Motion in One and Two Dimensions - Lab Report Example

Lab Report on Motion in One & Two Dimension The theories on motion in one dimension and two dimensions will be used to help analyze the data to be obtained from experiments. The two experiments entail using the floating hockey puck and the carbon paper. This apparatus will help to conduct the one- dimensional motion experiment and the two- dimensional experiment. The data obtained from experiments will be used to calculate the earth or space gravity, the acceleration due to gravity and various slopes of lines drawn when analyzing and interpreting data. The kinematic equations will be used to calculate gravity and acceleration of floating hockey puck due to the earth’s gravity. Introduction The velocity of an object or a body on motion in one dimension is one of factors that keep changing. For instance, when an object is released with a zero velocity and subject only to the gravitational field of the earth, it moves with uniform acceleration to the center of the earth. However, if an object is thrown at a certain set angle above the horizontal, independent motions in two dimensions come into effect. These motions are; the accelerated motion along the vertical and constant motion along the horizontal. Objectives The objective of motion in one dimension experiment is to help in measuring the acceleration of the earth or space gravity. On the other hand, the objective of motion in two dimension experiment is to demonstrate the independence of accelerated motion and uniform motion in a body or an object moving at an angle between the vertical and horizontal motions. Data analysis and discussion The purpose of the floating hockey puck and carbon experiment is to measure the acceleration due earth gravity and show the independence of the motion. To ease the curbing effects of friction on the carbon paper, these experiments use floating hockey pucks that move over the carbon paper. The floating hockey puck is set to move at an angle theta between the X direction and Y direction. The floating hockey puck’s acceleration between the two directions should be a = gsin theta. On punching, the dots on the carbon paper, displacement measurements can be collected, and the puck’s velocity be calculated. These data will help to calculate acceleration due to gravity. The acceleration is vital because is used to calculate the experimental gravity (g) from the expression a = gsin theta. In the first experiment, which is motion in two dimensions, the size of spaces between successive dots increase with an increase in time in the Y direction; while that in X direction decreases with time taken, by the floating hockey puck to punch dots on the carbon paper On plotting, the points for a graph of positions of Y direction in centimeter against the time taken, the points tend to depict a curved line that curves upward to the right from the left. The points for the graph of positions of X direction in centimeter against the time taken to punch the successive dots also depict a curve on plotting the points. However, this line curve arcs downwards to the right from the left. When the graph of positions in Y direction and positions in X direction are plotted together on a single graph against the time taken to make the successive dots, a clear curve is obtained. It curves upwards. The curved line illustrates that the experiment had to independent motions in place, the Y direction motion and the X direction motion. One motion was moving along the vertical, and the other was moving along the horizontal. The same trend is shown by the velocity of X and Y directions. The velocity of the floating hockey puck in the Y direction increases with time while it velocity in X direction decreasing with time taken to punch the dots on the carbon paper. The velocity increases due to accelerated motion along the vertical and decreases because of the uniform acceleration along the horizontal. A graph of velocity in X direction against time depicts a straight line. On drawing the best fit line through the points that seem to align in a line, a straight line is clearly shown up. This line slopes to the right from the left with a slope or gradient of - 0.0128 and line equation of y= -0.0128x + 0.0361. The graph of the velocity in Y direction against time depicts also straight line. The line slopes from right to left showing that the velocity increases with time take to make the successive dots. The line equation is y= 0.0528x + 0.011 with a positive slope of 0.0528. In spite of the velocity in X direction decreases with time to make the dots, its displacement velocity increases as the floating hockey puck punch dots successively while the displacement velocity in Y direction reduces from one dot to the next. Using kinematical equations, the acceleration due to gravity in Y direction is 0.0528 cm/ms^2, the gravitational force to the hockey puck is 0.88 cm/ms^2 and the angle between Y and X directions give sine (theta) equivalent to 0.06. The summary to the description to this projectile motion are: Free Fall Motion Along the y-axis: y = vyot - ½ gt2 vy = vyo – gt ay = - g Uniform Motion Along the x-axis: x = vxot vxo = constant ax = 0 Where: vxo = vo cos θ And vy = vosin θ. This part of the kinematic equations in the experiment is used to determine the acceleration due to gravity (g) and free fall by measuring the acceleration and computing values obtained from the  floating hockey puck as it move on the carbon paper. The second experiment is a one- dimensional motion experiment. It involves one direction, that is, Y direction. According to data collected from the experiment, the size between the punched successive dots increases from one dot to the next as the puck makes dots along the carbon paper. Similarly, the velocity of the floating hockey puck increases with time taken to make the successive dots. However, the displacement velocity between the successive points decreases downwards from one dot the next. By using kinematic equations, the displacement velocity is 0.018491 cm/ms^2. The graph of the velocity in this specified direction against time shows a straight line. The points are plotted, on the same note; the best fit line is drawn along the points that seem to align into a line. This line slopes from the right hand side to the left hand side. It has a positive slope of 0.5201. The floating hockey puck’s velocity against time curve is a straight line with slope equivalent to gravitational pull and its displacement against time curve must be quadratic in time (t) (Giancoli 81). The kinematical equations that are used to rule this motion are: y = yo + vyot - ½ gt2 vy = vyo – gt ay = - g Conclusion The motion in one dimension experiment is every important. It helps scientists to measure the acceleration due to gravity both on earth and at space using one- dimensional motion of an object or a body. The second experiment on the motion in two dimensions is also used by scientists and physics students to demonstrate the independence of motion along two perpendicular axes in the projectile motion; that is, the accelerated motion along the vertical axis and uniform motion along the horizontal axis. Therefore, knowing the theories and concepts of linear motion, as well as motion in one dimension and two dimensions, helps scientists and other scholars to a great extent. The concept will facilitate the conduction of the above experiments. . Works Cited Giancoli, Douglas C. Physics for scientists & engineers. Upper Saddle River, N.J.: Prentice Hall, 2000. print. 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