« back to all changes in this revision
Viewing changes to 105/exp03/exp03.tex
- browse files at revision 109
- compare with another revision
- download diff
- download tarball
- view history from revision 109
- Committer: rami
- Date: 2009-09-20 22:06:21 UTC
- Revision ID: rami@rami-desktop-20090920220621-oletvkrz1dnnceqa
applying changes asked by Dr. Shikakhwa
added
removed
105/exp03/exp03.tex
5
5
\usepackage{amsmath}
6
6
\usepackage{wrapfig}
7
7
\usepackage{fancyhdr}
8
\usepackage{enumitem}
8
9
\setlength{\headheight}{15.2pt}
9
10
\pagestyle{fancy}
10
11
\newcommand{\helv}{\fontsize{9}{11}\selectfont}
40
41
\textit{\textbf{GENERAL}}
41
42
\end{flushright}
42
43
In order to move an object that is initially at rest, we must apply \textbf{a force} on it. Force is a vector quantity and its SI unit is the \textbf{Newton} (N).\\
43
44
44
The vector sum of several forces acting on an object is called their \textit{resultant}. A resultant force is required to accelerate an object. Remember that acceleration is the rate of change of velocity. We know from experience that a resultant force must act on an object initially at rest to set it into motion and eventually the object speeds up. Similarly a resultant force is required to slow down or stop an object that is already in motion. Certainly, we need to apply a resultant force on a moving object to change the direction of its motion. In all of these cases, the object accelerates (changes its velocity) under the action of the resultant force.\\
45
45
\newline
46
46
The acceleration of an object is directly proportional to the magnitude of the resultant force $\vec{F}$ exerted on it. When we double the force, the acceleration is also doubled. This means that, the ratio of the magnitude of the force to the magnitude of acceleration is a constant. This ratio is called the \textbf{mass} $m$ of the object. Therefore, we may write
47
47
\begin{equation}
48
48
m=\frac{F}{a} \,\,\,\,\,or\,\,\,\,\, F=ma
49
\end{equation}
49
\end{equation}
50
50
This last relationship is called Newton's second law of motion. Note that both $\vec{a}$ and $\vec{F}$ are vectors and they are in the same direction.
51
51
When several forces act on an object moving in the xy-plane, the method of components yields
52
52
\begin{equation}
90
90
\textit{\textbf{EQUIPMENT}}
91
91
\end{flushright}
92
92
93
\begin{itemize}
93
\begin{itemize}[label=$-$]
94
94
\item \textbf{Rotary Motion Sensor}.
95
The Rotary Motion Sensor is a bidirectional position sensor. It measures the the angular frequency, the number of cycles that an object rotate in the unit of time. The standard unit of angular frequency is $rad/s^2$. To measure the linear quantities using this sensor you have to mutliply the angular quanities by the raduis of the rotating object. The data logger do this conversion process automatically if the linear quatities are chosen to be sampled. The rod clamp can be mounted on three sides of the sensor case, allowing the Rotary Motion Sensor to be mounted on a rod stand in many different orientations. The end of the Rotary Motion Sensor where the cord exits the case provides a platform for mounting a clamp-on
96
Super Pulley. Figure \ref{fig:rms} shows the rotary motion sensor.
97
\begin{figure}\begin{center}\includegraphics[scale=0.5]{rms.png}\label{fig:rms}\caption{The rotary motion sensor with the 3-step pulley}\end{center}\end{figure}
95
The sensor is a device that measure physical quantities automatically without the human intervention. The rotary motion sensor in our experiment will measure displacement, velocity, and acceleration. When you connect the sensor to the data logger, the data logger will be able to read the measured values, the samples, store and analyze them. Out of the stored values the data logger can display figures and calculate the statistical results. Using a sensor is more accurate and easier because of the automatic high sampling rate which is hard to do manually. Figure \ref{fig:rms} shows the rotary motion sensor.
96
97
\begin{figure}
98
\begin{center}
99
\subfloat[The rotary motion sensor with the 3-step pulley]{\label{fig:rms}\includegraphics[width=0.7\textwidth]{rms.png}}
100
\subfloat[The holder with a mass]{\label{fig:holder}\includegraphics[width=0.3\textwidth]{holder.png}}
101
\caption{The equipment}
102
\label{fig:equipment`}
103
\end{center}
104
\end{figure}
98
105
\item \textbf{3-step pulley}.
99
The 3-step Pulley has three main grooves each with different radius. The values of the radiuses are measured and stored in the data logger which will use them to convert the angular quantities to linear ones.
100
\item \textbf{Two hangers}.
106
The 3-step pulley has three main grooves each with different radius. The values of the radii are measured and stored in the data logger which will use them to convert the angular quantities to linear ones.
107
\item \textbf{Two Holders}. See Fig.(\ref{fig:holder}).
101
108
\item \textbf{Three brass masses}.
102
109
\item \textbf{Thin thread}.
103
110
\item \textbf{Data Logger}.\\
113
120
\label{fig:atwood_exp}
114
121
\end{center}\end{figure}
115
122
\begin{enumerate}
116
\item Check if the experiment setup as shown in Figure \ref{fig:atwood_exp}. The experiment is setup as follows:
117
\begin{itemize}
118
\item The two hangers tied to the ends of the thread.
119
\item The thread allocated on the largest groove of the 2-step pulley.
120
\item Two equal masses attached to each hanger and the system is balanced. The system and the masses do not have to be held.
121
\item One of the masses is close to the ground and the another is close the sensor.
122
\end{itemize}
123
\item \label{step:setup}Arrange the apparatus as in shown in Fig.(\ref{fig:atwood_exp}). First pass the thread through the largest groove of the 30step pulley , then attach the mass holder to its ends. Attach one of the two equal brass masses to each mass holder. Arrange these such that one of the masses is close to the pulley while the other is close to the ground.
123
124
\item Turn the data logger on.
124
\item Connect the rotary motion sensor to the data logger. If the model of the rotary motion sensor is CI-6538, the sensor must be connected to the Digital Adaptor PS-2159 which would be connected then to the data logger.
125
\item Once the sensor is connected to the data logger, a new pop up menu will appear choose the second choice which is The rotary motion sensor. Now, a new graph will be created.
126
\item Navigate to the sensors proprities window, by choosing the sensors entry from the home page. Modify the sensor paramers as the following:
127
\begin{itemize}
128
\item Linear Position Scale option is set to Lg. Pulley (o-ring).
129
\item All the linear readings are visible.
130
\end{itemize}
131
\item Return to the graph and choose the linear velocity for the y-axis and time for the x-axis.
132
\item Add the difference mass to the upper mass while holding the upper mass.
133
\item Simulatenously,
134
\begin{itemize}
135
\item Release the upper mass which is heavier.
136
\item Start the sampling process by pressing the run button in the data logger.
137
\end{itemize}
138
\item Stop the sampling procedure when the heavier mass reach the ground.
139
\item You have to repeat the procedure if:
140
\begin{itemize}
141
\item The velocity measured is negative. The rotation of the pulley must be reveresed. Switch the side of the heavier mass to get positive readings.
142
\item The linear graph obtained is not close to the origin. The sampling must be started at the same time the heavier mass was released.
125
\item Connect the rotary motion sensor to the data logger. If the model of the rotary motion sensor is CI-6538, the sensor must be connected first to the Digital Adaptor PS-2159 which would be connected then to the data logger.
126
\item Once the sensor is connected to the data logger, a new pop up menu will appear on the data logger screen which contains the available sensors that the data logger can detect. Select the second choice ``The rotary motion sensor'' option. Once you selected the appropriate sensor, a new graph will be created.
127
\item To change the sensors properties, Go to the Home Screen and select the sensors icon. Modify the sensor parameters as the follows:
128
\begin{itemize}[label=$-$]
129
\item set the ``Linear Position Scale'' option to ``Lg. Pulley (o-ring)''.
130
\item set the ``Linear Position'' to ``visible''.
131
\item set the ``Linear Velocity'' to ``visible''.
132
\item set the ``Linear Acceleration'' to ``visible''.
133
\end{itemize}
134
\item Return to the Home Screen. Select the graph icon. Change the y-axis to display the linear velocity and the x-axis to display the time.
135
\item \label{step:start}Add the difference mass to the upper mass while holding it.
136
\item Now, your sensor and the data logger are now ready to start sampling the data. To do this you need to release the upper mass and, \textbf{at the same time}, press the run button in the data logger which will start the sampling process.
137
\item Stop the sampling process when the heavier mass reaches ground.
138
\item \label{step:end}You have to repeat the procedure if:
139
\begin{itemize}[label=$-$]
140
\item The velocity measured is negative. The rotation of the pulley must then be reversed. Switch the heavier mass side to get positive readings.
141
\item The linear graph obtained is not passing through the origin. The sampling must then be starts at the same instant the heavier mass is released.
143
142
\end{itemize}
144
143
\item Answer the questions (\ref{q:slope}-\ref{q:height}) in the Data \& Results sections.
145
\item Do the experiment again with measuring the linear distance instead of the linear velocity.
146
\item Print the graph you obtaind for distance vs. time.
147
\item Answer question \ref{q:dvst} in the the Data \& Results section.
144
\item To save your work, go to the Home Screen and then select the Files icon. Save the file already open which contains the data you collected using the sensor.
145
\item Return to the graph and change the y-axis to display the linear position.
146
\item Arrange the experiment setup as it was in step \ref{step:setup}. Repeat the steps(\ref{step:start}-\ref{step:end}) to get the graph of the displacement vs. time.
147
\item Print the graph you obtained for the displacement vs. time.
148
\item Answer question \ref{q:dvst} in the Data \& Results section.
148
149
\end{enumerate}
149
150
\newpage
150
151
\begin{flushright}
153
154
\begin{enumerate}
154
155
\item \label{q:slope}Using the data logger, report the slope of the best line and the error in the slope.\\
155
156
$m \pm \Delta m$ = . . . . . . . . . . . . .
156
157
157
158
\item What is the quantity that the slope represents ? What is its unit ?\\
158
159
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
159
160
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
161
\item Examining the graph of velocity vs. time, what kind of motion does each puck have? Why?\\
162
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
163
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
164
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
165
\item Can you say that both pucks have the same motion? Explain your answer.\\
161
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
162
\item Examining the graph of the velocity vs. time. What kind of motion does each puck have? Why?\\
163
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
164
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
165
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
166
\item Can you say that both masses have the same type of motion? Explain your answer.\\
166
167
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
167
168
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
169
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
169
170
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
171
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
172
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
172
173
\item Calculate the gravitational acceleration $g$. Show your work.\\
173
174
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
174
175
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
175
176
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
176
177
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
177
178
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
178
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
179
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
179
180
\item Calculate the tension $T$ in the cord. Show your work.\\
180
181
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
181
182
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
189
190
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
190
191
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
191
192
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
192
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
193
\item \label{q:dvst}What is the distance the mass passed before hitting the ground ? Does it equal to height you calculated before ?\\
194
\newline$distance=$. . . . . . . . . . . . .\\
195
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
196
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
197
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
193
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
194
\item \label{q:dvst}What is the displacement of the falling mass ? Does it equal to height you calculated before ?\\
195
\newline$displacement=$. . . . . . . . . . . . .\\
196
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
197
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
198
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\
198
199
\end{enumerate}
199
200
200
201
\textbf{Comments and Discussion}
Loggerhead is a web-based interface for Breezy
Version: 2.0.1