Measurement of g using an electronic timer
This experiment gives a direct measurement of the acceleration due to gravity.
Apparatus and materials
Release mechanism (may be electromagnetic)
Trip switch (hinged flap)
Power supply, low voltage, DC
Ball bearing ball, steel
Retort stand and boss
Leads, 4 mm
Health & Safety and Technical notes
It may be useful to stand the trip switch in an up-turned box lid to catch the ball after its fall.
Science equipment suppliers offer slightly different versions of the mechanisms for the release that starts the timer and the trip switch that stops the timer.
i) In one version, there is no electromagnet in the release mechanism. Instead, the ball is held in position manually, so that it completes a circuit between two of three pegs. When you release the ball, the break in circuit starts the timer.
If you are using this arrangement, you may prefer to release the ball by holding it from a thread passing through the top of the support. This ensures that you do not obstruct the motion of the ball with your hand: the ball will be in free fall immediately the circuit is broken.
At the bottom of its fall, depending on its design, the mechanism may either make or break a second circuit, stopping the timer.
ii) Another version employs an electromagnet.
a Set up the apparatus as shown in the diagram. You may need to adjust the distance of fall and the point at which the ball strikes the flap.
b Arrange the timer so that it starts when the electromagnet is switched off and stops when the hinged flap opens.
c Check that the flap does open when the ball strikes it. You may need to make the distance of fall larger, or move the flap so that the ball strikes it further from the hinge.
d Measure the distance h from the bottom of the ball to the hinged flap. Be careful to avoid parallax error in this measurement.
e Measure the fall time three times and find the average.
f Repeat step e for a range of heights between 0.5 m and 2.0 m.
g Plot a graph of 2h against t2.
h Use the graph to find g.
1 The value of g is calculated from s = 1/2 at2. In this case h = 1/2gt2. With students at intermediate level, it will be sufficient to obtain an average value for t at just one height, h. Omit steps g and h.
2 Steps g and h: With more advanced students, repeat the experiment at different heights and find the gradient of the graph. They will see that the graph does not pass through the origin. An intercept on the t2 axis indicates that there is an apparent time of fall even when the ball falls no distance at all, a systematic error. This is the time that it takes the electromagnet to release the ball once the current through it is switched off, in other words, the time for the magnetism to fall sufficiently to release the ball.
3 How Science Works Extension: This experiment provides an opportunity to discuss experimental design and how it can be used to reduce or eliminate errors. The experiment contains two sources of systematic error: the time-delay in releasing the ball (as discussed above in note 2), and a similar delay in switching the timer off, because the hinged flap may not switch the timer at exactly the instant when the ball strikes it. Both of these will give rise to measured times which are longer than the time during which the ball is in free-fall.
You could discuss with the class how to reduce or eliminate these errors. One approach is to improve the basic design of the experiment so that the time-delays are less or zero. You could compare this method of measuring g with others and discuss their relative merits.
Another approach is to consider how this experiment can be analyzed to reduce the systematic errors. The ‘true time of fall’ is less than the measured value t by a fixed amount terror (equal to the sum of the two time delays discussed above). How can we discover or otherwise eliminate this error? Here are two ways:
Think about the situation where h = 0. The ball will take zero time to fall through this height, but the timer will still show a time equal to terror Plot a graph of t against h. Extrapolate back to h = 0. The graph will reach the axis at t = terror. Now this value can be used to correct the measured values of t. (Students will need extra columns in their results tables to allow for this.) Plot a graph of 2h against t2 as before.
Alternatively, think about the situation where h is infinite, or at least very large). The value of t will be very large, so the error in it will be small or negligible. So large values of h will give more accurate values of g. In the results table, add a column for 2h/t2; the values should approach an accurate value for g. Plot a graph of 2h against t2 as before; it will be curved, but at the high end it will approach a straight line through the origin whose gradient will be a good value of g.
This experiment was safety-checked in May 2005