PROJECTILE MOTION
GOAL
To determine the initial velocity of a sphere fired from spring “gun”, based on the
measurements of horizontal and vertical displacements of the sphere.
PREREQUISITES
College Physics, Serway and Vuille
, chapter 4
.
EQUIPMENT
Ballistic Pendulum Set
Meter Stick
Ruler
THEORY
The spring gun from the ballistic pendulum set hu
rls a sphere in a
horizontal direction. After release the sphere exhibits what we call
projectile motion
. It
moves in two dimensions under the influence of only the gravitational force. The force of
gravity points down and is responsible for the vertical a
cceleration of the sphere
a
y
=g=9.8 m/s
2
.
Thus, we have the free

fall motion in the vertical direction. At the same
time there are no forces acting on the sphere in the horizontal direction
a
x
=0
and the
sphere moves uniformly with the same initial velocity
v
i
, supplied by the spring gun.
Note, that we can neglect the influence of air resistance due to relatively small initial
velocity of the sphere and relatively small traveled distances.
You have to measure the horizontal displacement of the sphere
R
–
the horizontal
distance between the point at which sphere lost the contact with spring and the point
where sphere hit the floor
R=v
i
∙t,
where
t
is the elapsed time. To determine the point at which sphere hit the floor it is
handy to use clean sheet of p
aper. The sphere leaves a noticeable trace on the paper
which allows you not only to determine the final point of travel but gives you possibility
to estimate the accuracy of your measurements.
The time of flight
t
is governed by another quantity you hav
e to measure
–
the
vertical displacement of the sphere
H
H=½gt
2
.
H
has to be measured as a vertical distance between the point of release and the point
where the sphere hit the floor. Think about this distance carefully
–
you have to
determine which point of the sphere you have to follow to take into account the final si
ze
of the sphere correctly.
It can be shown from kinematic equations that
the initial velocity
v
i
is given by:
PROCEDURE
Position the assembled ballistic pendulum at the edge of a table or lab
bench.
CAUTION: Use care when operating this device. Do not stand or place hands
or any part of your body in the path of the projectile.
Fire the sphere
out onto a clear area
on the floor to determine approximately
where it will fall. Put a clear sheet of paper
on the determined place.
Fire the sphere again and measure its horizontal and vertical displacements.
CAUTION: Use care when operating this device. Do not stand or place hands or any
part of your body in the path of the projectile once the mechanism is a
rmed.
Repeat the measurements at least five times recording the results in the table
together with relevant errors of measurements.
R
H
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Average value
ANALYSIS
1.
Calculate the average values for both measured quantities.
2.
Use averages to find the value of initial velocity.
3.
Using the data from your table try to estimate the accuracy with which
you have found initial velocity of the sphere.
Use average, min and max
t
o specify the experimental error.
LAB REPORT
1.
Write your name and list names of all your partners.
2.
Write the date of experiment.
3.
Write the title, goal, and list of equipment of the experiment.
4.
Supply the table with your results.
5.
Give the derivation of the
working formula and your calculations of the
sphere’s initial velocity.
6.
Examine the possible sources of errors in measurements. Identify where
the largest errors come from. Write a small (a few statements) essay.
7.
Estimate (on the physical level) how error
s of measurements are
transformed in the error of calculation of sphere’s initial velocity.
8.
Show how the equation
is derived from the basic Galilean
kinematics equations.
Ed. 1/2012 D. Boucher
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