Projectile motion and Conservation of Energy

Projectile motion and Conservation of Energy - Michael Lin...

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Michael Lin Tuesday Section Partners: Josh Narciso, Bryant Rolfe Due Date: 2/21/07 Projectile Motion and Conservation of Energy Michael Lin The objective was to use trajectory equations for an object undergoing two- dimensional projectile motion to predict the landing position of a projectile. A launch tube was used to launch a metal and plastic ball into projectile motion separately. For the first trial of the metal ball experiment, the predicted landing position was at 47.03 +/- 9.41 cm on the x-axis, and the measured distance was 47.08 +/- 0.25 cm. The predicted landing position of the second trial was 61.88 +/- 7.26 cm, and the measured was 62.21 +/- 0.21 cm. For the first trial of the plastic ball experiment, the predicted landing position was at 54.51 +/- 8.44 cm on the x-axis, and the measured distance was 50.21 +/- 0.05 cm. The second plastic ball trial had a predicted distance of 67.44 +/- 7.11 cm, and the measured distance was 63.74 +/- 0.06 cm. All four trials were in good agreement with predicted distances and uncertainties. INTRODUCTION Energy conservation is the principle that describes the transformation of energy from one form to another: for a given system, as long as all the types of energy within the system are accounted for, the total energy of the system (closed) must be constant. This experiment is a demonstration of energy conservation in that the gravitational potential energy at the start of the launch is partially converted to kinetic energy (translational as well as rotational) when the object reaches the launch point of the launching track. Because of the loss of energy due to friction and that there still exists gravitational potential energy at the point of launch, not all of the potential energy is converted to kinetic energy. Nevertheless, energy conservation is the principle behind which this experiment functions. Mechanical energy is used to broadly define kinetic energy and potential energy, and the different types of each. Kinetic energy due to translational movement is described by the equation (1/2)mv 2 , where m is the mass of the object in motion and v is the velocity. In this experiment, the object is undergoing rotation also, so rotational kinetic energy must also be accounted for. Rotational kinetic energy is defined as (1/2)Iω 2 , where I (moment of inertia) is (2/5)mR 2 for a sphere and ω is v/R (for an object that does not slip). Substituting I and ω into the equation gives a rotational kinetic energy of 1/5mv 2 . Therefore, the sum of the kinetic energies for a spherical object undergoing translational as well as rotational motion is the sum of 1/5mv 2 and 1/2mv 2 , which is 7/10mv 2 . Potential energy (gravitational) in this experiment is described by the equation U = mgh, and the change in gravitational potential energy is ΔU = mgΔh. In order to truly demonstrate energy conservation in the real world, one must take into account losses of energy due to friction as well. Therefore, change in total energy of a closed system is defined as the sum of the changes in kinetic and potential energies minus the work done by friction, and this must equal zero. In this experiment, the work done by friction was measured by trial and error;
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