Kinematics in 2-Dimensions

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© 2004 Penn State University

Physics 211R: Lab


Kinematics in 2
-
Dimensions

EC Physics








Name __________________

Kinematics in 2
-
Dimensions

Projectile Motion



A medieval trebuchet by Kolderer, c1507

http://members.iinet.net.au/~rmine/ht/ht02.html#5


Reading Assignment:

Chapter 7, Sections 7
-
2 and library and Internet resear
ch


Introduction:

In medieval days, people had a very practical knowledge of projectile motion. They may not have understood the
exact trajectory that a projectile would take, but by practice they could place a projectile on a target consistently
from a d
istance of well over 200 yards. During a long siege of a castle, it was not uncommon to hurl bodies of
animals (and yes, captives) back into the besieged castle’s water supply (an early form of biological warfare).
Similarly, a modern day hunter does not

need to know the actual path that a bullet takes to a target in order to hit the
target. A sharpshooter, however, does know the path and can make adjustments in the aiming in order to hit a target
at many different ranges. In this lab, you will become a
sharpshoot
er of sorts. You will determine the launcher
angle that gives the best distance for the projectile.


Neglecting frictional forces, such as air resistance, an object projected from a launcher undergoes a motion that is
the simple vector combinati
on of uniform velocity in the horizontal direction and uniform acceleration in the vertical
direction. For a pr
ojectile launched
it can be shown that the trajectory caused by such a combination predicts a
paraboli
c shape.


Goals:



Predict the range of a pr
ojectile.



Determine which launcher angle gives the greatest range.


Equipment

List
:

p
rojectile
l
auncher

s
teel projectile

m
eter
s
tick or
t
ape
m
easure

ring stand

test tube clamp

protractor


Lab Activity 1: Determining Launch Velocity (Tabletop to tabletop
launch)


1.

Set up a projectile laun
cher at an angle of 2
0
o
using a ring stand and test tube clamp.

The launcher should be
adjusted so that it
projects the projectile onto another

tabletop. The angle that you set,



is measured with the
bottom clip even with the edge of the tabletop
.
DO NOT

point your launcher in the direction of the
computer monitors!

© 2004 Penn State University

Physics 211R: Lab


Kinematics in 2
-
Dimensions




2.

Prepare the launcher by
depressing the
internal spring with the wooden rod and
inserting the
ring
pin throug
h the holes in
the side of the launcher and through the slot
in the wooden rod.

3.

Carefully measure the angle.

4.

Place a steel projectile in the launch tube.

5.

Fire the

launcher and have another person

note the approximate position that the
projectile strikes th
e table.

You will need to
do the same for their launcher.

Tape a piece
of paper to the tabletop and place a sheet of
carbon paper (carbon side down) on top of
the taped paper. It is not necessary to tape
the carbon paper to the table.



6.

Fire the laun
cher several times to obtain an average landing position. Estimate the center position of your
pattern and measure the horizontal distance from this point to a point directly below the launching position of
the projectile. This is the horizontal range,
x
.


7.

Repeat with varying values of angles between 20
o

and 70
o

(be sure to include a data point for 45
o
)

Record the
angles and ranges in your data table.



Launch Angle (degrees)

Range (meters)




































8.

Using Grap
hical Analysis
, make a graph of
Range vs. Angle
.


9.

Based upon your graph,
what angle
does the ma
ximum range occur at?


10.

From your graph, generate an
estimated

list of
pairs of angle measures that yield the same range values? Is each
pair a set of complemen
tary angles? Explain.