PH1004_Experiment_5

PH1004_Experiment_5 - PH1004 Exp 5: Acceleration Due To...

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PH1004 Exp 5: Acceleration Due To Gravity. Free Fall and Pendulum. 1 PH 1004 Laboratory Instructions Experiment 5 Acceleration Due to Gravity. Free Fall and Pendulum. Introduction Both the free fall of a body and the oscillation of a simple pendulum occur due to the existence of gravity on earth. It is the purpose of this experiment to observe these phenomena and to obtain a value of the acceleration due to gravity. In the first part of the experiment, the student will measure the displacement as function of fall time for a mass in free fall, and then calculate its acceleration. In the second part of the experiment, a value for the acceleration due to gravity will be obtained from the measurement of the period of oscillation for the simple pendulum. Background The magnitude of the gravitational force acting on a body of mass m near the surface of the earth is given by Newton’s law of gravity: 2 ) ( h R GmM F + = (5-1) where G is the universal gravitational constant, M is the mass of the earth, R is the earth’s radius, and h is the distance from the body to the earth’s surface. Typically, the distance of the fall is small compared to the radius of the earth ( h << R ); therefore h can be neglected in Equation 5-1. Then, using Newton’s second law, the magnitude of the gravitational acceleration , usually denoted with the letter g, can be expressed as 2 R GM m F g = = , (5-2)
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PH1004 Exp 5: Acceleration Due To Gravity. Free Fall and Pendulum. 2 L F T m mg mg sin θ mg cos θ θ s Figure 5-1 so g is independent of the mass and size of the body. At or near the earth’s surface the value of g is approximately 9.8 m/s 2 . The distance R to the earth’s center varies with position on the earth’s surface, thus the exact value of g is different for different places on the earth. The value of g is also influenced by the earth’s rotation, and it decreases with altitude. If you do the experiment carefully, you will be able to obtain three significant figures for the acceleration due to gravity in New York City. The free fall of a body under the influence of the earth’s gravitational attraction is the most familiar example of motion with constant acceleration. As early as the 16 th century, Galileo argued that a body should fall with the same downward acceleration regardless of its size and mass. In addition to the earth’s gravitational force, several other factors can affect the acceleration of a freely falling body, the most important of them being air resistance. To diminish the effect of air resistance, a massive, rounded object should be used in experiments. A simple pendulum consists of a small spherical mass suspended by a string (Fig. 5-1). When the mass is pulled to one side of its straight-down equilibrium position and then released, it oscillates about the equilibrium position. Many familiar situations such as a wrecking ball on a crane’s cable, and a child on a swing can be modeled as a simple pendulum. Let us consider the motion of a
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PH1004_Experiment_5 - PH1004 Exp 5: Acceleration Due To...

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