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# lab - Lab 1 Free-Fall Acceleration INTRODUCTION In this lab...

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Lab 1: Free-Fall Acceleration INTRODUCTION: In this lab, we will measure the acceleration of earth’s gravity. Using a piece of paper tape, with a weight suspended on the end, we will drop it from some point. A machine will make dots on the paper at even intervals as it falls. The distance between the dots represents the distance the paper fell during each interval. By graphing the distance between the dots as the interval number increases, we can find a value for gravity using the slope of the best-fit line. This calculated number should theoretically be the same as the universally accepted value for gravity. THEORY: This lab deals with finding the constant acceleration at which things fall towards earth, or the measure of gravity. The equation for the force of gravity between an object of mass m and the earth of mass M is F = GMm/R 2 , where G is the universal gravitational constant and R is the radius of the earth. The R in the denominator actually stands for the distance between the two objects, but for an object near earth’s surface, we can assume the distance to equal earth’s radius. Finding the value of gravity requires dividing both sides of the equation by m (since F=mg). This gives g = GM/R 2 . Newton’s second law states that F = ma, or in terms of acceleration: a=F/m. This means that an object of mass m with a force F acting upon it has an acceleration equal to a . Since gravity is the acceleration of objects towards earth, we can set Newton’s second law and law of gravitation equal to each other: a = GM/R 2 . From this equation, scientists were able to find the value of g on earth to be 9.81 m/s 2 .

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