Lab_02 - Laboratory 2 Motion with Uniform Acceleration...

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Laboratory 2 Motion with Uniform Acceleration Introduction In this laboratory, we will examine two different situations where the acceleration of an object is constant. The Frst will be a glider on an inclined plane; the second will be a glider attached to a hanging mass. The goal of this experiment is not to teach you any radically new physics; rather, it is to give you a chance to practice your statistical analysis and to develop your ability to analyze various errors and their effects on your measurements. In each experiment, consider what factors will cause the magnitude of the acceleration to go up or down. Pay attention to the similarities in position vs. time graphs of uniformly-accelerating objects, no matter what the source of the acceleration is. Almost every problem you analyze in introductory mechanics will involve objects just like these. Theoretical Background: Motion with Constant Acceleration Much of the physics you will encounter in lecture will involve motion with uniform, or constant, acceleration. This means that the acceleration an object experiences does not depend on the ob- ject’s position or velocity; it is just a single vector with constant direction and magnitude. Later on, you will learn more about situations that generate conditions of constant acceleration. There are four equations that completely describe one-dimensional motion with constant acceleration (shown in Table 1). The quantities that appear in these equations are x 0 Initial position x Position at time t v 0 Object’s speed at starting point v Object’s speed at x a Acceleration (constant) t Time it takes object to go from x 0 to x . Problem 2.1 Say you have a series of measurements of position vs. time for a falling object. Which of the four equations in Table 1 should you use to obtain an estimate of the object’s acceleration? What’s wrong with the others? What if you had a series of measurements of velocity vs. time? 11
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Equation Variable You Can Ignore v = v 0 + at x x = v 0 t + 1 2 at 2 v v 2 = v 2 0 + 2 ax t x = 1 2 ( v 0 + v ) t a Table 1: Four equations relating key quantities for motion with constant acceleration. Theoretical Background: Newton’s Laws No mechanics laboratory manual would be complete without some discussion of Newton’s laws, so we list them here for reference purposes. Newton’s second law forms the foundation for nearly everything you will do in lecture and lab for the remainder of the course, so spend some time appreciating it! Newton’s First Law states that a body remains at rest or in uniform motion unless acted upon by a net force. The term “uniform motion” means motion in a straight line with constant speed (the object’s velocity vector is constant in time). Newton’s Second Law states that a body acted upon by a force moves in such a manner that the time rate of change of momentum (the product m ° v ) equals the force. If the mass of the body remains constant while the force is acting on it, we can write this as ° F = m ° a , which is the familiar form of Newton’s Second Law that we all know and love.
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Lab_02 - Laboratory 2 Motion with Uniform Acceleration...

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