Hands
On Physics
The Great Bungee Jump
Core Project
Step 3: Calibrating the Timer
Overview
This page shows how to get your timer working accurately. The idea is
to time intervals you already know. By finetuning your timer, you can
get it to accurately predict these values you know. Then it should be very
accurate under similar conditions used in the Bungee Jump.
Computing the time
We will use freely falling objects to generate short, known times. An
object, starting from rest, requires a time, t, to fall a distance, d,
in free fall under the influence of gravity, g. The realtion between these
variables is
d = (1/2)*g*t^2
In this equation, t^2 means "t squared". To understand where
this equation comes from, see the math
concepts page.
This equation can be solved for t, to give
t = sqrt(2*d / g)
In this equation, sqrt(...) means "take the square root of everything
inside the parentheses". This equation tells you how long it takes
for an object to drop from rest through a distance, d.
In the SI system of measurement distance is measured in meters,
acceleration in meters per second squared, and time is measured
in seconds. To sufficient accuracy, g is 9.81 m/s^2.
Calibrating the Timer
Your timing circuit reports voltage (actually, millivolts). Your task is
to relate these voltage readings to time. For times much less than the
product R*C, the voltage is proporational to the time. This can be written
as
t = k*V
where k is some constant. Your goal is to figure out what k is. You
can think of it as a "fudge factor" because it is the number
needed to make V read in seconds. The fancy word for this is a "calibration
constant".
One way to compute k is to plot t as a function of V, using different times.
You should get a straight line through the origin and its slope will be
k. You measure V with the voltmeter and compute t from d. So this means
you have to do a series of measurements for different distances, d, of
fall.
From the mathematics of the circuit, we know what k should be:
k = R*C/Vo
Here Vo is the voltage applied to the circuit, R is the value of the
resistor, and C is the value of the capacitor. It is hard to measure C
accurately. If you have the instruments to measure C, you can just compute
k. Go ahead with the experiment anyway to see whether these two different
ways of measuring k give the same result.
The Experiment
1. Set up the experiment. Use your tower and timing circuit.
Measure the power supply voltage Vo. If the voltage is accidentally changed,
you need to be able to reset it exactly, otherwise you will have to recalibrate
your timer at the new voltage.
2. Take a first measurement. Move switch 2 near the bottom of the
tower. Measure the distance, d, from the mass when it is held in clothespin
to switch 2. Think about exactly what points on the mass and switch to
measure between. Drop the mass several times until you get consistent voltage
readings. Average your good readings.
3. Repeat your measurement. You want ten measurements for approximately
evenlyspaced times. Figure out what distances you need for this. Repeat
the measurement process for each height. Record your data in a table.
4. Analyze your data. Make a graph of the data showing time
of fall as a function of millivolts. Draw a bestfit straight line
through your data. Compute k.
Challenges
 Is the plot on your graph a straight line? Does is go through the origin?
 If your plot is a straight line, what does this tell you about the
function of your circuit as a timer? What if the plot is not a straight
line?
 What is the maximum number of seconds that can be timed with your circuit?
How far would the weight fall in that time?
 Using k, determine the value of the capacitor
in your circuit.
 Is the velocity of the falling object constant, or does it change?
Determine the acceleration from your data. Describe how you do this.
Reporting
Report your data and graph. You should also make a sketch of the falling
object and identify the forces on it using vectors.
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