Relationship Between Spring Constant and Horizonta Essays - Physics

Relationship Between Spring Constant and Horizonta Essays - Physics Relationship Between Spring Constant and Horizontal Displacement Introduction: The crossbow is believed to have originated from China and Europe in approximately 6th to 5th century BC. According to evidence found by today's archaeologists, the common usage for a crossbow was for military purposes in China during the Warring States Period. However the crossbow is no longer used in modern warfare, it is now instead used for hunting purposes. At my grandfather's house he own a crossbow which uses to hunt. Every summer I go to his house and we hunt for deer. As I grew older i had started to become more curious in the functionality of a crossbow, the elastic that draws the marble back in order to fire it to be more specific. I wanted to better understand the relationship between the spring constant ( k ) and the distance an object will go after getting hit with a a force . As a result of my curiosity as a child i decided to investigate this relationship between the distance a block will go off of a table (the height of the table will be referred to as h ) in the horizontal axis ( d ) after getting hit by a certain magnitude of force. I investigated this relationship by first building a crude version of a crossbow with hooks that will allow me to change the drawback elastic. T he crossbow is an instrument which utilizes elastic force (will be referred to as F e ) in order to launch a projectile off the launch track and through momentum and impulse, the marble will hit a block and launch it into projectile motion. The schematics of the crossbow made by Leonardo Da Vinci are shown in figure 1. Figure 1 : Crossbow schematics made by Leonardo Da Vinci After the block has been launched off the track and into projectile motion the block will land a certain amount of distance from the starting position (the table). The objective of the experiment is to determine the relationship between the spring constant of an elastic and the final displacement of a solid object after undergoing projectile motion due to the transfer of momentum in an elastic collision. The assumption that can be made in this experiment are that the force of friction caused by the track can be ignored due to a low friction material being used to build the track of the crossbow. The assumption that air resistance is negligible can also be made due to the experiment being tested indoors, therefore there will be no wind blowing. As a result of my assumptions made an equation for the displacement in the horizontal axis for the block can be made. Even though these assumptions have been made, some allowing us to ignore some variables, there are still others va riables that can affect the results in precision and accuracy of this lab. Before the variables are discussed, the system has to be know before. The system has been to picked to include only the marble and the blood of wood so that in both the conservation momentum and conservation of energy is there impulse or work because all energy and momentum was conserved inside the system, therefore there is no need to go looking. Independent Variable: The independent variable is the spring constant. The springs constant is changed to observe the relationship between the spring constant and the displacement of the dependant Variable which is a wooden block. Dependant Variable: The dependant variable in this investigation is the displacement of a solid wooden block after receiving a transfer of momentum and undergoing projectile motion. Control Variables: In order to see the relationship between the independent variable and dependant variable all other variables present in the investigation must remain constant in order to assure that the most precise and accurate results will produced through the experimentation. Masses Mass of Marble The mass of the marble is kept constant so that when there is the momentum transfer only the velocity ( v ) will vary. The velocity will vary because much like the displacement of the wooden block, it is also dependant on the spring constant Mass of wooden block The mass