Lab 1: Free Fall
INS Physics
Winter 2003, Weeks 1-3

Lab notebooks are due in the box outside my office by 12 noon on the Monday after lab.

Schedule

Times (approximate)
Activity
Location
9:00 am - 9:30 am Lab Lecture: Introduction to free fall; required equations CAL
9:30 am - 11:30 am Free fall experiments  Bridges between Lab I and Lab II
11:30 am - 12 noon Free fall in vacuum demo;

data analysis using Excel

 CAL

Introduction
In this lab we explore the motion of objects subject to the earth's gravitational force during free fall. An object experiencing a constant acceleration, a, over a time interval, t, will move a distance, d, according to the equation:

                           d = (1/2)at2                 (1)

Since the acceleration due to the earth's gravitational force, called g, is approximately constant near the surface of the earth, the above equation applied to free fall becomes:

                           d = (1/2)gt2                 (2)

Here, the value of g is approximately 9.8 m/s2. Equation (2) holds when the earth's gravitational force is the only force acting on an object (i.e., when an object falls in a vacuum). However, in this lab we will use it as an approximation for objects falling through air, keeping in mind that it will not be accurate in certain cases.

Free Fall Experiments
We will be dropping objects from the bridges between Lab I and Lab II in order to gain an understanding of how objects behave during free fall. Please do not drop objects while people are passing under or around the bridges.

You should work in groups of 4, with 2 people on the bridges and 2 people on the ground. The following equipment will be provided for each group: (1) a field tape (2) stop watches, (3) balls and other objects of various sizes and masses, (4) scratch paper, and (5) air rocket launchers.

I. Comparison Experiments (45 minutes)
The goal of this portion of the experiment is to gain a qualitative feel for how objects behave when falling. You may want to start by creating a table in your lab notebook that gives shorthand notation for the various objects you will be dropping (e.g., whiffle golf ball) along with some description of the object if needed (e.g., size of a golf ball but hollow and with holes in surface).

Compare the falling time of various objects from a given height by dropping pairs of objects from that height. Keep track of your observations in a table that lists the pairs of objects you drop, the height from which they were dropped (i.e., which bridge), how the falling times of the two objects compared, and any other important observations. You do not necessarily have to measure the actual falling times or the bridge heights for this part of the experiment.

Some questions to think about:

Do identical objects hit the ground at the same time?
How does mass affect falling time?
How does hollowness affect falling time?
How does shape affect falling time?
Is there any sideways motion during the free fall?
Is the observed behavior repeatable? (i.e., Don't rely on just one trial.)
Is the behavior the same for different heights? Some ideas for getting at these questions: Drop a pair of identical objects
Drop objects of similar size but different mass
Drop a ball and a fir cone, a ball and a rocket, etc.
Drop two identical pieces of paper in different shapes
(e.g., one loose, one crumpled)
Try all of your experiments more than once
Try dropping from different heights II. Vertical and Horizontal Movement (15 minutes)
From the top bridge, drop a rocket at the same time that you shoot a rocket aimed parallel to the ground. What do you observe about the falling times? Repeat this experiment a few times with the different types of rocket launchers. Try it with a pair of balls where you drop one ball and throw one ball out horizontally.

From this experiment, do you think that movement in the x-direction (horizontal) is independent of movement in the y-direction (vertical)?
 

III. Estimating Acceleration Due to the Earth's Gravity, g(60 minutes)
Using the results of the comparison experiments, choose a single type of object that you think will give the most reliable results for estimating g. The idea is to measure the time and distance during free fall, then use equation (2) to calculate g from the measured values.

(1) Using the field tape, measure the heights from which you will be dropping your chosen object.

(2) Drop the object several times from each height and have 2 people measure the fall times. You might average these two numbers for a single data point, taking several data points for each height.

(3) Enter all your measurements in a table in your lab notebook to be graphed later.

(4) During the experiment, take one or two data points and do a quick calculation using equation (2) to see if you're getting approximately the right value for g (9.8 m/s2).
 

Free Fall in a Vacuum Demonstration
We will demonstrate free fall in an evacuated tube and qualitatively compare the results to our experiments with free fall in air.

Data Analysis
The final step in this laboratory is to graph the distance/time data from the quantitative part of the free fall experiments and use the graph to estimate the value of g, the acceleration due to the earth's gravity. We use a graph because it allows us to visualize any trend in the data and is a convenient way to average out experimental error.

Here are two approaches to estimating g based on a graph of your data. Try both and compare the results.

Power Function - Graph distance as a function of time (d on y-axis, t on x-axis). Fit a power function trendline to the data and display the equation of the trendline. Use the constant in front of the power function trendline to estimate g by comparing it to equation (2) above.

Linear Graph - Graph distance as a function of time squared (d on y-axis, t2 on x-axis). (Remember that you can use Excel to calculate t2 from t.) Fit a linear function with a y-intercept equal to 0 to the data and display the equation for this trendline. Use the slope of the trendline to estimate g using equation (2).