# Acceleration of Gravity Free Fall Method Experiment

Prior to Lab: Derive the numbered equations (Equations 1, 2 and 3) in the lab instructions using the definitions of velocity and acceleration (a=dv/dt and v=dy/dt).

Object: The object of this experiment is to determine the value of the acceleration of gravity by measuring the rate of acceleration of a freely falling object. In addition, one will be able to compare theory with experiment for constantly accelerated motion.

Discussion: An object dropped near the earth’s surface will accelerate uniformly with the acceleration due to gravity (g) toward the earth. The magnitude of g at the Berks Campus is 9.801 m/s2. Thus according to the equation describing motion for a uniformly accelerated object, its position y as a function of time t is [pic](1)

where down is assumed to be the positive direction and its initial position is at the origin of the coordinate system used. A graph of this equation would yield a parabolic curve as shown in the example below.

The speed can be determined from the equation (1) by differentiating the displacement equation with respect to time yielding [pic](2)

which when graphed is the straight line as shown

[pic]

where the y-intercept is the initial speed vo and the slope of the line is the acceleration g.

|[pic] [pic] |Apparatus: The experiment makes use of the Behr Free Fall | | |apparatus shown at the right, a dc source to power the | | |electromagnet needed to hold up the falling object (plummet) and | | |a high voltage spark generator to mark the spark tape every 1/60 | |...

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