v*",+o,,"\,4 4*
*\h
*.o,
ob:
tt
m]
4nu>\;*
Yr
t{
I
o
L
L
)
z l
h
,L
J
I
J
L+
o
b
I
4.o
Va.*,,'
tt>l
4t
tr'/c
o>r
r>
a1
h
r)
?
7
!
ah
)
,Ll
!k
b
2
)(
rr>4
)
,.0.
r 2
s. ,IU
[.
t2
Ow
Ot4^
)
r1
dn'^ . )o1
()
&
r..rn,
t
ot^
q
I
t
L
A
)o
(
az
\Irru +
r,^a)Fh
sl, Vt

,\
4/
Lab 5: Ballistic Pendulum
due at the beginning of Iab two weeks after data collection
will
strike the floor.
Objective
Use consen,ation of er.rergy and momentum to predict the location that a ball
Equipment
Ball + launcher, balance, ruler, I  and 2meter sticks, triangle, tape, paper, carbon paper, laptop.
Procedure
I
Detach the arm from the ballistic pendulum. Measure its mass. Measure the mass of the ball (the
projectiie).
2
ball in the arm. Find the location of the center of mass of the arm + ball by locating its
balance point. Mark this point with a small piece of tape, if necessary. (Later, we will leam that
we can calculate tire change in gravitational potential energy ofthe anl + ball by considering the
total mass of the arm + ball to be at the location of the center of mass.) Reattach the arm.
Place the
3
Obtain an expression for the initial velocity ofthe projectile that is fired into the ballistic
pendulum in terms of the change in height of the center of mass and other measured quantities.
Do this using conservation of momentum and energy. (Hints: Is momentum conserued during the
collision? Is energy conserved? ls momentum conserved during the swing of the pendulum? Is
energy consen/ed?) Present a derivation ofyour results.
4
Fire the ball into the arm eight times and measure the change in height of the center of mass of
the ann assembly each tirne. Calculate the initial velocity of the ball for each trial, and find the
average, maxirnurn and minimum of these velocities.
5
Measure the initial height of the ball above the floor. Calculate the time the ball will be in the air.
Using the average, maximum, and minimurn velocity and the initial height of the ball above
the floor, calculate the horizontal distance the ball will travel when fired horizontally from the top
of the lab table to the floor. The maximum and minimum velocities will yield maximum and
minimum distances traveled. The average velocity will yield a typical distance traveled.
6
Make a papercarbon paperpaper "sandwich" to measure the actual distance ffaveled by the ball.
Place the sandwich on the floor where you expect the ball to land. On the top sheet, draw and
label lines for the average, maximum and minimum distances.
Fire the ball at the paper eight times. Measure all eight distances and find the average,
maximum and minimum horizontal distances that the ball moves. Comment on any discrepancies
between your predictions and your observations.
Sample Data Tables
These are sample data tables for your final report. Do not take your data on this sheet.
0bserved
mu.:1,fr. fo (hcu)i
mhell:
I
I
. \.!,,v1
Calculated
(hcrrl)r
2t.Zta
) ,i.1.n t.bcn
Ahcu
Vball
Vavel
Observed
heieht:
Calculated
time:
drve!
d*!
dmin!
A full uncertainty analysis
is required
for this lab writeup. Be sure to think
about this while vou are taking data.
distance
duve!
dmax!
Vmu!
Vmin!
Observed
dmin!
Diablo Valley College
IMPORTRNT
Physics 130
Rodriguez
Fall2018
Guidelines for Lab Reports
(How to Get Full Credit on Lab Reports and Make Everybody Happy)
Summary
Keep it simple, but keep it complete. A short repofi that is well organized and contains all of the necessary
a higher score than one that is much longer that contains essentially the same information.
Make it easy to readdon't make the reader work harder than necessary to understand the results of your lab
information will get
Lab WriteUp Guidelines
Your lab reports should be short and to the point, and should address the most important aspects of the lab. You
must type your reports.
Every lab report should have the following sections, in order:
l. Lab partners' names in top righthand comer.
6.
7.
8.
9.
2. Title
3. Objective
4. Results Summary (include uncertainties)
5. Data Tables and Graphs
Discussion/Error Analysis
Conclusion (if not redundant)
Formulas and Sample Calculations
Original data sheets (pen only)
Section 4 should address only the content of Section 3. For example, in the first lab of Physics 130 you might be
measuring the acceleration due to gravity. Your results should be presented as in the following table.
g (m/s2)
fractional uncertainty (69/9)
t
0.09
9.3
0.8
Your goal is to measure a quantity as accurately as possible. However,
the true value of the measured quantity should lie within your error. These
two constraints work in opposite directions, and keep lab interesting. Note
that here I have reporled
value for g. A common error is to report
several values, each based on a different set ofdata.
ry
Section 5 should have all data presented neatly in tables. For Tables:
include units and uncertainties; include lines; don't break tables across
pages. For Graphs: label axes; include error bars, equations oftrendlines,
and R3 values; do not connect dots. Be sure that I know what I am looking
at when I read your reportif you need to be there to explain your report to
me, your report can be improved.
Section 6 should concentrate on major sources ofuncertainties (usually
instrument and use), and should explain how you arrived at the estimates of
uncertainties presented in the Results Summary. We will use a simple
method for propagating uncertainties. Usually, in the labs that you will do,
differences between careful (e.g., quadrature) and simple (e.g., MinAvlax)
propagation of uncertainties will be overwhelmed by instrument/use
uncertainties. Also, uncertainties can arise in two somewhat different ways:
(l) uncertainfy in measurement and (2) combining the results of several
trials. Be sure to distinguish between these two in your report, if relevant.
Section 8 should contain the derivation of each nontrivial formula you
used, as well as a numerical example of using every formula you used. This
allows me to, among other things, give partial credit for incorrectly
calculated uncertainties.
Section 9 must contain your original data sheets (ifapplicable). These
must be taken clearly and legibly by hand, in pen, and must be initialed by
the professor in lab on the date the data was taken.
Uncertainties Rules
1. Experimental uncertainties
must have one significant
figure.
2. the last significant figure
in
a measured quantity must
be of the same order of
magnitude (in the same
decimal position) as the
uncertainty in that quantity.
The Three Most
Common Reasons for
Lost Points
. Defective Results
Summary
o
.
BreakingUncertainties
Rules
No units
Diablo Valley College
IMPORTONT
Physics 130
Rodriguez
Fall2018
Uncertainty
measured value of x
:
xr.rt
*
fractional uncertainty
6x
:
6ry'xu",t
"How Do I Calculate 5x?"
Often one of the most important and most difficult things to do is to calculate 6x, the uncertainty in x, where x is a
directly measured quantity. Here are two methodsthe "Official" method and the "Fudge" methodthat are
acceptable in this class. In your lab reports, always be sure to indicate which you're using.
Utlicial Method
In the Official Method, we say that 5x: dxr + 6xu, where 6x is the "Total uncertainty," 5x1 is the "Instrument
uncertainty," and 6xu is the "Use uncertainty." You usually should address these while you are taking data.
:
6x
Total uncerlainty
6xr
Instrument uncertainty
6xu
Use uncertaintv
6xr + 6xu
Usually, half of the smallest division (or onethird, depending on your taste).
For a ruler, for example, this is often 0.5 mm.
Due to the User. Examples: Parallax in reading a ruler, not putting the ruler
exactly at the end of the object being measured, not holding the ruler parallel
to the object, unevenness ofend ofobject being measured, etc. etc. etc.
Determining 6x_is the step that often gives students the most trouble.
Fudge Method
In the Fudge Method, there must be several independent measurements of the same value. We choose the
minimum 5x such that some large percentage (say, 80%) of the data points lie within 6x of xu,".ur.. This is easiest to
understand by looking at some examples, such as those below.
7
7
4
6
6
Data
3
2
5
5
3
5
2
6
I
2
4
9
I
I
1
3
2
3
4
8
10
8
7
3
3
4
5
4
1
5
5
9
2
5
6
4
I
3
3
Average
Fudge 5x
2
2
Propagating Uncertainties or "How Do I Get 6Q from 6x, 6y, ...?"
How do you calculate the uncertainty in an indirectly measured quantity? You "propagate" the uncertainties in the
directly measured quantities. Three ways to propagate error are 1. Fudge (described above),2. Min/Max (described
below), 3. Quadrature (possibly described in earlier classes). You are welcome to use any of these three methods. In
your writeup, clearly indicate which method you use.
Max/Min Method: Imagine that we are trying to indirectly measure a quantity Q, which is related to two directly
measured quantities x and y. Data is taken in sets: (x + 6x, y 5y). We estimate the uncertainty 5Q (Q*  Q)/2,
where Q* is the maximum value of Q and Q is the minimum value of Q.
t
:
For example, if
x'tan(y)lz3,then
Q: x/y, then Q*: (x + 6x)/(y 6y) and Q: (x  6x)/(y + 6y). Another example: if Q:
Qr: (x + Ex)tan(y + 6y)l(z 6z)3 and Q  (x  6x)tan(y  6y)/(z + 6z)3
Note that this simply gives the uncertainty in Qfor each data sel. If several values of Q are averaged together to
produce one reported value, then there are (at least) two uncertainties in Q: the individual 5Q for each set, and the
spread of the Q values, often modeled by taking the standard deviation, o. If the number of data sets is small (less
than 4 or so), you should use the above method to estimate the final reported value of 6Q. If the number of data sets
is larger, you can use the standard deviation or a graphing/fifting method. In the latter cases, however, be sure to
report the individual 6Q in your lab report.
Purchase answer to see full
attachment