AP Physics C

LAB ONE

Experimental Determination of “g” Locally

Introduction

The kinematics of one-dimensional motion is usually the first material covered in an

introductory physics course. When confined to the case of constant acceleration, onedimensional

kinematics provides a subject that is amenable to classroom analysis and laboratory

study both in non-calculus and calculus-based courses. The kinematics equations describe the

position x and the velocity of an object in terms of its initial position x0, its initial velocity v0, the time t, and the object’s acceleration a. The kinematics equations used in this lab are found on your formula sheet, with the most useful one probably being:

x = x0 + v0t + ½ at2

If the object of interest is falling freely near Earth’s surface, the magnitude of the

acceleration is commonly denoted by g, which has a nominal magnitude of 9.80 m/s2. In this lab, a local, precise value of g will be measured. We dilute g by having the object accelerate down an inclined plane. We also reduce the friction that the object experiences by using a low-friction cart on a track.

When we raise one end of the track so that it makes an angle with respect to the horizontal,

the acceleration down the inclined track is given by the equation:

a = gsin

When working with the angle, it is best to substitute the quotient H/L = sin as shown in the figure below, as opposed to trying to measure the angle directly.

Be very careful to level the track initially, then measure the height and length with great accuracy. Remember to use as length the distance between the two supports, not the entire length of the track.

In developing a procedure on your own, you should consider the analysis functions built into the Logger Pro program. Specifically, the program can perform curve fitting of a variety of function types and yield quite accurate coefficients. Study the kinematics equation, above, and the curve fitting options carefully as you choose your methodology.

Experimental Method:

Using the background information above, your group is to find the local value of g (the acceleration due to gravity). Your experimental method and final report should meet the following requirements / restrictions:

  1. You must find this value as accurately as possible, using at least three TRUE significant figures in your final value.
  1. You must verify that this value is independent of the object’s mass, by demonstrating results for at least three different masses.
  1. You must provide sufficient detail in your written procedure to allow a person with moderate knowledge and skills to repeat the experiment based solely on your report. More importantly, I should be able to follow the procedure and find no errors or missing/unclear steps.
  1. Your acceptable list of equipment and software includes: track and included carts/accessories; computer with Logger Pro software; LabPro interface device; Motion Detector.
  1. You must include a graph of position vs. time for each mass used.
  1. Graphs of velocity and acceleration generated directly by Logger Pro software are notacceptable, but discussions of their potential errors and reasoning for not using them are encouraged.

Final Product:

Please turn in within one week of beginning this project: One report per person, clearly indicating the final value of g in this room. The report must be computer generated, and may be submitted electronically if desired. The format of the report must meet the specifications set forth above, as well as the generic lab report format handed out in class. It should also not be a copy of another group member’s report – I want to see your own work in your own words.