Acceleration due to Gravity

Introduction

The purpose of this lab is to test the accepted value of g.

An object that falls through the earth’s atmosphere is subject to two forces: gravity and air resistance. In this experiment, we will ignore the effects of air resistance and assume free fall acceleration. Since the distance that the object falls is small, we can assume that the force of gravity is constant. Newton’s second law can be written as follows:

ΣF = ma

W = ma

mg = ma

a = g

Note that the force of gravity is actually larger than mg, but the non-inertial reference frame of the earth observer creates the illusion of reduced weight. The value of g will mostly depend on elevation, which changes weight, and latitude, which changes apparent weight. There is also a subtle effect on g due to local geology. An equation1 that takes into account altitude and latitude is the following:

[1]g = 9.780327[1 + 0.0053024(sinθ)2 – 0.0000058(sin(2θ))2] – 0.000003086h

θ = latitude

h = altitude in meters

You will probably find it extremely helpful to use Excel for calculations and graphs. I am happy to assist you with your calculations. Please see the general lab instructions for help with graphs.

Experimental Procedures

1)Chemeketa lies at an altitude of 59 m and latitude of 44.98˚.Use equation [1] to calculate a theoretical value for g.

2)Use the free-fall apparatus as directed. Please be extremely careful since this is a high voltage device.

a)Unplug the spark generator.

b)Inspect the wires to check that they are attached and straight. Check if the apparatus is vertical.

c)Install tape so that it is vertical and completely covers the back wire.

d)Turn on the electromagnet and attach the object.

e)Inform bystanders that you intend to plug in the spark generator.

f)Plug in the spark generator.

g)Press and hold the button on the spark generator.

h)Turn off the electromagnet.

i)Wait for the object to fall to the bottom, and then quit pressing the button on the spark generator.

j)Unplug the spark generator.

k)Remove and inspect the tape.

l)Repeat the experiment if too many dots are missing or unclear.

m)You may beg, borrow, or steal a better tape if you are dissatisfied after two attempts.

3)Beginning with the first clearly individual dot, measure and record the displacement (Δx) of the body and the corresponding time interval (Δt) for every sixth marked spot. Be very thoughtful in your estimate of the error and clearly justify your estimate. The manufacturer of the spark timer claims that it emits a spark 60 times per second, so every sixth dot represents 0.1 s. The claimed accuracy of ± 0.05% can be ignored as negligible.

4)Calculate the elapsed time which is a running total of the time intervals.

5)Calculate the average velocity of the body for each time interval using the equation vave = Δx/Δt. Calculate the error.

6)Make a graph of average velocityas a function of elapsed time. Include a trend line with R2 and the equation. The slope of the line is an estimate of g. Please pay close attention to the general lab instructions regarding graphing in Excel. Check with me before you print a graph.

7)Calculate the change in velocity, Δv.

8)Calculate the average acceleration of the body for each time interval using the equation aave = Δv/Δt.

9)Make a graph of acceleration as a function ofelapsed time.Do not include a trend line. Please pay close attention to the general lab instructions regarding graphing in Excel. Check with me before you print a graph.

10)Are your data for acceleration consistent with the theoretical value for g? If not, are your data consistent with a different value?

1 accessed 7 October, 2008.