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\title{PHYS 201/202 and 207/208 Lab Manual \\
  MECHANICS, WAVES and HEAT}
\author{R.~Rollefson, H.T.~Richards and M.J.~Winokur}

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\begin{document}
\section{MC-4~~NEWTON'S II$^{nd}$ and III$^{rd}$ LAW}
%\input{toolbar/s01_tb0}

\noindent OBJECTIVE: {Newtons second law is deceptively simple: the acceleration of a body
is proportional to the {\underbar{\bf total}} {\underbar{\bf net force}} applied 
on it, and is inversely 
proportional to its mass. \nx
$$ \vec F = M \vec a~~~~\rightarrow ~~~~\vec a= {\vec F}/M$$
(Newton did not express it in this way because vectors had not been yet
invented.) \nx
The third law appears even simpler:
If body A  interacts with body B the force exerted  by A on B
is equal in magnitude, and opposite in direction to the force exerted  by B 
on A.
$$ {\vec F}_{AB} = - {\vec F}_{BA} $$
These laws, established in the XVII century are still valid. They are 
used to predict the motion of planets and satellites, basketballs and rockets.
 Corrections 
due to   Einsteins Relativity Theory
 are needed if the velocity of the body in question is
 a significant fraction of the speed of light.
& {FORCE, MASS and\nextline ACCELERATION 
 }}
 
\end{document}
\end




{\underbar {\bf{IN THIS EXPERIMENT}}} \nextline
A cart on an inclined plane is accelerated by the force provided by a 
string. The string is attached to both the cart and to a mass and mass 
hanger as shown below. You will measure the acceleration of the cart and
the force applied on it.
%\vfill \eject

 When the the cart moves, its displacement is equal in magnitude to
the displacement of the mass. As a consequence the magnitudes of the 
velocities and the
accelerations of the two objects will be the same. 
You will measure the acceleration $\bf a_{ex}$ of the cart, and the 
value of the tension $\bf T_{ex}$
that accelerates it. 
You will then consider the free body diagrams
of the cart and of the mass of the hanger separately, and calculate the 
theoretically expected values $\bf a_{th}$ and $\bf T_{th}$ of these 
quantities, then
compare them with your experimental results.
\vfill \eject

\begin{figure}[h] \hspace*{.65in}
\includegraphics[width=4.7in]{fmc4-2.eps} 
\caption{The apparatus}
\end{figure} 

\centerline{Fig~1}
%\vfill \eject
{\underbar {\bf YOU NEED TO KNOW}}
\tablist { 
The equations that describe the motion of an object that 
moves with {\bf{constant acceleration}} are: \nx
$v =v_0 + at$ \nx
Where $v_0$ is the velocity of the 
object at time $t=0$, and $a$ is the acceleration of the object
and is  the slope of the graph of velocity versus time. \nx
$x = x_0 + v_0t + {\half} a t^2$ \nx
$x_0$ indicates the position of the object at time $t=0$.
 & { THE EQUATIONS \nx OF MOTION}}
%\vfill \eject
\vskip 5pt
{\underbar {\bf TWO MORE THINGS YOU NEED TO KNOW}}
\tablist{ 
I)-Newton's third law implies that if a
string connects bodies A and B, then the force exerted on body A
is equal in magnitude and opposite in direction to the force 
exerted on body B. The magnitude of these forces is
called the tension of the string.& STRINGS}
%\vfill \eject
%\line{\hfill}
\begingroup
\epsfxsize=8cm
\epsfbox{fmc4-1.eps}
\endgroup
%\vskip -8cm
\centerline {$\abs{{\vec F_{BA}}} =\abs{\vec F_{AB}}$ }
\vskip 5pt
\centerline{Fig~2}
%\vfill \eject
\tablist{
II)-Newton's second law refers to the {\ub{\bf total}} {\ub{\bf net force}}
 applied 
on a body, one must therefore consider all the forces acting on {\bf{one}} body
without consideration of the other body. This is called the free 
body diagram. If there is more than one 
body, then each must be considered separately in turn. & 
FREE BODY DIAGRAMS}
\vfill \eject
{\underbar {\bf{THE EQUIPMENT}}}
\item {\Rightarrow } A Gateway Personal Computer  with monitor, keyboard and
mouse.
\item {\Rightarrow } A PASCO position sensor 
emits a series of short pulses of sound, and receives 
the echo of the
sound reflected by a nearby object. The length of the 
time interval between the emission
and the reception of the sound pulse depends on the distance to the reflecting
object. \nx
This method of locating an object is the same as the one used by bats to find
flying insects or by navy ships to locate submarines.
\item {\Rightarrow } A PASCO Signal Interface converts the time interval
between the emission and reception of the sound pulse to digital form 
(i.e. numbers that can be then plotted on the monitor.) \nx
\item {\Rightarrow } A PASCO dynamic track with magnetic bumpers and pulley
mounted on a labstand.
\item {\Rightarrow } A PASCO cart with reflecting vane and Force Sensor.
The Force Sensor produces a voltage proportional to the force applied on the
hook. The voltage is positive if the force is toward the sensor, negative if the
force is away from the sensor. 
\item {\Rightarrow } A set of masses, a mass hanger and a foam pad. \nx
Tape, rulers (1 m \& 2 m long) 
and a pan balance are available in the Laboratory.\nx
%\vfill \eject
\vskip 5pt
{\underbar {\bf{PRECAUTIONS}}}\nextline 
\item {\Rightarrow } Try and follow the instructions carefully. If you get
lost, go to the top right corner of the screen, and click on the Exit box 
($\times$) at the
right of the SCIENCE WORKSHOP header.
You should be back at the beginning of the exercise.  Call your instructor
 to start you off again if all else fails. \nx
\vfill \eject
\item {\Rightarrow } When the program asks whether you wish to SAVE, be sure {\bf{not to save}}; as 
this would change the program for the next user! \nx
\item {\Rightarrow } Always have the cart lying on its side 
when not on the track: otherwise it could
easily roll off the table and be damaged.  
 \vskip 5pt
\medskip
{\underbar {\bf{UNITS}} \nextline 
Distances are measured in {\bf{ meters}}. The symbol for this is $m$;
One meter is approximately 39 inches, a little longer than one yard. \nx
The rulers in the laboratory are divided in centimeters; one centimeter 
is one hundredth of a meter: $1 \ cm = 10^{-2} \ m$
\vskip 5pt
Velocities are measured in{\bf{ meters per second}} ($m/s$). \nx
Accelerations are measured in{\bf{ meters per second squared}} ($m/s^2$). \nx
Forces are measured in{\bf{ Newtons}} ($N$)

%\vfill \eject
{\underbar {\bf PROCEDURE I}\nx
\item{1.0} PRELIMINARY MEASUREMENTS  ( 30 min) 
\vskip 5pt
\tablist{
The readings provided by the force sensor do not usually correspond
to the forces applied to it when the setup is started initially.
 This must be checked and corrected: its readings 
must be set to the proper values.& TARE}
\item {1.0} CONDUCTING THE EXPERIMENT \nx
\qskip\item {1.1}  The PC, the monitor and the Pasco Signal Interface 
should be on. 
Check that these three pieces of equipment have their pilots lights indicating
this.
\vskip 15pt
\hrule
\vskip 5pt
\begingroup
\tenpoint
TARE from the arabic {\bf{tarhah}}: that which is thrown away. A 
deduction from gross weight, made to allow for the weight of
a container.
\endgroup
 \vfill \eject
\qskip\item {1.2}  The monitor screen should show various ``icons''.
DCLK on the ``PHYSICS 103'' icon, DCLK on the ``MECHANICS" folder, 
you should now see a frame with various icons. DCLK on NEWTON, 
\qskip\item {1.3} The monitor screen should now display a 
maximized setup window (shown in Fig~3) below, a table and a position 
vs. time graph (partially covered by the Setup Window)

%\vfill\vfill

\epsfxsize=6 truein
\epsfbox{fmc4-3.eps}
\centerline {Fig~3}
\item{1.4} Prepare a table like the one shown below.
\vskip 10pt
\centerline {TABLE I}
\vskip 5pt
\begintable
Mass of Cart $M_c$ (kg) \hfill |\hskip 4cm \cr
Total mass of hanger  and masses on hanger $M_h$ (kg) | \cr
Tension at rest $T_r$ (N) \hfill | \cr
$ \sin \Theta$ \hfill |  \cr 
$ \Theta$ \hfill |\endtable
\vfill \eject
\vskip 5pt
\item{1.5} Use the pan balance to weigh the cart 
(with vane and force sensor). Do not unplug the force sensor from the PASCO
interface: bring the balance to your experimental setup instead.\nx
 {\bf{ BE SURE}} {\bf{ TO PUT}} {\bf{ THE CART}}
{\bf{  ON THE}} {\bf{  PAN
ON ITS SIDE }} otherwise it will roll off and get damaged.  
Record the value $M_c$ of the mass of the cart.

\item{1.6} Set the cart with force sensor 
and vane on the track without any weight on the
force sensor hook. 

\item{1.7} Put the cart at the end of the track, against
the bumper. 
Make sure that the mass does not touch the force sensor hook. \nx
Make sure that the high end of the track is aproximately 20 cm above the table. 

\item{1.8} DCLK on the force sensor icon, labeled ``F'' in the
setup window. 

\item{1.9} Have your partner gently press the cart against the bumper.
Press firmly on the ``TARE'' button on the side of the force sensor.

\item{1.10} Check that the ``High Value'' is 0.00 and CLK on ``READ'' just to
the right of it. If the high value is not 0.00, CLK on the end of the value, 
erase using the leftarrow key $\leftarrow$ at the top of the keyboard, and enter
0.00, then CLK on ``READ''.

\item{1.11} Hook the string on the force sensor 
hook, over the pulley, and hang the mass
hanger on the string. A piece of tape on the string and mass holder hook will 
keep them from coming apart. 
Put a 500g mass on the track to prevent the cart from moving.

\item{1.12} Put 100g of mass on the 50g mass hanger. 
Put a piece of tape across the slot of the mass, it  will
keep it from falling off the mass hanger. Record 
the mass of 150 g in table I. Place the foam pad on the floor.
\vfill \eject 

\item{1.13} With the cart at rest, and held against the bumper by your
partner, type in -1.47.
for the ``Low Value'' and CLK on the READ 
just to the right of it. 
Make sure the cart was not jiggled while this was done.\nx
{\bf{NOTE}} The force sensor produces negative values if one pulls 
on the sensing hook, and positive values if one pushes. The tension
is a positive quantity nevertheless: disregard the sign!


\item{1.14} CLK on OK. 
The force sensor is now ready to provide the correct values of the forces. 

\item{1.15} Check that the force sensor records the proper value:
With 500 g mass still on the track, and the cart stationary DCLK
on RECORD. The values of the force on the table should read
approximately -1.47 \nx
If the force recorded on the table does not look sensible, 
you probably did not press the 
TARE button firmly, or you jiggled the cart while entering the lower and 
higher values. Try again! Record this value of $T_r$ in Table~I.

 \item{1.16} Measure the length of the track and the height above
the table of both ends of the track with the 
wooden ruler; {\bf {do this very accurately}}.  Calculate 
the the angle of inclination, and record $\Theta$ and $\sin \Theta$ in Table~I.
\vskip 5pt
\begingroup
\epsfxsize = 10cm
\epsfbox{fmc4-4.eps}
\endgroup
\vskip 5pt
\vskip 5pt
%\vfill \eject
{\underbar {\bf PROCEDURE II - THE INCLINED PLANE}}  ( 60 min) 
In this procedure you will observe and measure the motion of the cart, and the 
force that accelerates it.
\item{1.0} CONDUCTING THE EXPERIMENT
\item{1.1} CLK on the double ``RESIZE'' (2) button to make the 
experiment setup window small. 
\vfill \eject
\item {1.2} CLK on the Graph setup button (8), then CLK at the 
end of the header ``Velocity versus Time'' , 
type your name and that of your
lab partner , then CLK ``OK''. This will identify the printer output as 
belonging to you.
%\vfill \eject
\item {1.3} Prepare a table as shown.
\vskip 5pt
\centerline {Table~II}
\vskip 5pt
\begintable
EXPERIMENTAL | PREDICTED | \% DIFFERENCE \nr
\hskip 4cm   | \hskip 4cm   |\hskip 4cm   \crthick
$a_{ex}=$ \hfil | $a_{th}=$ \hfil | \cr
$T_{ex}=$ \hfil | $T_{th}=$ \hfil | \endtable
\item{1.4} Place the Motion Sensor about 8-10 cm above the table, 
approximately $40 \ cm$ from the end of the
track and aim it up toward the vane on the cart while it is on the track.
\item{1.5} Make sure the force sensor cable will not get caught 
or drag excessively when the cart moves. Check that the string does not
rub at the edge of the table and that  a bumper is firmly mounted near 
the top end of the track, just beyond the location the cart has at the 
instant the falling mass hits rge foam pad.
\item{1.6} Place the cart at the low end of the track. 
Make sure the experiment
control window titlebar is blue. (CLK on it if it is not.)
\item{1.7} One partner should release the cart; the other partner should CLK
on REC immediately after. 
Be very careful not to jiggle the cart as it is released. The data will
stop being taken automatically. Repeat three or four
more times. If the cart does not  accelerate when released, lower the track
slightly, and redetermine the angle of inclination before trying again.
\vskip 10pt
\item{2.0} ANALYSIS OF THE DATA \nx
\item{2.1} Choose the run (DCLK on RUN \# in the experiment 
control window) with the most
linear velocity vs. time graph. 
\vfill \eject
\item{2.2} 
With the
mouse CLK and draw a rectangle around the straight line. CLK on the statistics
button on the graph so that the statistics are shown. If a linear fit appears,
okay. If ``no statistics selected'' is shown, CLK on the statistic ($\Sigma$) 
button, select ``Curve Fit'', then ``Linear Fit''. 
The variables $a_1$ and $a_2$ correspond to $V_0$,the initial 
velocity, and $a$, acceleration. Record the acceleration  $\bf a_{ex}$ in
table II. 
%\vfill \eject
\item{2.3} CLK on ``file'' and 
``print active display'' to
print the graph 
\item{2.4}CLK on the head bar of the Force Table. Select the part of 
the data in the table that corresponds to the motion of the cart by dragging 
the cursor over it.
\item{2.5}  CLK on its statistic 
icon ($\Sigma$) of the force table, 
and record the mean value of the tension $\bf T_{ex} $ in table II
 \vskip 5pt
\item{3.0}CALCULATION OF THEORETICALLY 
EXPECTED VALUES \nx
\item{3.1} Draw the free body diagram for the hanger and mass. Write
the corresponding II Law equation.
\item{3.2} Draw the free body diagram for the cart. Write
the corresponding II Law equation.
\item{3.3} Solve the two simultaneous equations and 
calculate and record the theoretical acceleration $\bf a_{th}$ of the cart
the theoretical tension $\bf T_{th}$ of the string.
%\ciao
\item{4.0} QUESTIONS
\item{4.1} Explain why the tension at rest in Table~I is different from
the tension you measured while the cart was accelerating.
\item{4.2} What is the percentage difference between the measured and 
theoretical values of the acceleration?
\item{4.3} What is the percentage difference between the measured and theoretical
values of the tension?
\vfill \eject
\item{4.4} What are some possible reasons for these differences?
%\ciao
\vskip 5pt
NOTE: The percent difference between your experimental and calculated values
is $D = \abs{ 100 \times   (a_{ex} - a_{th})/ a_{th}}$
\ciao
\vfill \vfill
\begingroup{
\tenpoint
\hrule
\vskip 5pt
TARE, from arabic {\bf {tarhah}} that which is thrown away. \nx
A deduction from gross weight made to allow for the weight of a
container.
\ciao
\item{1.6} Set the cart with force sensor 
and vane on the track without any weight on the
force sensor hook. DCLK on the force sensor icon, labeled ``F'' in the
setup window. 
\item{1.7} Press the ``TARE'' button on the side of the force sensor.
Check that the ``High Value'' is 0.00 and CLK on ``READ'' just to
the right of it. If the high value is not 0.00, CLK on the end of the value, 
erase using the leftarrow key $\leftarrow$ at the top of the keyboard, and enter
0.00, then CLK on ``READ''.
\item{1.8} Put a 500g mass on the track to prevent the cart from moving. 
Hook the string on the force sensor 
hook, over the pulley, and hang the mass
hanger on the string. A piece of tape on the string and mass holder hook will 
keep them from coming apart. Be sure that the 500 g mass does not touch
the hook of the force sensor. 
\item{1.9} Put 200g of mass on the 50g mass hanger. 
Put a piece of tape across the slot of the mass, it  will
keep it from falling off the mass hanger. Record 
the mass of 250 g in table I. Place the foam pad on the floor.
\vfill \eject
\item{1.10} 
With the cart at rest , type in -2.45 
for the ''Low Value'' and CLK on the READ 
just to the right of it. CLK on OK. Record this value of $T_r$ in Table~I
The force sensor is now ready to provide the correct values of the forces. 

