"g" by free fall

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This apparatus is a simple timing method for estimating the acceleration due to gravity.

Description

A ball bearing is dropped from rest to a plate a separated by a height, h. The time taken, t, for the ball to hit the plate from release can be used to evaluate the acceleration due to gravity, g. The size of the apparatus and conceptual simplicity means it is often used as a demonstration.


Theory:

The time the ball bearing takes to fall a fixed distance will be related to the acceleration the ball is experiencing. As the ball is clamped, the ball's velocity, initially, is zero.
If pupils are familiar with the equations of motion, the “suvat” equations , these should be used in the form: s=ut +1/2 a t2
where u =0m/s, s=h and a=g giving:
h=1/2gt2 and rearranging
g=2h/t2


Special apparatus

General

Often schools will have a version of this equipment. If this is the case, the accompanying instructions should be followed. Various forms of the apparatus exist, however, the timing is normally done electronically. A laboratory timer reading to milliseconds is usually required. Cost and complexity for commercial kits may affect choice of apparatus. One form has an electromagnet holding the ball bearing which is released when the current to the magnet is interrupted. Alternatives have a circuit break mechanism which uses the ball as part of the circuit. Often these rely on an internal power supply in the timer. In the magnet case the ball bearing may be delayed for a short while due to residual magnetism. The second case may have “bounce” on the switch (false triggers). The bounce may be removed by electronic circuitry, either in the apparatus or in the timer. This is often done by means of a “schmitt trigger”. Some circuits may require external power.
The bottom timer switch is usually in the form of a gate (or trap door). As the gate is opened the timer is stopped. An alternative is one where a sudden pulse or contact is made as the ball hits a plate.
The exact operation will depend on your timer and apparatus you have.

Making your own (expect disappointment)

Try your timer with a simple on-off switch to see if your timer will be useful, pay attention to how the different inputs are controlled.
This is suggested as many timers have two trigger states: “circuit made” and “circuit broken” and have their own built in power. These are often used with complementary switches. That is one that opens with one that closes. Unfortunately, the mechanical nature of switches often means that unmodified switches cannot be used with a normal laboratory timer. Sadly having specifically designed apparatus often sends the wrong message that all experiments require special kit. A timer is a bit complex to make, but using “home made” switches does show how accessible the methods can be. A pc based oscilloscope can make a good timer and will show far more physics. This will be discussed later. Electronic know-how may be mandatory to create a successful home made switch run on a timer. Some methods of switch manufacture are discussed below.

...and don't forget these methods

A dropped mas can easily have the timing made by using a ticker timer, camera or video camera. In the UK the mains frequency is 50Hz or one dot every 0.02 seconds. The PAL video system is only just short of 1/25th of a second per frame (1/24.98 s requires source for reference). Or use a strobe and long exposure camera.

Simple break to start switch

This can be manufactured from a wooden test tube holder and nuts and bolts. Two holes are drilled in the cavity of the test tube holder. Two 2.5mm machine screws or bolts are used make the contacts. Crocodile clips can then be used to make contact.

a simple switch

Double pole switch used with an electromagnet

As a component, a double pole single throw switch has four connections. These connections are usually arranged so that the switch acts as two on off switches on the same toggle. One circuit is connected to the electromagnet, the other to the timer.

Momentary contact switch

A flexible membrane with a conductive underside held in isolation above a conducting plate, can be used to make a momentary switch. As the ball depresses the film, a circuit is made.
Cling film and photomount spay on aluminium foil can be used. A cd case is a convenient size.


Using recorded data to measure "g"

Whilst direct timing methods are not easy to manufacture, the use of datalogging or storage 'scope displays is easy to achieve. Any of the switch methods discussed above may be used. But a voltage source is usually required.
The following method is suggested for a pc based oscilloscope but may easily be adapted to a storage scope or datalogger using two voltage sensors.

PC based oscilloscope method

The following was achieved using the tong release method and a piezoelectric (uncased) transducer (costing only in the tens of pence each).The transducer converts mechanical deformation into electrical energy. This allows the oscilloscope to pick up a signal without an extra power source.
Two channels are required. Channel “A” is used to trigger the event and the channel “B” is used to record the strike of the ball on the plate.

A transducer on a retort base

The piezoelectric transducer was stuck to the base of a retort stand using superglue and some 4mm sockets soldered to the fly leads. This was done for convenience, although a bnc lead would reduce noise. The base was used to reduce the footprint of the apparatus. The release mechanism's circuit is a simple series circuit. The negative of a battery of two cells is taken to the earth/shield/black terminal of a bnc adapter connected to channel A. The +3V is then taken to tone side of the tong switch. The other side of the tong switch is connected to the signal/red connector of the bnc adapter.
When a ball is placed between the contacts the channel goes to +3 volts, when released it will drop to 0V.

Choice of oscilloscope settings.

The duration of data recording will depend on the height the ball is above the retort stand base. For an approximate 1m drop a time base of 100ms/division was chosen. Using two cells the drop on channel “A” was expected to be 3V to 0V and so a setting of +/-5V dc was chosen. After a quick trial, the voltage out from the transducer with a 13mm ball-bearing was about 5V maximum. Channel “B” was also set to +/-5V dc.
Triggering (starting recording) is an important issue. Mechanical bounce, as discussed earlier, interferes with interpretation. However, the software does allow “pre-trigger” information to be displayed. A 1% pre trigger based on the voltage falling to a nominal 1V (below a single cell) was used, although a 5% will allow a better image of the switch bounce, for discussion, and initial release.

a typical trace

Notes

The advantage with the PC based software is that the areas of interest can be zoomed in to so readings become more accurate.
The height of the ball should be measured to the base of the ball.
An extension of this method would be to use the secondary bounces to determine the coefficient of restitution for the ball bearing and the base. The time between two marks is twice equivalent of the time taken for the ball to be dropped from maximum height. The coefficient of restitution is the ratio of initial to final velocity on bounce.
--D.B.Ferguson 17:46, 22 March 2011 (UTC) Back to Physics Equipment and Apparatus
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