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 a water sensitive mat
Wayne
D. Peterson
Brigham Young University
Physics and Astronomy Department
C-135 ESC
Provo, Utah 84602
801 422 3144
wayne_peterson@byu.edu
Abstract
An
ÒAquadoodle Tangent Trajectory ApparatusÓ is made using a water sensitive mat
(called ÒaquadoodleÓ) made by Spin Master Ltd. A wet ball makes a circular path
when circulating around the inside of a cylinder placed on the mat. 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.
Construction of Apparatus:
Start with an 18 inch turntable which is commonly
called a Òlazy SusanÓ, a six inch plastic cylinder, a Spin Master ÒaquadoodleÓ
mat, and a ÒsquashÓ ball from a sporting- goods store. Peel the cover off of
the top of the turntable. Using a screwdriver, pry loose the fastener that
sticks up through the center of the turntable. Remove the ball bearing ring and
housing from underneath the turntable. Remove the glue that was left from peeling
off the top cover (the glue should come off by pushing the glue into a ball of
glue with your thumb or fingers). The top of the turntable has a raised rim on
its perimeter. The top of the turntable has a groove which separates the top
surface into an outer ring and a central island. The central circular island
will be covered with ÒaquadoodleÓ mat. Cut out a circular section of
ÒaquadoodleÓ mat that is a little bit larger than the central island.
1 sided glue method:
Mask the turntable so that only the central
island is showing. Coat the central island with a layer of Spray Glue. With the
Òwrite on sideÓ up, fold the ÒaquadoodleÓ mat slightly so that the middle of
the ÒaquadoodleÓ mat can be put down on the center of the island first. Flatten
the ÒaquadoodleÓ mat by pressing it down from the center to the outside. Trim
the excess mat with a razor blade so that the mat covers the top of the island
exactly.
2 sided glue method:
The procedure is the same as the one sided method
except the back side of the mat gets sprayed also.
The
cylinder used for this demonstration needs to be heavy so that it will stay in
place when its platform gets tipped back and forth. A PVC Bushing was chosen,
but another type cylinder might work just as well. The bottom end of the PVC
Bushing is the end without an inner rim. Sand the bottom end of the cylinder
with #60 grit sand paper. This roughens the bottom surface of the cylinder. The
rough surface provides enough contact friction between the cylinder and the mat
to keep it in place when tipped back and forth. A plastic jar filled with water
is used to wet the surface of the squash ball.
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:
Place the cylinder on the center of the
ÒaquadoodleÓ mat. Wet the entire surface of the squash ball. A squash ball is
used because it is somewhat hydrophilic. Place the ball on the inside of the
cylinder against the inside wall. Pick up the turntable. Tip it and move it in
a circular type motion to get the ball moving around the inside of the
cylinder. Keep the velocity of the ball low so that it does not ride up on the
cylinder wall. Set the turntable down on a flat surface. Lift the cylinder
straight up off of the surface, releasing the ball. The ball will trace a path
that is tangent to the circular path. The groove in the turntable helps to keep
the ball from coming back across the mat after it bumps the rim of the
turntable. To do the demonstration again, the warm air from a small hair dryer
could be used to erase the path of the ball.
Apparatus Photos:
ÒTangent PathÓ shown using the ÒAquadoodle Tangent Trajectory ApparatusÓ
Equipment and costs
required to construct the apparatus:
Description/
Item Source Part
Number Cost
____ ______ __________ ____
18 inch turntable Bed Bath and
Beyond Copco 14.99
(lazy Susan) (Orem,
Utah) Non-Skid
Turntable
2555-9524
Wilton
Industries, Inc
PVC cylinder Sprinkler
World 6
inch IPSxPIP
9.21
(Harward
Irrigation Bushing
431-060 ¼
Systems
Inc.
Springville,
Utah)
Aquadoodle Wall Toys R Us Spin
Master 14.98
Mat (Orem,
Utah)
Squash Ball Sports
Authority Prince
Sports Inc
2.99
Plastic Jar Maceys
(Grocery Store Western
Family Round
2.49
Provo,
Utah Servables
2 Cup
Spray Adhesive Lowes Dap
All-Purpose
7.02
(Orem, Utah) Spray
Glue
SprayÕNStick
Sand Paper Lowes 3M
Aluminum Oxide
2.27
(Orem,
Utah) #60
grit 9x11 5 pack
Razor Blades LoweÕs single
edge 10 pack
1.98
(Orem,
Utah) item
# 79621
Total $55.93