EXPERIMENT 9. CONSERVATION OF LINEAR MOMENTUM
3. Calibrate the scale of the video using the image of the meter stick by clicking the Set
Scale button and drawing a line the length of the meter stick and entering 1 m for
the line length.
4. Position the pl
EXPERIMENT 10. BALLISTIC PENDULUM
2. Consider the bob of a pendulum of mass m moving at speed vr at the bottom of the
arc of the pendulums motion. Using conservation of energy, nd the maximum height
hmax that the pendulum bob will swing to.
3. For a pendu
Experiment 2
Measurement and Precision
Objective
To determine the value of from the ratio of the circumference to the diameter of a circle
while properly accounting for uncertainty.
Theory
It has been known since ancient times that the ratio of the circum
EXPERIMENT 10. BALLISTIC PENDULUM
move the angle pointer to 0 . While holding the base rmly against the table re the
cannon by pulling up on the trigger. Observe carefully the angle indicator to ensure
that it stays at the maximum angle (if it slides back
EXPERIMENT 2. MEASUREMENT AND PRECISION
your measured value as x0 x where x0 is the average value from your measurements and
x is called the uncertainty and is half the deviation from the largest to smallest measured
values.
Note that the number of signic
EXPERIMENT 10. BALLISTIC PENDULUM
paper. Repeat 10 times. If you have properly calculated your uncertainty 7 out of the
10 trials should hit between the lines.
Figure 10.2: Projectile motion from the cannon
7. Does the value of the range calculated using
EXPERIMENT 2. MEASUREMENT AND PRECISION
1. If the length of the paper is measured twice using a ruler marked with 1mm increments,
and the measurements give values of l=298 mm and l=294 mm, what value should be
used for l? for l? Express your answer in the
EXPERIMENT 2. MEASUREMENT AND PRECISION
Figure 2.1: Example of correlated and uncorrelated measurements
The randomness of the values of the dice ensure that, on average, the spread in values you
get with multiple rolls is less than when you only roll once
EXPERIMENT 2. MEASUREMENT AND PRECISION
be careful not to quote more than the appropriate number of signicant gures in your
value of and to include the uncertainty in your result. To calculate the uncertainty
in c/d given your measured uncertainties in c
EXPERIMENT 2. MEASUREMENT AND PRECISION
If the function g (a, b, . . .) = a b . . . or g (a, b, . . .) = a/b . . . is the product or quotient of
two or more quantities the resulting uncertainty in g is found from
dg
ga =
a
da
dg
b
gb =
db
dg
where for g (
EXPERIMENT 2. MEASUREMENT AND PRECISION
In the rst row in the example data table the calculated value of is 3.17 0.08 meaning,
within the experimental uncertainty a value as low as 3.09 or as high as 3.25 would be consistent with our measurement, therefor
EXPERIMENT 10. BALLISTIC PENDULUM
before the collision with the velocity of ball plus pendulum after the collision, according to
mb v0 = (mb + mp )vr
Conservation of energy relates the initial (kinetic) energy of the pendulum to its nal (potential) energy
EXPERIMENT 1. STATISTICS
equal. The uncertainty in a measured value is not determined by how close the
measurement is to some expected value.
Figure 1.2: Histogram showing the distribution of ages for students in a class
Often we have to calculate a quant
EXPERIMENT 9. CONSERVATION OF LINEAR MOMENTUM
2. Record the time of collision as a parameter. Select User parameters. . . from the
Data menu, and add a parameter t0 for this quantity, giving it an appropriate name
and recording the numerical value. While
EXPERIMENT 1. STATISTICS
Figure 1.3: Graphical representation of how uncertainty in x aects uncertainty in f (x)
Frequently we wish to measure the same quantity in two dierent ways to validate our measurements, or we wish to compare our measured values to
EXPERIMENT 9. CONSERVATION OF LINEAR MOMENTUM
7. Add a calculated column for the magnitude of total momentum
ptot =
p2 + p2
x
y
where you use the appropriate columns for px and py .
8. Add a calculated column for the angle of total momentum
tot = tan1
py
EXPERIMENT 1. STATISTICS
Figure 1.4: The measured heights of Alice and Bob have ranges that overlap
Practice
Please complete the following questions before beginning the lab.
1. You drop 10 quarters and 10 nickels onto the oor and count the number of each
EXPERIMENT 9. CONSERVATION OF LINEAR MOMENTUM
5. Compare your initial and nal momentum (magnitude and angle) for both collisions.
Was momentum conserved?
6. Compare your initial and nal energy. What percent of the initial energy was lost
in the collision
EXPERIMENT 1. STATISTICS
(a) Based on these histograms, how many times did 3 quarters land heads up?
(b) Based on these measurements do nickels and quarters have the same probability
of landing heads up?
2. Consider the expression for the height of an obj
EXPERIMENT 1. STATISTICS
Analysis
1. Think about the uncertainty in your measurement of distance the ruler has fallen after catching it are you measuring to the top of your ngers, the bottom? How well
do you know the original position of the ruler?. Deter
Experiment 10
Ballistic Pendulum
Objective
To use a ballistic pendulum to determine the velocity of a projectile. To verify this velocity
by measuring the range of the projectile.
Theory
We use measurements obtained from a ballistic pendulum to review ene
EXPERIMENT 1. STATISTICS
Report
In addition to the standard elements of a well written lab report described in the introduction
to this manual, your report must include
1. An appropriate title
2. The objective of the lab
3. A description of the experiment
Experiment 11
Rotational Dynamics
Objective
To investigate the relationship between torque and angular acceleration and to verify the
work-energy theorem for rotational motion.
Theory
The rotational analogue to F = ma is = I where is torque, I is the mome
EXPERIMENT 12. ANGULAR MOMENTUM
4. Spin the aluminum bar that is attached to the rotation sensor at a speed of a few
on the data logger to begin
radians per second, once it is spinning freely, press
collecting rotation data. Hold the second aluminum bar a
EXPERIMENT 12. ANGULAR MOMENTUM
2. Change the label on the velocity column to Angular velocity of bar 1 or similar.
Plot this versus time.
3. Identify the time in the middle of the interval over which the angular collision occurred.
There should be a rapi
PHY2048L
Spring Semester 2016
Instructor: Anupama Yadav
E-mail: yadav.anupama@knights.ucf.edu
Office Hours: Monday 9 am to 12 pm
Grading
For each experiment (each week):
Grading will be based on assignments provided and submitted through the Webassign int