Wayne D. Peterson

Brigham Young University

 

C-135 ESC

Provo, UT  84602-4604

801-422-3144

wayne_peterson@byu.edu

 

 


Showing the Expanding Universe using a Mug Rack Expander

 

Abstract (50-75 words)

The expanding universe has been demonstrated using tennis balls connected to a bungee cord, marks on expanding latex strips, marks on expanding balloons, and balls on expanding springs. Using a Mug Rack Expander, students can visualize a reference point from which objects move away. The reference point can be made stationary with respect to the student or it can be shown moving with respect to the student.

Construction of Apparatus: 

Plastic Expander:

 

A Mug Rack Expander can be purchased off the shelf from stores. I found one made of wood at Kmart. I found another one made of plastic at Rite Aid. Home Products International Inc. apparently distributes the plastic expander to Rite Aid. I used the plastic one in the following way. Drill a hole at each central pivot point on the back side of the expander. Use either a number 29 drill bit or a 9/64 drill bit. Screw a spring doorstop into each hole. Push a 20D 4inch nail through the center of each Styrofoam ball. Do this by putting the Styrofoam ball on a semi rigid surface to avoid having part of the ball split off where the nail exits the ball. Four balls are used on the plastic expander. One of the balls is painted using special paint that will not dissolve Styrofoam. This colored ball can be used as a reference point. The particular spring doorstops I used have a hole in the end. Insert the nail tip into the hole. Each ball should fit snugly against the ends of the spring doorstops.

 

Aluminum Expander:

 

A more substantial many ball expander can be made from flat aluminum pieces and aluminum rods. For a five ball system, use twelve long flat pieces (length=12 inches, width= .75 (3/4) inches, thickness= .125(1/8) inches) and eight short flat pieces (length= 6.5 inches, width= .75(3/4) inches, thickness= .125(1/8) inches). Drill 5/16 inch diameter holes .5 inches away from each end of all the flat pieces. Center these holes along the width. Also drill 5/16 inch diameter holes in the center of the long flat pieces (centered along the length and width). Sand or file the ends of all the flat pieces so that they are rounded.

 Make eight small diameter aluminum rods (length= 5 inches, diameter= .5(1/2) inches). Make five large diameter aluminum rods (length= 5 inches, diameter= .75(3/4) inches). Drill and tap the ends of the rods so that a half inch 8-32 bolt will fit into the ends. Lathe the ends of the rods so that the diameter at the ends is just under 5/16 of an inch (.3035 inches) and the lathed part is .2813(9/32) inches long.

 Make a Òdoorstop/nylon-spacer pieceÓ in the following way. Thread the hole in the nylon spacer using an 8-32 tap. Screw a spring doorstop into one end of the nylon spacer. Screw an 8-32 x 1 inch bolt into the other end. Now place the head of the bolt into a vise. Tighten the vise so that the head is held in a stationary position. Cut the head of the bolt off using a hacksaw. Grind or file the cut end so it is flat. Grind or file that same end so it is slightly tapered. Prepare five doorstops attached to nylon spacers as explained above.

Assemble the prepared pieces. Place small strips of tape (that can be removed later) on four of the shorter flat pieces. Place small strips of tape (that can be removed later) on six of the longer flat pieces. Set the larger diameter rods in one place and the smaller diameter rods in another.

 Insert the end of a large diameter rod into the Òcenter holesÓ of two of the longer flat pieces. Two long flat pieces fit over each end of the rod. The ÒtapedÓ flat piece goes on the end of the rod first. The Ònon-tapedÓ flat piece goes on second. Secure the flat pieces to one end of a rod with an 8-32 x ½ inch bolt and a washer. Put a washer onto the threaded part of a doorstop/nylon-spacer piece. Screw this piece into the other end of the large diameter rod. This will secure the flat pieces on that end of the rod. You will need to repeat this process with two more, large diameter rods (remember that the ÒtapedÓ flat piece goes on the rod end before the Ònon-tapedÓ flat piece).

 Now insert the end of a large diameter rod into the ÒendÓ holes of two short flat pieces. Two short flat pieces fit over each end of each rod. The ÒtapedÓ flat piece goes on the end of the rod first. The Ònon-tapedÓ flat piece goes on second. Secure the two flat pieces to one end of a rod with an 8-32 x ½ inch bolt and a washer. Put a washer onto the threaded part of a doorstop/nylon-spacer piece. Screw this piece into the other end of the large diameter rod. This will secure the flat pieces on that end of the rod. You will need to repeat this process with one more, large diameter rod.

 You now have five sections, three sections with long flat pieces and two sections with short flat pieces. Take one of the sections having long flat pieces. Spread the flat pieces apart with the Òdoorstop/nylon-spacer piecesÓ up. This section should now be able to stand up on itÕs own without falling over. Make a row using the sections having long pieces. Take one of the sections having short flat pieces. Rotate the short pieces to one side so that it will stand on its own. Do the same with the other section having short flat pieces. Place one of these sections on each end of the row. Now connect each section to the one next to it by inserting the small diameter rods. The flat end pieces go onto the rods in pairs. A ÒtapedÓ flat end piece goes on first. A Ònon-tapedÓ flat end piece goes on second. The flat pieces might have to be rotated around to get each matched pair for each rod end. Secure each pair of flat pieces to each end of a rod using an 8-32 x ½ inch bolt and a washer. The assembly is done except for the balls.

Begin preparing the balls by pushing a 20D 4inch nail through the center of each Styrofoam ball (five balls are used on this expander). Do this by putting the Styrofoam ball on a semi rigid surface to avoid having part of the ball split off where the nail exits the ball. One of the balls is painted using special paint that will not dissolve Styrofoam. This colored ball can be used as a reference point. The particular spring doorstops I used have a hole in the end. Insert the nail tip into the hole. Each ball should fit snugly against the ends of the spring doorstops.

Use of Apparatus: 

The characteristic frequencies in the light (light spectra) from distant galaxies are lower than normal. This is called Òred shiftÓ. The red shift could mean that galaxies are receding from the earth and from each other. This concept can be shown in two ways using the expander. First, a student might imagine looking into the night sky and seeing objects moving away from him. To show this with the expander model, the instructor holds the blue colored ball stationary with respect to himself using one hand. The other hand moves the expander. The other balls are seen to be moving away from the blue colored ball. Second, a student might imagine himself looking into the night sky from an object in space other than the earth. He would see the earth moving away from him and at the same time objects would be moving away from the earth by the same distance. The blue ball is placed in a position somewhere other than at the end of the expander. Using one hand, the instructor holds one end of the expander stationary with respect to himself. Using his other hand, the instructor moves the expander. The balls surrounding the blue ball are seen to moving apart equally.  

 

Apparatus Photos:

 

 

Plastic Expander – used to demonstrate the expansion of the universe

 

 

 

Aluminum Expander– used to demonstrate the expansion of the universe

 

Equipment and costs required to construct apparatus:

Item

Source

Part number

Cost

Alloy 6061 aluminum rod (1/2Ó dia. 6Õ length)

McMaster Carr (www.mcmaster.com)

8974K33

12.11 ( used 8,

            5.25 inch

             pieces)

Alloy 6061 aluminum rod (3/4Ó dia. 3Õ length)

 

McMaster Carr (www.mcmaster.com)

8974K11

 

 

 

11.58 ( used 5,

            5.25 inch

             pieces)

Flat aluminum (1/8Óx3/4Óx72Ó)

 

 

 

 

Machine screws(bolts) 8-32 x 1Ó

 

 

Machine screws(bolts) 8-32 x1/2Ó

 

 

Washers #8

 

 

 

Nylon Spacers

 

 

Spring doorstop

 

 

 

Styrofoam ball

 

 

 

Nails

 

 

 

Blue paint

 

CAL Ranch (Spanish Fork, Utah) (distributed by National)

 

 

 

Home Depot (Orem, Utah)

 

 

Home Depot (Orem, Utah)

 

 

Home Depot (Orem, Utah)

 

 

CAL Ranch (Spanish Fork, Utah)

 

Home Depot (Orem, Utah)(www.stanleyworks.com)

 

Wal Mart (Orem, Utah)

(www.styrofoamcrafts.com)

 

Home Depot (Orem, Utah)(Primesource Building Products, Inc.)

 

JO-ANN Fabrics and Crafts (Orem, Utah)

(www.floracraft.com)

1/8Óx3/4Óx72Ó

 

 

 

 

 

8-32 x 1Ó

 

 

 

8-32 x1/2Ó

 

 

 

#8

 

 

 

3/8Ó OD x .141Ó ID x 1Ó

 

 

Stanley DP57-1020

 

 

 

2.5 inch

 

 

 

Grip Rite 20d 4ÕÕ

 

 

 

Smooth Finish SFP4BL

17.37 ( used 12,

             12 inch

             pieces and

              8, 6 inch

              pieces)

 

   .88 ( 8 items/pkg,

            6 items used)

 

 

 1.76 ( 2 pkg,

            8 items/pkg,

            16 items used)

 

 2.64 ( 3 pkg,

           12 items/pkg,

            26 items used)

 

  1.15 ( 5 items used,

            .23 each)

 

  3.45 (5 items)

 

 

 

2.97 (6 items/pkg

           5 used)

 

 

2.23 (1 lb box

            4 nails used)

 

 

3.49 (4 oz.

             ? used)

 

Total Cost   59.63