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 a
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
h
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
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 ensur
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 s
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
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
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 w
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 unc
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 i
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
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 (kineti
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
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 app
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 mea
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 calculate
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 a
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 p
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
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
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 measur
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
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 a
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
c
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