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 “Tangent Trajectory Apparatus” 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 Newton’s 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 “lazy 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 “Tangent Trajectory Apparatus”. 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 “Tangent Trajectory Apparatus” 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:

 

“Tangent Trajectory Apparatus”

 

“Tangent Trajectory Apparatus” on the overhead projector

 

“Tangent Path” 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