolley 1 and with 500 g mass added to each of the trolleys for two different initial velocities. 4.) Errors 4.1) Systematic errors The smallest sub-division of the ruler used for all length measurements involved in the experiment was 1 mm. Therefore a systematic error of +/- 0.5 mm occurred. 4.2) Reading errors A parallax error occurred during all length measurements, due to the angle at which the value was read. 4.3) Random errors The speeds before and after collision were average speeds. The distance and time values were those measured in the time of approximately 7-11 gaps. Therefore the speed which was used in the calculations is not the exact speed directly before and after the collisions (discussed in chapter 7). Friction between the table surface and the trolleys influenced the movement by delivering a decelerating force which acted on the moving trolleys (discussed in chapter 7). Kinetic energy was converted into other forms of energy during movement respectively collision (discussed in chapter 7). 8

9 5.) Results Aim of the analysis is to prove the laws of conservation of momentum and kinetic energy with the help of the data obtained from the experiment. Momentum is defined as as shown in the chapter 1, while kinetic energy is defined as ½ the mass (m) of a body times the squared velocity (v) of that body. Mathematically the definition of kinetic energy is expressed as in the following equation: Where E (kin) is the kinetic energy of the movement. The law of conservation of momentum respectively kinetic energy states that the momentum respectively kinetic energy before the collision must be equal to the momentum respectively kinetic energy after the collision. Therefore the momentum of trolley 1 before the collision must be equal to the momentum of trolley 1 and trolley 2 combined after the collision. The same is true for the kinetic energy involved in the movement. Those connections are expressed in mathematically terms in the following equation: For momentum: For kinetic energy: In both equations the same two physical quantities are involved, namely velocity and mass. Therefore those two quantities before and after the collision have to be determined to be able to prove the laws of conservation of momentum and energy. Firstly, the masses of the trolleys were determined. During the carrying out of the experiment the masses of both trolleys were measured by weighing them with the help of a scale. The mass of trolley 1 was kg, while the mass of trolley 2 was kg. Those two values were the masses of the trolleys without any masses added to them. However, as described in chapter 3, overall four readings were made during the experiment. Two with no added masses to the trolleys but with different initial velocity and two with 500 g masses added to each trolley carried out for two different initial velocities. In the following those 4 different readings are called experiment 1 (no mass added, slower initial velocity), experiment 2 (no mass added, faster velocity), experiment 3 (500 g masses added, slower initial velocity) and experiment 4 (500 g masses added, faster initial velocity). If it is referred to the experiment as a whole it will simply be stated with the experiment or similar expressions. 9

10 To get the combined mass of both trolleys during experiment 1 and experiment 2 the two measured mass values which were stated above were added as shown in the following calculation: The mass of the combined trolleys in experiment 1 and 2 was therefore approximately kg. In experiment 3 and g masses were added to each of the trolleys. Therefore the masses of each trolley could be calculated by adding 0.5 kg to each mass of the trolleys. This is shown in the following: The mass of trolley 1 during experiment 3 and 4 was therefore kg, while the mass of trolley 2 during experiment 3 and 4 was kg. To gain the mass of both trolleys combined, those two values were added as shown in the following calculation: The combined mass of trolley 1 and 2 during experiment 3 and 4 was therefore approximately kg. All mass values obtained by the calculations above are shown in table 1 to 4. Afterwards the velocities of trolley 1 before and trolley 1 and 2 combined after the collision had to be determine to obtain all values which were needed to calculate the momentum respectively kinetic energy before and after the collision. Velocity (v) is defined as displacement (d) travelled per time (t). Mathematically this is expressed by the following statement: Hence, a displacement and a correlating time period needed to be found. (N.B. in the case of this experiment speed and velocity virtually mean the same, because the considered movement is only in one direction. The positive displacement was therefore chosen to be in the direction of the movement.) Principally the velocity of trolley 1 directly before the collision and the velocity of trolley 1 and 2 combined after the collision after the collision had to be determined. This was done with the help of the recordings of the ticker tape timer. As stated in chapter 1 the moment (in time not the physical quantity) of the collision was equal to the point on which the velocity 10

11 of the movement (i.e. the distance between the points on the ticker tape) changed to a large extent; so the recordings on the ticker tape could be split up into the movement before and after the collision. The distance between two points (i.e. one gap) represented the distance trolley 1 (i.e. trolley 1+2) had moved in 1/50 s. In consideration of the definition of velocity, the velocity between two points on the ticker tape can therefore be obtained by dividing the distance between those two points by 1/50 s. However, for convenience it was not measured the distance between each two points but between eleven points, which meant the distance covered in 10/50 s (10 gaps: 10 x 1/50 s = 10/50 s). In all four recordings of the four experiments the points describing the movement of trolley 1 alone before the collision could not be evenly subdivided into eleven point packs. Therefore, the point pack directly before the collision did not consist of eleven points but of points of a number between one and eleven. The correlating time period to that distance was therefore the number of gaps between the points divided by 50 (number of gaps/50 s); the unit was seconds. However, in experiment 1 and 3 the distance directly before the collision was 3 gaps. Unfortunately, the actual distances between those 4 points were not measured during the experiment. For the calculation of the velocity of trolley 1 before the collision, the velocity between point one and point eleven on the ticker tape was used, ignoring the four points after point eleven. In experiment 2 and 4, the first counted unit of points did not contain eleven points. The distances between those points were measured. Therefore the correlating time to that distance and therefore the velocity between those two points could be obtained. For the speed of trolley 1 and 2 after the collision the average speed between point 1 and point 11 after the collision was considered for all four experiments. In the following the calculations of the speeds of experiment 2 before and after the collision of trolley 1 respectively trolley 1 plus 2 are shown. This calculation is an example calculation; the speed calculations of the other three experiments were carried out in the same way. The data needed for the calculations, which were obtained by the experiment is shown in table 1 to 4: a) Velocity of trolley 1 before the collision: The trolley needed the time which passed between 6 gaps to travel a distance of m. The calculation for the average velocity of trolley 1 is shown in the following calculation: 11 The average velocity of trolley 1 before the collision in experiment 2 was therefore 0.8 ms -1.

12 b) Velocity of trolley after the collision: The trolley needed the time which passed between 10 gaps to travel a distance of m. The calculation for the average velocity of trolley 1 and 2 combined after the collision is shown in the following calculation: The average velocity of trolley 1 and 2 combined after the collision in experiment 2 was therefore ms -1. The speeds of trolley 1 before and trolley 1 and 2 combined after the collision for experiment 2 and the other three experiments are shown in tables 5 to 8. All the data needed to determine the momentum respectively kinetic energy before and after the collision was therefore obtained. This data is shown in tables 5 to 8. In the following, the calculations of the momentum and kinetic energy of the movement before and after the collision is shown for experiment 2. This calculation should serve as an example calculation; the momenta and kinetic energies of the movements before and after the collision of the other three experiments were done in the same way with corresponding data: Firstly, the momentum of the movement before and after the collision of experiment 2 was calculated: i. Momentum of the movement before the collision: The only body involved in the movement before the collision was trolley 1. Therefore the momentum of trolley 1 before the collision is the total momentum of the motion before the collision. As stated in chapter 1 the momentum of a movement is defined as in the following equation: The mass of trolley 1 was kg (M 1 ), while its speed before the collision was 0.8 ms -1 (v 1 ). Therefore the momentum of movement before the collision could be obtained by multiplying those two values as done in the following calculation: The momentum of the movement before the collision in experiment 2 was therefore kgms -1. ii. Momentum of the movement after the collision: 12 After the collision trolley 1 and trolley 2 moved as one combined body. Therefore the only body involved in the motion was the body of trolley 1 and 2 combined. The mass

13 of that body was obtained by adding the masses of the trolley to each other. Therefore the mass of the body trolley 1 and 2 was kg (M ). This body moved with a velocity of ms -1 (v 2 ) after the collision. Therefore the momentum of the motion after the collision could be obtained as shown in the following calculation: The momentum of the movement after the collision in experiment 2 was therefore kgms -1. Secondly, the kinetic energy of the movement before and after the collision of experiment 2 was calculated: I. Kinetic energy of the movement before the collision: The only body involved in the movement before the collision was trolley 1. Therefore the kinetic energy of trolley 1 before the collision is the total kinetic energy of the motion before the collision. As stated above the kinetic energy of a movement is defined as in the following equation: The mass of trolley 1 was kg (M 1 ), while its speed before the collision was 0.8 ms -1 (v 1 ). Therefore the kinetic energy of the motion before the collision could be obtained as shown in the following calculation: The kinetic energy of the movement before the collision in experiment 2 was therefore J. II. Kinetic energy of the movement after the collision: After the collision trolley 1 and trolley 2 moved as one combined body. Therefore the only body involved in the motion was the body of trolley 1 and 2 combined. The mass of that body was obtained by adding the masses of the trolleys to each other. Therefore the mass of the body trolley 1 and 2 was kg (M ). This body moved with a velocity of ms -1 (v 2 ) after the collision. Therefore the kinetic energy of the motion after the collision could be obtained as shown in the following calculation: The kinetic energy of the movement after the collision in experiment 2 was therefore J. 13

14 The calculated momenta and kinetic energies before and after the collisions of the other experiments are shown in table 9 to 12. Gaps Distance (m) Trolley 1 before collision 10 (as stated above, 3 more gaps directly before the collision were ignored) Trolley after collision Table 1: Movement data obtained from experiment 1 Gaps Distance (m) Trolley 1 before collision Trolley after collision Table 2: Movement data obtained from experiment 2 Gaps Distance (m) Trolley 1 before collision 10 (as stated above, 3 more gaps directly before the collision were ignored) Trolley after collision Table 3: Movement data obtained from experiment 3 Gaps Distance (m) Trolley 1 before collision Trolley after collision Table 4: Movement data obtained from experiment 4 Mass trolley 1 (M 1 /kg) Speed trolley 1 (v 1 /ms -1 ) Mass trolley 2 (M 2 /kg) Mass combined trolleys (M = M 1 + M 2 /kg) Speed combined trolleys ( v 2 /ms -1 ) Table 5: Speed and mass data of the bodies involved in the motion before and after the collision in experiment 1 Mass trolley 1 (M 1 /kg) Speed trolley 1 (v 1 /ms -1 ) Mass trolley 2 (M 2 /kg) Mass combined trolleys (M = M 1 + M 2 /kg) Speed combined trolleys ( v 2 /ms -1 ) Table 6: Speed and mass data of the bodies involved in the motion before and after the collision in experiment 2 14

15 Mass trolley 1 (M 1 /kg) Speed trolley 1 (v 1 /ms -1 ) Mass trolley 2 (M 2 /kg) Mass combined trolleys (M = M 1 + M 2 /kg) Speed combined trolleys ( v 2 /ms -1 ) Table 7: Speed and mass data of the bodies involved in the motion before and after the collision in experiment 3 Mass trolley 1 (M 1 /kg) Speed trolley 1 (v 1 /ms -1 ) Mass trolley 2 (M 2 /kg) Mass combined trolleys (M = M 1 + M 2 /kg) Speed combined trolleys ( v 2 /ms -1 ) Table 8: Speed and mass data of the bodies involved in the motion before and after the collision in experiment 4 Momentum before collision (M 1 v 1 ) (kgms -1 ) Momentum after collision (M v 2 ) (kgms -1 ) Kinetic energy before collision (1/2M 1 v 1 2 ) (J) Table 9: Momentum and kinetic energy before and after the collision in experiment 1 Kinetic energy after collision (1/2 M v 2 2 ) (J) Momentum before collision (M 1 v 1 ) Momentum after collision (M v 2 ) Kinetic energy before collision (1/2M 1 v 2 1 ) Kinetic energy after collision (1/2 M v 2 2 ) Table 10: Momentum and kinetic energy before and after the collision in experiment 2 Momentum before collision (M 1 v 1 ) Momentum after collision (M v 2 ) Kinetic energy before collision (1/2M 1 v 2 1 ) Kinetic energy after collision (1/2 M v 2 2 ) Table 11: Momentum and kinetic energy before and after the collision in experiment 3 Momentum before collision (M 1 v 1 ) Momentum after collision (M v 2 ) Kinetic energy before collision (1/2M 1 v 2 1 ) Kinetic energy after collision (1/2 M v 2 2 ) Table 12: Momentum and kinetic energy before and after the collision in experiment 4 6.) Conclusion/Evaluation The obtained values of momentum respectively kinetic energy before and after the collision were as predicted in chapter 1 not exactly the same; the values after the collision were in two cases smaller than before the collision. That means that kinetic energy respectively momentum was converted into different forms of energy respectively split to different movements. 15

16 The biggest amount of kinetic energy was lost (i.e. converted) during the collision itself. When the trolleys collided the plasticene was deformed, and so swallowed some energy. Thereby kinetic energy was converted into thermal and sound energy as well. The movement can not to be considered to be totally friction less. Therefore some kinetic energy was converted into thermal and sound energy during the acceleration respectively decelerating phase as well. However, in experiment 2 and 4 the momentum after the collision is higher than before the collision. This is very unlikely to be realistic because no external force was involved in the movement which could have accelerated the movement. Those values are probably due to measuring mistakes as outlined in chapter 4 and in the following paragraphs. Another reason for the differing values of momentum respectively kinetic energy before and after the collision lay in method which was used itself. Instead of measuring the velocity of the vehicle(s) directly before and directly after the collision the average speed of the trolleys from its staring to the point of collision respectively from the point of the collision to the 10/50 s after the collision were taken as the value for the speed directly before respectively directly after the collision. This average speed however did not give the exact speed directly before respectively after the collision. On the other hand, if the trolleys were assumed to be almost friction less, this error source before and after the collision could balance each other out, because the time for which the average speed was taken before and after the collision was nearly the same. This would lead to a decrease of the magnitude of the momenta respectively kinetic energies, but not changing the equality of momenta respectively kinetic energies before and after the collision. However, one way of getting a value of speed directly before and directly after the collision could have been reached by only taking the last gap directly before and directly after the collision into account to measure the speed of the trolley(s). On the other hand this way of obtaining the speeds before and after the collision could also lead into a even more dramatic error because the distance measurement of this single gap had to be very accurate, because even a slight mistake in the reading could have dramatic consequences in the speed calculations. Instead of dividing the distance by 10/50 s (i.e. times the distance by 5s) the distance had to be divided by 1/50 s (i.e. times the distance by 50 s!) to obtain a result of the speed before respectively after the collision. This point is furthermore stressed because it is very likely that the collision occurred during a single time period of 1/50s; therefore it could be that collision and therefore a deceleration occurred in between the time period which is represented by the distance between two points on the ticker tape. This would lead into a wrong length measurement because the corresponding length to the actual speed directly before the collision would be large than the speed which were measured with the help of the ticker tape recordings. If this method of taking only a single gap before respectively after the collision for speed calculation into account, the gap before the gap in which the collision occurred respectively 16

17 after the gap in which the collision occurred should be taken into account (the gaps are marked in figure 3). Those two gaps are more unlikely to be distorted by the collision itself. Figure 4: Possible points of consideration to measure the speed directly before respectively after the collision The percentage errors which occurred in all four experiment for momentum respectively kinetic energy measurement were calculated as shown in the following calculation. It shows how the percentage error in change of momentum and kinetic energy before and after the collision as it was measured in experiment 2 was obtained. It serves as an example calculation for the other three readings. The percentage errors of those experiments were therefore obtained in the same way with the data obtained from these experiments: a) Percentage error of momentum determination after the collision with respect to the momentum before the collision: The percentage error of the measurement of the momentum before and after the collision in experiment 2 was therefore % (+/- 0.5 %). b) Percentage error of kinetic energy determination after the collision with respect to the kinetic energy before the collision: The percentage error of the measurement of the kinetic energy before and after the collision in experiment 2 was therefore % (+/- 0.5 %). The percentage errors for momentum respectively kinetic energy measurement before and after the collision of experiment 2 and the other three experiments are shown in table

18 Percentage error in momentum measurement (%) Percentage error in kinetic energy measurement (%) Experiment Experiment Experiment Experiment Figure 5: Percentage errors made during measurements of momentum and kinetic energy before and after the collisions for the four readings The percentage errors made during momentum measurements looked almost reasonable but not 100% accurate, while the percentage errors made during the measurement of kinetic energies looked dramatically big. However, these extremely big percentage mistakes are due to the very small values of kinetic energy involved in the movement. Therefore small mistakes in measurement went with relatively high percentage mistakes. Notwithstanding the results for both momentum and kinetic energy measurement did not seem very satisfactory. The mistakes made during the experiment arguably summed up to a big overall mistake which led to the inaccurate results. To gain more accurate results the experiment should be repeated with the speed determination carried out in the way describe above. 7.) Bibliography 7.1) Note Note 1, 2, 3, 4, 6: Tsokos, K. A.; Physics for IB Diploma. (2005). Cambridge University Press. Note 5: Adams, Steve; Allday, Jonathan. Advanced Physics. (2000). Oxford University Press. pp ) Figures Figure 1: Adapted from: Tsokos, K. A.; Physics for IB Diploma. (2005). Cambridge University Press. 18

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