- Controlled variable: the slope/gradient at which the curtain track is placed at, height adjuster, by not changing the slope or height at the end of the slope, this has to be kept constant or else it will not be a fair test, also the type of the ball (keep and use the same ball), and the track
- Independent: the height at which the ball is released, mark down specific heights on the curtain track in order to release the ball at those heights and measure the velocity and the maximum height it reaches
- Dependent: height, going to observe and measure this using a ruler, and velocity by using a light gate and the computer
- Safety precautions:
- make sure that the ball being released does not hit anyone, and do not fool around or play around with it
- make sure that the pin is tightly adjusted to the table, in order for the curtain track to not flick/snap up
- do not run around in the lab
Working Out:
Kinetic Energy (KE) = ½ mv2
Potential Energy (PE) = mgh
KE converts to PE or the horse hits the wall
½ mv2 = mgh if 100% efficient
½ mv2 = mgh
v2 = 2gh 2g = 20
v = square root of h or v2 = h if v * 2 h * 4
Therefore, the height is proportional to velocity squared, h α v2.
Results/Calculations:
The curve type I will choose to prove that the height is proportional to velocity squared is y = ax + b. In this case, a = 2.439, and b = -1.233. The following graph represents my data, and it is clearly shown that the line of best fit does not match the scattered points, as it also does not start from the origin at (0,0).
Conclusion:
The purpose of this investigation was to find out whether height is proportional to velocity2. In other words for example if we double the height then the velocity will quadruple. Through the process of my research I have found out that the purpose, aim and hypothesis were somewhat true. I have found out that height is fairly proportional to velocity2; this is because when I look at my graph of height proportional to velocity2 I see that the points are close to the curve of the line. This does prove that my hypothesis is rather right, as my hypothesis states that height directly affects the speed and velocity that it travels, which is not quite true, however, when we do double velocity the height does quadruple. For example, when we double the velocity of .53, the answer is 1.06, and the height is truly quadrupled from 0.3 to 1.1, which are extremely, just about the results that I measured and calculated. And therefore, the results that I have measured and calculated and found out, do match my hypothesis.
The results that I have reached do not fit in entirely with what I have learnt about science law and concept during science lessons or from scientific knowledge from other sources like books, etc. This is because during class, my colleagues and I learnt only about motion and Newton’s three laws, even though it does consider motion in some way. In this case I chose to make my experiment unique and different from my other colleagues, so I chose to create a model about horse jumping, and so I made it difficult for myself, in order that I had to research about the effects and formulas of Kinetic and Potential Energy.
My data is not very reliable, this is because the method I had used to calculate my measurements was not entirely reliable to start with, and this directly affected the results and my data. The results I had reached were according to height proportional to velocity2, which affected the trends and patterns found in the graph. The pattern that I found in the graph was that each time the velocity doubled, the height quadrupled. This means that when the speed of a horse doubles, then it will have better effects on the result, as the height it achieves will quadruple; and this is obviously a good result for the horse and its trainer/rider. It is difficult to make predictions of any figures using un-accurate data, and a non-satisfying method.
The resources that I have used for information and explanation of the formulas of Kinetic Energy and Potential Energy are taken from the Internet and are placed as an appendix at the end of the lab.
Evaluation:
The method that I had used to calculate and test my aim and hypothesis was not very reliable, this is because the method that my colleague and I used involved human error and inaccuracy, as we plotted down the height that the ball reaches using our eyes’. When accounting the graph very closely I realised that there were some anomalous results that did not match the curve of the line. This was because of the human error and inaccuracy and also because of factual errors. The human errors that were issued during the experiment are as follows: the error of the accuracy of measuring the height using a 30cm ruler, and when looking at the graph, the line does not cross the origin, as this might also have been because of human error and fault. This is because when the ball was released, the centre of the ball might not have been crossed through the light gate, and only the edge of the ball, which makes it seem that the speed is higher (velocity increases), and therefore the ball maybe might not have cut the light gate, so the distance is bigger than the actual value. In this case, I conclude that this method is unreliable and inconsistent, because of many limitations and faults. An example of a result that did not seem to fit into the pattern was at the speed/velocity of 1.21. When setting up the light gate and the computer I was afraid that it would not calculate the speed/velocity of the ball, as it might not sense its presence. But however, fortunately it did work and the velocity after all turned out to be quite accurate.
If I redid this investigation, I could improve my method in a number of ways. One way is to set up the light gate on the other computer in the lab, as to the other computer is attached a video web cam, as it would give us the opportunity of videoing the maximum height the ball reaches, as it would save us more time and the results would be more accurate. And before we start videoing the ball, we should mark down the heights on the piece of paper that will be later on placed on the safety screen.
The above-suggested improvements would widely change the results that would be calculated, as it would make the experiment more accurate, and it would also become a fair test.
Appendix 1
As appendix 1 put picture of the program and information and how to build the light gate
Appendix 2
Kinetic Energy
Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy* of a point mass m is given by
Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it quantifies the amount of work the object could do as a result of its motion. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.
For an object of finite size, this kinetic energy is called the translational kinetic energy of the mass to distinguish it from any rotational kinetic energy it might possess - the total kinetic energy of a mass can be expressed as the sum of the translational kinetic energy of its center of mass plus the kinetic energy of rotation about its center of mass.
*This assumes that the speed is much less than the speed of light. If the speed is comparable with c then the relativistic kinetic energy expression must be used
Kinetic Energy Concept
Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy of a point mass m is given by
Energy as the capacity for doing work is a convertible currency. To give something kinetic energy you must do work on it. This development uses the concept of work as well as Newton’s second law and the motion equations. It is a special case of the work-energy principle, a powerful general principle of nature.
More Detail on Kinetic Energy Concept
Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy of a point mass m is given by
Nave, R. "Kinetic Energy." 15 Oct 2007 <http://hyperphysics.phy-astr.gsu.edu/hbase/ke.html>.
Appendix 3
Potential Energy
Potential energy is energy which results from position or configuration. An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field (electric potential energy), or a magnetic field (magnetic potential energy). It may have elastic potential energy as a result of a stretched spring or other elastic deformation.
Potential Energy Function
If a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case satisfies the derivative condition
The integral form of this relationship is
which can be taken as a definition of potential energy. Note that there is an arbitrary constant of integration in that definition, showing that any constant can be added to the potential energy. Practically, this means that you can set the zero of potential energy at any point which is convenient.
Potential Energy Concept
Negative Signs in Potential
Potential Energy Derivative
If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential.
Potential Energy Integral
If the force is known, and is a conservative force, then the potential energy can be obtained by integrating the force.
Conservative Force
A conservative force may be defined as one for which the work done in moving between two points A and B is independent of the path taken between the two points. The implication of "conservative" in this context is that you could move it from A to B by one path and return to A by another path with no net loss of energy - any closed return path to A takes net zero work.
A further implication is that the energy of an object which is subject only to that conservative force is dependent upon its position and not upon the path by which it reached that position. This makes it possible to define a potential energy function which depends upon position only.
Nave, R. "Potential Energy." 15 Oct 2007 <http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html#pe>.
