4: Acceleration Due to Gravity
- Page ID
- 114095
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)To learn, understand, and visualize how the acceleration due to gravity affects falling objects
Method:
The method we will use takes data from an ultrasonic sensor on the velocity, position, and acceleration of an object in front of it. The computer creates graphs of each quantity on a computer software tool. For most objects, the acceleration should roughly match -9.8 m/s as this is the acceleration due to gravity. But it may not always be the case, and that is what you are exploring now.
Set up:
To set up this lab experiment, we have to protect the sensor. We accomplish this by putting a metal cage or basket around the sensor and taping it to the ground (\(\PageIndex{2}\)). This allows the object to fall towards the sensor while not directly impacting the sensor, this also allows the sensor to see through the cage to record the data. We also need to raise the sensor up to the ceiling of the cage. This is so the cage will not be detected by the sensor, and the sensor will only detect the falling object. We do this by placing two wood blocks and taping the sensor on top of those blocks (Figure \(\PageIndex{1}\)). We also need to connect the wire from the sensor to the computer. To do this, pass the wire through any one of the holes of the cage so that the bottom of the cage remains flat. Also, to make use of the gaps in the cage the sensor was centered on the hole (the gold circle) to ensure the least amount of interference.
Vernier LoggerPro is the software that is used to retrieve data from the sensor. To start collecting data, press “Collect” in the software. When the sensor is in the process of collecting data, there will be a clicking sound, and the graph will show the data being collected.
To ensure that the sensor is working hold an object close to the sensor after pressing “Collect” in the software. While doing this, make sure the object is far enough away as there is a minimum distance (20mm) where the sensor can not see.
Procedures:
First, hold the object over the sensor and cage as shown in \(\PageIndex{3}\). Then start the sensor reading and drop it over the sensor and cage at the same time. Be sure to raise it to a height where the sensor can see it as it is falling, but also not too high where it is completely out of range of the sensor.
You will diffrent drop objects onto the sensor, which will record its position, speed, and acceleration. For example a ball, frisbe, and a coffee fillter of which the ball is shown.
Analyzing the graph:
Only a small portion of the graph will be of the ball’s free fall, so you will have to identify where that is on the graph. Understanding the relationship between position, velocity, and acceleration can help when analyzing the graph, as by default, the software shows the graph of position over time and velocity over time.
To find the rate of change, look at the velocity graph, find the slope of the section of the falling object, and then that will give you the acceleration. Use the software’s built-in linear fit analysis to show the rate of change of a linear line between two points in time of the velocity graph which is acceleration. To use this analysis feature, press analyze located at the top right of the software window a drop-down menu will appear. Find the two points on the time-axis of the object's free fall that you want to analyze, and it will find the slope of that section, giving you acceleration.
|
Velocity (m/s) |
acc ( |
Time (s) |
|---|---|---|
|
-0.004 |
-0.094 |
0.16 |
|
-0.009 |
-0.114 |
0.18 |
|
-0.010 |
-0.047 |
0.2 |
|
-0.009 |
-0.029 |
0.22 |
|
-0.009 |
-0.087 |
0.24 |
|
-0.015 |
-0.040 |
0.26 |
|
-0.015 |
0.165 |
0.28 |
|
-0.007 |
0.328 |
0.3 |
|
0.002 |
0.311 |
0.32 |
|
0.008 |
0.155 |
0.34 |
|
0.006 |
0.104 |
0.36 |
|
0.007 |
0.242 |
0.38 |
|
0.017 |
0.286 |
0.4 |
|
0.033 |
-0.372 |
0.42 |
|
0.011 |
-1.613 |
0.44 |
|
-0.028 |
-3.223 |
0.46 |
|
-0.103 |
-5.556 |
0.48 |
|
-0.251 |
-7.783 |
0.5 |
|
-0.433 |
-9.055 |
0.52 |
|
-0.628 |
-9.491 |
0.54 |
)
Certain objects with different characteristics will feel the same acceleration, but when graphing their velocity and acceleration, they will show up differently. This is because the air resistance force is greater than the force of gravity pushing it down at sertan speeds. Things like weight and surface area can affect the speed at which an object will fall. This is called terminal velocity, which is the maximum speed that an object can fall on earth
In this lab you were able to compare the properteis of different objects under the influence of earth’s gravity.