Lab_04 - Laboratory 4 Projectile Motion Introduction We...

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Laboratory 4 Projectile Motion Introduction We have spent the past two laboratories investigating one-dimensional motion. In Laboratory 2, we looked at a situation where an object was subject to a constant force (and, hence, acceleration) while in Laboratory 3 we looked at a situation where the force was not constant. However, in both of these labs, the motion of the objects and the net forces they experienced were parallel ; the forces served to speed the objects up or slow them down, but the objects always moved along the same [one-dimensional] line. In most of life, things are not this simple. In projectile motion, which we will explore today, things get more complicated, because the acceleration can be perpendicular to the object’s velocity, parallel to it, or somewhere in between depending on how the object is launched. This laboratory marks the start of our exploration of two-dimensional motion. In two-dimensional motion, the net force and velocity vectors lie in a plane, but are not necessarily parallel to each other. This describes the majority of situations you will encounter in the rest of the course. Theoretical Section: Two-Dimensional Motion In Table 1 of Laboratory 2, we encountered four equations relating the variables x (displacement), v 0 (initial velocity), v (Fnal velocity), a (acceleration), and t (time). Recall that each equation allows you to use three variables to solve for a fourth; the Ffth is ignored. To extend these equations to two-dimensional motion, we must simply apply the principle of dimensional independence , which means that forces, displacements, accelerations, etc. happening in one direction do not affect those happening in a perpendicular direction. Because of this very important principle, we can write two sets of equations, using subscripts to denote velocities and accelerations happening in the x and y -directions, shown in Table 1. The only variable that is the same for both dimensions is time; we will exploit this fact repeatedly in our analyses of two-dimensional motion. One cannot study two-dimensional motion effectively without understanding the ideas of vector addition and component vectors , which we already encountered in Laboratory 2. A full analysis of these concepts can be found in any introductory physics text. 32
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Parameter x -dimension y -dimension Initial position x 0 y 0 Position xy Initial velocity v 0 x v 0 y Final velocity v x v y Acceleration a x a y Time tt Table 1: All of the variables for the x and y dimensions are distinct, except for time. Theoretical Section: Projectile Motion A projectile is any object propelled through space by a force that ceases after it is launched. While it is in ±ight, the only force that acts on it is gravity. Using the coordinate system shown in Figure 1, we can make a table showing the relevant kinematic quantities in the x and y -directions (see Table 1).
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This note was uploaded on 09/13/2011 for the course ECONOMICS 101 taught by Professor Gerson during the Spring '11 term at University of Michigan.

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Lab_04 - Laboratory 4 Projectile Motion Introduction We...

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