Apple electronically released from platform; fall time given by special circuit and digital display.
What it shows:
This is a free-fall-from-rest experiment in which an apple (or any other object of comparable size) is dropped from the lecture hall ceiling into a catching bucket on the floor. By measuring the (1) distance and (2) duration of the fall, an accurate (± 0.022%) determination of the acceleration due to gravity can be made:
How it works:
A special suspension/release/timing mechanism was designed so that the duration of the fall can be measured to ± 10 µsec. A technique for measuring the distance of the fall to ± 1 mm was also developed. Detailed information has been fully documented and published elsewhere 1 and will not be presented here—only the salient features.
The free-fall object can be any material, shape, or size. A few kilograms can be accommodated with the present design. Ideally, it ought to be large enough to assure visibility to everyone in the lecture hall. In the demonstration as originally conceived by David W. Latham, 2 a historical reference to Newton is made by dropping a real apple. The suspension/release/start-timing mechanism is attached to the lecture hall "skyhook," approximately 6 m high. The object to be dropped is suspended by a short length of copper wire. The release of the object is achieved by "instantaneously" vaporizing the suspension wire which is accomplished by discharging a large capacitor through the wire. The vaporization of the wire (the instant of object release) is detected by a simple circuit which provides the "start" pulse for the interval timer.
A catching/stop-timing bucket apparatus sits on the floor. Partially filled with wood shavings, it safely catches the falling object at the end of its drop. A photogate fixed to the inside of the bucket provides the "stop" pulse for the interval timer. A collimated light source as well as the power supply for the photodetector and light are also permanent fixtures inside the bucket. The actual distance is measured during the lecture or beforehand. The duration of the free fall is about 1.08 seconds and is displayed on a video monitor.
The value of g for Cambridge MA is 9.8038 m/s2. Because of the high accuracy obtained in this demonstration experiment, air resistance (the drag coefficient) plays a significant role and the values obtained for g will depend very much on the object that is dropped. For example, a large (7 cm dia.) apple drops with an average g value of 9.657±0.017 m/s2 while a brass ball (3.8 cm dia.) falls at 9.768±0.002 m/s2. These numbers are within the predicted values of the theory when hydrodynamic effects are taken into account.
Setting it up:
The entire setup takes 20 to 30 minutes, so plan ahead and leave enough time to try it out. The lecture bench directly below the skyhook has to be moved off to the side or out of the hall entirely. If the demonstration is to be a one shot event, the hijacker can be moved out of the hall when the setup is complete. However, if the lecturer intends to repeat the demonstration using different objects to drop, for example, then the hijacker should be left in place (even though it will block one blackboard). It's probably a good idea to leave it in place in any case; if something unexpectedly goes wrong, at least the demonstration has a chance of being salvaged if the hijacker is already there in place.
All the control and measurement electronics sits on the lecture bench next to the catching bucket. Except for the timer, 3 the electronics is home-made and documented in the cited AJP publication. A video camera/monitor displays the duration of the fall to the audience.
The first step in setting it up is mounting the holding/release mechanism on the skyhook—the bottom of it should be level to the eye. Next a special dedicated plumb line is used to line up the catching bucket. Remove the condensing lens of the photogate light source. The bare light bulb will give a sharp shadow of the plumb line—align the bucket so that the plumb line is in the middle of the bucket (eyeballing it is close enough) and its shadow falls on the photodetector pinhole aperture. Wind up and remove the plumb line.
Plug in one of the suspension-wire/banana-plug "modules" into the suspension/release mechanism. Make sure you have enough on hand for several trials—if not, make some. A soldering jig kept with the rest of the paraphernalia should be used to insure that the wires will be 7/8" long when complete. Suspend the object (let's assume it's an apple) to be dropped by hooking it onto the wire. 4 This is illustrated in (a).
Attach the tape measure 5 to the measuring arm, swing the arm into place and adjust it vertically so that the end of the measuring tape just barely touches the bottom of the apple as illustrated in (b). Lower the body of the tape measure down into the catching bucket and measure the distance to the photogate. The easiest way to do this is to hold some sort of straight-edge at right angles against the measuring tape. Slide the straight-edge up or down until the shadow of the intersection of the straight-edge and the measuring tape coincides with the photodetector pinhole aperture (~ 1 mm dia.). With care it is possible to measure the total distance to ± 1 mm. Of course such accuracy is not necessary when an apple is being dropped--an apple is typically so out-of-round that ± 5 mm is good enough. Swing the measuring arm (with attached tape) out of the way. Take care in all of this not to bump the apple. It easily falls off its support wire.
Hooking up the cables: There are two cables that run down from the suspension/release apparatus. The coaxial cable with the BNC connector goes to the black box which houses the release sensing circuitry and is battery operated—turn it on. Its output is a positive TTL pulse that goes to input A (start pulse) of the HP timer. The other cable is a shielded four conductor with two dual banana plugs. The color coding identifies where to plug them in on the control box. Yellow is for the solenoid switch actuator (110 VAC); polarity obviously doesn't matter. The other banana plug is for the 300 VDC supply. Here you must observe the polarity: red goes to red...the black is ground. Also run a patch cord from the green ground terminal on the black box to the black side of the 300 VDC connector. This is a redundant ground so we don't have to rely on the coax cable. Turn on the 300 VDC supply and charge up the capacitor. Monitor the charging on the two gauges...the voltage should exponentially rise to 300 and the current should die down to zero. If they don't, something is quite wrong and must be fixed before going further.
You are now ready to turn on the rest of the electronics. Light bulbs have finite lifetimes so we normally leave the photogate light off until the experiment is to be performed. Remember to turn it on! In fact, we usually supply the lecturer with a "crib sheet", which is a reminder as to the order in which things must be done:
(1) turn on photogate light (switch on top)
(2) reset the counter/timer and make sure there's no "c" on its display (a "c" means its already counting—that's not good)
(3) flip the toggle switch from "charge" to "release"
The wire vaporizes explosively and, in a tad more than a second, the experiment is over. If the experiment is to be repeated, all the toggle switches must be in the red dot positions. This insures that you won't get zapped by any residual charge left on the capacitor when you attempt to install another suspension wire. This holds true for removing the apparatus from skyhook too. The red dot positions for the toggle switches are:
· HV supply off
· "Quick Discharge" on
· "Charge/Release" in Charge position
We thought this experiment was good enough to write up and publish. It's pedagogically simple because there are no initial velocities to deal with mathematically. It is quite accurate and gives excellent quantitative results (unless you're bent on measuring the value 9.8038 m/s2 for g). The humor of the presentation is enhanced by the lecturer eating the apple after the experiment. It does consume an appreciable amount of lecture time (15 to 20 minutes, total) and the lecturer needs to decide whether it's worth it.
1 W. Rueckner and P. Titcomb, Am J Phys 55, 324 (1987). "An Accurate Determination of the Acceleration of Gravity for Lecture Hall Demonstration". The theory as well as the apparatus is discussed. A reprint of this paper is available in the Prep Room.
2 Smithsonian Astrophysical Observatory, Harvard University.
3 We have been using an HP 5302A universal timer capable of nanosec timing interval resolution. We typically use 100 µsec resolution which most of today's interval timers can easily accommodate.
4 A #8 crochet hook is pushed through the apple and hooks onto the wire. Other objects have the hooks already mounted on them.
5 Stanley 7.5 m - 25 ft tape measure.