Energy is conserved. An object has potential energy because it is a certain distance above the ground. As it rolls down an incline, some of its energy changes into kinetic energy
What You Need
- aluminum track used to secure shelving in bookcases. This is the type hung vertically on the sides of the bookshelf and holds clips that support the shelves. This track should be flexible enough so you can bend it to form a circular shape. (You don't want the heavy duty shelving tracks you would use to set up a bookshelf to hold all your physics textbooks.)
- 1 marble or steel ball that smoothly rolls in the track
- circular object to use a guide, such as a small bucket or a one gallon paint can
- frame to mount the frame on
- incline (2 feet long × 3 inches wide × ¾ inch thick will do fine)
- bottom 3 feet × 3 inches × ¾ inches
- vertical brace 1 foot × 3 inches × ¾ inch
- small right-angle bracket to support the vertical brace
- you may want to add some kind of net to catch the marble at the end, so you don't have to chase it every time
- small flat-head wood screws—the smaller the better, but just larger than the screw holes in the track
- a meterstick
This apparatus is also commercially available, as shown in Figure 63-2.
Building the track
- Assemble the frame by attaching the pieces of wood, as shown.
- Form a circular loop by carefully bending the track around the form. Note, the channel should be toward the inside of the circle when you do this.
- Predrill holes for the wood screws in the wood using a drill bit a size or two smaller than your screws.
- Secure the loop to the frame using the wood screws. It is important that the (flat) heads of the woods screws do not interfere with the motion of the ball. If you find your wood screw protrudes into the path of the marble, you can work around this by enlarging the holes or by countersinking the holes in the track, so the screw head is flush with the bottom of the track.
- Align the track as shown in Figure 63-1. The loop should be as symmetrical as possible with the overall path making a vertical loop. Also, make enough separation between the part of the track going into and out of the loop, so there is enough clearance between the marble and the track.
- You can (optionally) attach some kind of catcher (a net or cup) to avoid chasing marbles.
- Take a guess as to where the marble must be placed to negotiate the loop. Here are some choices: a) equal to the radius, b) equal to the diameter, c) greater than the diameter, or d) twice the diameter. (Take into account there will be some friction.)
- Pick your starting point and observe what happens. Find the minimum point to consistently negotiate one loop. What happens to the marble if you release it at a point that is higher or lower than this minimum point? See Figure 63-1.
With a low-friction sliding object car, such as a cart with wheels or a roller coaster car, the height must be at least 2.5 times the radius of the loop. Actual loops require slightly greater height to overcome friction.
For rolling objects, such as a steel ball or marble, some of the potential energy is tied up in rolling, so the height must be at least 2.7 times the radius of the loop (again, without accounting for frictional losses).
Why It Works
The potential energy you start with (by raising it to certain height on the track) is changed into kinetic energy. The higher your release point, the faster it goes. If the object is rolling rather than sliding, some of the potential energy is used to get the object rolling. If there is friction along the way, some additional potential energy is consumed.
To negotiate the loop, the centripetal force (provided by the track to maintain a circular path) must just equal the force of gravity. With less velocity, it will fall before completing the loop. With extra velocity, it will get through with some energy to spare.
Other Things to Try
Now that you have one loop down, you can try a similar track with more than one loop. You still only need one ramp to give the marble an initial velocity.
Total mechanical energy is conserved. Potential energy is converted to kinetic energy and vice versa.