John Lietz Paul Corsi Erica Crane Steven Ivanics Run to the Hills The basic purpose of our project was to investigate mechanical techniques in hurdling and relate them to some of the concepts and ideas we learned throughout physics this year. This includes such basics as the following: velocity, acceleration, mass, force, time, impulse, momentum, work, conservation of energy, potential energy, and kinetic energy. The most important element of hurdling, as in any race, is obviously speed – better known as velocity. This is a very simple equation; velocity=(distance/time). Using video analysis, we derived the time to be 1.1 seconds. The (horizontal) distance was 4.734 meters. The result was 4.3 m/s. Another important element is “getting out” of the starting blocks – better known as acceleration. Acceleration=(Vf-Vi)/t. The Vf was 4.3 and the Vi was 0; divided by 1.1 results in an acceleration of 3.9m/s2. We weighed Steve to find his mass and it equaled 71.1kg. Because F=ma, we multiplied the 71.1kg X 3.9m/s2, resulting in 300.77N.
DATA SAMPLING Wiimote analyzer - eziosoft time acceleration X acceleration Y acceleration Z roll pitch time/date IR mid X IR mid Y "0:0:0:45" 0.12 -0.04166667 1.166667 5.792385 -2.008152 4/17/2009 12:21:38 PM 0 0 "0:0:0:79" 0.12 -0.04166667 1.208333 5.59421 -1.939648 4/17/2009 12:21:38 PM 0.1890572 0.02736156 "0:0:0:82" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:83" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:83" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:84" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:85" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:86" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:87" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:88" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:89" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:89" 0.12 -0.08333334 1.208333 5.584335 -3.874742 4/17/2009 12:21:38 PM 1 0 "0:0:0:92" 0.12 -0.08333334 1.166667 5.781425 -4.011251 4/17/2009 12:21:38 PM 0.3717636 0.03908795 "0:0:0:93" 0.12 -0.08333334 1.166667 5.781425 -4.011251 4/17/2009 12:21:38 PM 0.3717636 0.03908795 "0:0:0:94" 0.12 -0.08333334 1.166667 5.781425 -4.011251 4/17/2009 12:21:38 PM 0.3717636 0.03908795 "0:0:0:100" 0.08 -0.125 1.083333 4.14096 -6.478632 4/17/2009 12:21:38 PM 0 0 After clearing one hurdle, it is important to keep going and at least maintain the same velocity. Here it is especially important to maintain your momentum over the hurdles and in between. Momentum=(mass)(velocity). This equals 331.53kg per m/s. Impulse is the change in momentum that results from force acting over a period of time. I=(f)(t). Therefore our impulse on the 77.1kg hurdler was (300.7)(1.1)=330.77. Work is the force applied over the hurdle. If he is not doing work, then he will not get over the hurdles and fail miserably. Work=(force)(distance), so (300.7)(4.734)=1423.5j. The law of conservation of energy is (-ke=pe), meaning that matter cannot be created or destroyed. Potential energy=(mass)(gravity)(height). It will always be the same as (-ke). It follows an essentially parabolic path (like when we did the demonstration in class with the pendulum, when it swung back and forth to the same point). The ideology is the same in hurdling, as you would ideally land the same distance beyond the hurdle as you take off from in front of the hurdle. The potential energy in our case equals 1796.77J. Energy=(1/2)(m)(v2), so (1/2)(77.1)(4.32)=712.78J. Energy is conserved. All of these physics elements we learned throughout the year came together to help us answer our questions about hurdling mechanics. The center of gravity does not fulctuate nearly as much as we anticipated. We found many things such as the velocity, acceleration, etc.
|
