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LAB# 14 PROJECTILE MOTION AND THE CONSERVATION OF ENERGY Figure 1: Equipment for the "Projectile Motion and Conservation of Energy" experiment showing the projectile launcher, projectiles, loading rod, photocells (photogates) and safety glasses. INTRODUCTION: Our objective in this experiment is to analyze projectile motion using kinematics and also using conservation of mechanical energy. Analyzing a system from different viewpoints often allows one to gain additional insight into the system, as well as into the methods used. We begin by using the kinematical relationships for a projectile moving with constant acceleration (the acceleration due to gravity here) to determine the initial speed (muzzle velocity) of a projectile fired horizontally. We than use this initial speed to predict the horizontal range of the same projectile fired at some angle to the horizon. We will also measure the initial speed of our projectile using photocells. We end by applying conservation of mechanical energy to our projectile to determine if initial kinetic energy and maximum gravitational potential energy are equal for a projectile fired straight up into the air. APPARATUS: Projectile launcher and kit, Plumb bob; a meter stick and a 2-meter stick; Carbon paper; White paper; C-clamp; LabPro Interface; Lab# 14 Projectile Motion program, safety glasses.
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Theory: Using the coordinate system shown in Figure 2 we have for the x and y positions of the projectile as a function of time, , 0 t v x x (1) . 2 2 1 0 0 gt t v h y y (2) Where v x0 and v y0 are the x and y components of the projectile’s initial velocity v 0 . h 0 is the projectile’s initial height above the origin and g is the acceleration due to gravity. Note that the negative sign in front of g comes from our choice of up as the positive y direction. The independence of the x and y components of the motion tell us that the time it takes the projectile to reach the ground is independent of the horizontal motion. That is, it does not matter how fast or slow the projectile is traveling horizontally. The time it takes the projectile to reach the ground depends only on the projectile’s initial height, its initial speed in the vertical direction, v y0 , and of course g. Given that, if we wish to measure the projectile’s initial speed, 0 v , we fire the projectile horizontally, 0 0 v v x , measuring the distance x Total it travels horizontally before it hits the ground, . 0 t x v Total (3) The time t is the time it takes an object to fall to the ground, y = 0, from an initial height of h 0 is, . 2 0 g h t (4) Direct measurement of x Total along with combining Equations (3) and (4), left as an exercise for you, will yield the initial speed of the projectile.
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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