Research Question: How does efficiency with which the bow transfers energy to the arrow depend on the mass of the arrow? Hypothesis: Efficiency will increase as the mass of the arrow increases, as Eff= Eout/ Ein. Variables: Independent – the mass of the arrow. In this procedure, this variable was calculated by weighing with an electronic balance to ascertain and acquire the margin of error. A series of different massed arrows were used to determine the change in efficiency of the energy transfer from the bow and to increase the level of precision.Dependent – efficiency with which the bow transfers energy. The dependent variable is the resultant, or the value that we are attempting to measure. As the equipment to measure this is out of our reach, we can only to calculate this value.
Controlled – the height of the bow. The height of the bow is kept at a constant height in order to maintain the precision of the procedure. If the height of the bow is not kept constant and controlled, then the displacement of the bowstring will differ, although slightly, and impair the precision of the experiment, as there will be a different force of gravity acting upon the string.1. Gather the necessary arrows and weigh on electronic balance. 2. One person measures the height of the arrow’s launch by staying at the top of the railing, with a metre stick.
3. Launch arrow to person on railing, attempting to keep launch as straight as possible and measuring the displacement of the bowstring with another metre stick. 4. Group member at the top of the railing records, based on estimation 5. Repeat for other arrows.6.
Measure distance from floor to railing. Note: Due to the difficulty of actually firing an arrow efficiently, we ran out of time to perform several more trials for some of the arrows. In addition, the displacement above is from the floor of the railing to the max height of the arrow. The total displacement should be the displacement indicated plus the distance from floor to rail (3.0m) minus the distance from the floor to the bow.Data Processing Efficiency vs.
Mass From Eff = Eout/ Ein, we can find the efficiency and graph the results. As the arrow is launched, there is an input of energy exerted by person launching the arrow, and as the arrow is launched, it produces an output of gravitational potential energy. Therefore, we can calculate the efficiency by calculating output (Ep= mgh) and divide it by the energy values we calculated from the previous lab (Refer to Figure 2 of Lab 1).*The total height should be the displacement indicated in the graphs above added to the distance from floor to rail (3.0m) minus the distance from the floor to the bow.
* Thus, by graphing our calculated results, we can see that the efficiency of the system increases as mass increases.ConclusionReferring to the research question, we have discovered through this lab that the efficiency of the arrow increases as the mass of the arrow increases. Also, the maximum efficiency of the arrow is 96.8%, and the minimum efficiency is 54.1%.
This can be observed from the graph, where the data points are presented in a linear function. However, it should be noted that the error margin for this procedure is quite large, as the measurements are largely based on human sight, on a single glance.Limitations: The range of uncertainty for this procedure is very large, due to error in human sight, and error in measuring tools such as the measuring tape and the metre stick. For one, we do not know exactly the distance the bowstring is pulled back each time.
The distance 9.0cm is a rough estimate, as we lacked the time to properly measure. Another limitation is the recorder at the top of the railing.
As we can only roughly estimate the maximum height of the launch, there is a huge variance.Improvement: Perhaps a more realistic method to perform this procedure is to attach some sort of string to the arrow. When launched into the air, the arrow will go up, bringing the string with it. During the peak moment, where there is a very brief pause, we will place a mark on the string (from the floor) and then measure afterwards.
Therefore, the limitation of human sight can be lessened. However, the string must be long enough and be light enough as to not corrupt the precision of the experiment. Of course, there will be a degree of error involved, but significantly reduced and smaller than the present one.