Apparatus Competition
2008 AAPT Summer Meeting
Edmonton, Alberta
Showing the Tangent Trajectory of a Ball coming from
Circular Motion when the Centripetal Force on the Ball is Suddenly Reduced to
Zero- using an overhead projector and alcohol/water sensitive translucent
plastic
Wayne
D. Peterson
Brigham Young University
Physics and Astronomy Department
C-135 ESC
Provo, Utah 84602
801 422 3144
wayne_peterson@byu.edu
Abstract
A
ÒTangent Trajectory ApparatusÓ is made using translucent plastic. The overhead projector
image of translucent vinyl or translucent mylar is dark. Light gets through
this dark image if common household isopropyl alcohol 70% or water is placed on
the plastic. A wet ball makes a circular path when circulating around the
inside of a cylinder placed on the plastic. If the cylinder is removed, the
ball leaves a straight line path that is tangent to the circular path. This
demonstration can be used as an example of how NewtonÕs laws apply to circular
motion. An advantage of this demonstration is that it can be seen in a large
classroom or auditorium. Another advantage is that with a simple wipe of a
paper towel it can be repeated immediately.
Construction of Apparatus:
Construction note: Translucent mylar drafting
film (used for technical drawing) can be used in place of the translucent vinyl
called out in these instructions. The advantage of translucent mylar is that plain
water (no alcohol) can be used with it. The advantage of translucent vinyl is
that it seems to be more readily available than the mylar drafting film.
Start with two 18 inch turntables which are
commonly called Òlazy Susans, two sheets (20x32 inches and 18x24 inches) of
transparent acrylic plastic, a sheet (12x12 inches) of translucent vinyl
plastic, and some thin type double stick tape. Peel off the covers that are
glued to the top surface of the turntables. Using a screwdriver, pry loose the
fastener that sticks up through the center of the turntables. Remove the ball
bearing rings and housings from underneath the turntables. Save one of the ball
bearing rings for later. The top of the turntable has a raised rim on its
perimeter. The top surface of the turntable has a groove which separates the
top surface into an outer ring and a central island. A jigsaw can be used to cut
an 11 inch diameter hole in the central island of one of the turntables. Cut a
16 and 7/8 inch hole in the other turntable which leaves the rim portion only.
Place the rim on top of the other turntable and press it down into place. Cut
out a 16 and 7/8 inch diameter transparent acrylic disk from the 20x32 inch
sheet (leaving enough sheet left over to cut out another disk 12 inches in
diameter). This 16 and 7/8 inch diameter acrylic disk is placed inside the
turntable and covers the 11 inch hole. Cut out two transparent acrylic disks
and one translucent vinyl disk. The transparent disks should be 15 and 1/4 inches
in diameter (cut from the 18x24 inch sheet) and 12 inches in diameter (cut from
the 20x32 inch sheet). The translucent vinyl disk can be cut with scissors and
should be 12 inches in diameter. These three disks are assembled together like
a sandwich. Put double stick tape in two or three places near the edge of the transparent
12 inch acrylic disk. Place the transparent 12 inch acrylic disk on top and in
the center of the transparent 15 and 1/2 inch diameter acrylic disk (the double
stick tape will hold the disks together). Now use double stick tape to attach
the translucent vinyl disk on top of and in the center of the 12 inch acrylic disk.
It is important that the bumpy side of the translucent plastic be down and the
less bumpy side be up (If mylar drafting film is used instead of the
translucent vinyl, the smooth shiny side of the mylar should be down and the
non-reflective side be up.) Center the ball bearing ring on the turntable.
Center the three disk sandwich on top of the ball bearing ring. This completes
the main portion of the ÒTangent Trajectory ApparatusÓ. Take a 6 inch diameter
food storage container and draw a mark around it 2 inches down from the top.
Tin snips or heavy duty scissors can be used to cut off the bottom portion of
the container. Discard the bottom portion and keep the top cylindrical part. A
squash ball rides inside this top cylindrical portion. The squash ball is made
wet by dipping it into a 5 inch diameter food storage container containing
isopropyl alcohol. A squash ball is used because it is somewhat hydrophilic.
Use of Apparatus:
Suppose a ball is in uniform circular motion. If
the centripetal force is suddenly reduced to zero, what will be the motion of
the ball? Some students might think it will exit the circle in a radial
direction. Others might think it will spiral away from the center of the
circle.
Physics:
For an object in uniform circular motion, the
velocity vector is always tangent to the circular path of the object. The
direction of the velocity changes so there is a force on the object called
centripetal force. The centripetal force is the only force acting upon the
object. This force only changes the direction of the velocity of the object.
Assuming no friction, no force is needed to keep the object moving. Therefore
if the centripetal force suddenly becomes zero, the direction of the velocity
does not change any more. The object then moves in the direction that the
velocity vector was pointing when the centripetal force became zero. Its path
is straight and is tangent to the circular path.
Procedure:
Center the ÒTangent Trajectory ApparatusÓ on an
overhead projector. Pour some isopropyl alcohol 70% into a container (5 inch
food storage container). Place the cylinder in the center of the translucent
plastic. Put the dry squash ball in the cylinder. Focus the overhead projector
on the ball. Using your left hand hold the cylinder in place. Place the ball
against the inside wall of the cylinder. Using a quick movement, push the ball
with your fingers so that the ball moves in a circle around the inside wall. Move
the cylinder and disks back and forth in a rocking motion to increase the
rotation of the ball. This will show the students that the ball moves in a
circle. Now wet the entire surface of the squash ball by dipping it into the
container of alcohol. Place the ball on the inside of the cylinder against the
inside wall. Get the ball moving with a rocking motion as described above. Keep
the velocity of the ball low so that it does not ride up on the cylinder wall.
The ball should be in uniform circular motion when you stop the rocking motion.
At this time remove the cylinder straight up off of the surface of the
translucent plastic. The ball will trace a path that is tangent to the circular
path. The rim of the turntable contains the ball and the edge of the 12 inch
acrylic disk keeps the ball from coming back across the translucent plastic. To
do the demonstration again, a paper towel can be used to erase the path of the
ball.
Apparatus Photos:
ÒTangent Trajectory ApparatusÓ
ÒTangent Trajectory ApparatusÓ on the overhead projector
ÒTangent PathÓ taken by the ball when the centripetal force is zero
Equipment and costs
required to construct the apparatus:
Description/
Item Source Part
Number Cost
____ ______ __________ ____
Two
18 inch turntables Bed Bath and Beyond Copco
29.98
(lazy Susan) (Orem,
Utah) Non-Skid
Turntable (14.99 each)
2555-9524
Wilton
Industries, Inc
Transparent acrylic The Home Depot .093-18x24
inches
5.97
sheet (Provo,
Utah) Optix
by Plaskolite
(cut
a 15 and 1/4
inch diameter disk
from this)
Transparent acrylic The Home Depot .093-20x32
inches
8.49
sheet (Provo,
Utah) Optix
by Plaskolite
(cut
a 16 and 7/8
inch and a 12 inch
diameter disk from this)
Translucent vinyl Roberts Craft Store 12x12
inches quilt
4.59
sheet (Orem,
Utah) pattern
template
For
a store locator go to Collins
brand
www.dritz.com/retailers/ Item # C98
Barcode # 033262100980
(3
sheets per package
only 1 used)
(alternate water
sensitive translucent plastic:
Translucent Mylar BYU Bookstore 18x24
inch Mylar
1.35
Drafting Film (Provo,
Utah) plain
sheet (purchased
(no
longer available several
years
at
the bookstore, ago)
possible
other source
is
Utrecht.com
Item
# 20402 or 20400)
Double-stick tape Maceys (Grocery Store Scotch
3.89
Provo,
Utah)
Plastic Jar Maceys
(Grocery Store Western
Family Round
3.69
Provo,
Utah) Servables
4.2 cup
6
inch diameter
Plastic Jar Maceys
(Grocery Store Western
Family Round
2.49
Provo,
Utah) Servables
2 Cup
Approx.
5 inch diameter
Squash Ball Sports
Authority Prince
Sports Inc
2.99
(Orem,
Utah)
Isopropyl Alcohol Maceys (Grocery Store Western
Family
1.16
70% Provo,
Utah)
Total $63.25