Determine the period of a recording timer.
INTRODUCTION - READ AND FILL THE BLANK FOR FULL CREDITS.
The recording timer is a device that helps you study motion. It consists of a simple electric vibrator through which paper tape can be drawn. A carbon paper disk placed between the vibrating arm and the paper tape leaves a mark on the tape each time the arm goes up and down.
When the recording timer is connected to a power source with constant voltage, its arm will vibrate regularly. The period of the timer is the time it takes for the arm to complete one vibration all the way up and all the way down.
The frequency (f) of the timer is the number of times it vibrates per second. The period (T) of the timer is the reciprocal of the frequency (T= 1/f), or the time for one vibration.
If the arm vibrates 60 times per second (frequency), its period is __________________ seconds.
If the arm vibrates 30 times per second , its period is _________________ seconds.
frequency is measured in Hertz (Hz). So 20 hertz means 20 vibrations per second, the period is _____________.
If the period is 0.01 s, the frequency is ________ Hz.
If the frequency is 60 Hz, the period is ________ second.
MATERIAL
Recording timer, C-Clamp, time tape, carbon paper discs, stop watch.
PROCEDURE
1. Assemble the apparatus as shown below.
2. Let's test the apparatus. Place a short strip of timer tape in the recording timer under the carbon paper. Make sure the paper tape moves freely. Turn on the timer (push the button) while at the same time you pull the tape at a constant speed. If no dot appears on the tape, check to see that the timer tape was placed under the carbon disk and the the inked side of the carbon disk was facing the timer tape. (make sure it is plugged on). Ask your teacher for assistance.
The number of dots on the tape is the number of times the arm vibrated while you pulled the tape through.
3. PLEASE READ THE paragraph BEFORE DOING ANYTHING. I DON't WANT TO WASTE TAPE.
Place the end of a 3m strip of tape into the timer. Pull the tape through the timer WITH A GENTLE CONSTANT MOTION. As you pull the tape through the timer, your partner will operate the timer and stopwatch.
After you pull the tape through the timer, ask your partner to start the timer and to begin timing for 3 seconds.
At the end of three seconds, turn off the timer.
4. Count the number of dots on the tape and calculate the frequency and the period of the recording timer.
Record your data in the TABLE below.
| time (s) | number of dots | frequency (vibrations/sec)= dots/sec | period (sec) = 1/frequency |
ANALYSIS
1) Would the value of the period for the timer be more accurate if you had drawn each tape through the timer for five seconds rather than for three seconds ?
2) The true period is 1/60 s . Find the relative error in %
relative error = 100 | your value for the period - (1/60) | / (1/60)
(absolute value means % error are always positive.
GOING FURTHER: periodic motion - motion that repeats itself in time -
examples: the mass of a pendulum swinging back and forth, the mass hanging on a spring moving back and forth.
1) READ There are two key
words that help us describe periodic motion: period
and frequency
From this definition, period must be measured in seconds/cycle. However, we don’t count cycles as a unit. Thus, period is just measured in seconds, and it is implied that this is the number of seconds per cycle. For example,
T = 24s
Frequency f : The number of cycles (or revolutions) completed per second.indicates a 24 second period. This means it takes 24 seconds for the motion to repeat itself.
From this definition, frequency must be measured in cycles/second. However, we don’t count cycles as a unit. Thus, frequency is measured in 1/seconds (often written as s-1). We call this unit a Hertz (Hz) in recognition of Heinrich Hertz.
For example: 24 cycles per second (the motion repeats itself 24 times every second)
is noted f = 24 /s = 24 Hz
From the definitions of period and frequency, we can see that they are inverses of each other.
Mathematically : T = 1/f and f = 1/T
2) An engine runs at 2400 rpm's. (revolution per minute )A) Find the frequency. (how many revolution per second)
(hint: convert revolutions per minute to revolutions per second. If you don't know how to convert, think. in one second do you expect less or more revolutions than in 1 minute ? so you multiply or divide ?)
f = ____ Hz
B) CAlculate the period of the engine in seconds
c) If the engine turns a disc (see below) with a radius of 0.05m, What is the speed of the disc on its perimeter?
hint: speed = distance / time. and you know that it takes T (period) seconds for a point on the disc to go over one entire cycle. perimeter of a circle = 2 pi r
and diameter = 2r
s= ________ m/s
D)Remember ? velocity is a _________, it has a ___________ (how much of what) and a _________ (which way).
We can call the magnitude of the velocity the speed.
Remember ? acceleration = change of __________ / ___________ acceleration is also a vector.
(when you divide or multiply a vector by a number, you change its magnitude but not its direction.
you change the length of the arrow. you reduce it and you enlarge it. but you don't change its direction)
Imagine a point on the edge of the disc. The point is going in circle with a speed s. Even through the speed is constant, the point still has an acceleration. explain what ? (no change in speed but .........................)
E) In 11th grade you will learn that an object that moves in a circle, at a constant speed, has an acceleration called
the centripetal acceleration ac. (accounts for the change in direction, not the change in speed or magnitude)
The formula for ac is ac = s2/r. s is the speed and r the radius of the circle.
Find the centripetal acceleration of a point moving in circle on the edge of the disc.
3)
Galileo was only 17 years old when he made a discovery about pendulum.
The period of a pendulum (time for the mass to complete a cycle = forth
and back) does not depend on the mass , does not depend on the
amplitude of the mass (see drawing) but depends only on the length of the string and on the gravity
9.8 m/s/s.
If you go to the cathedral in Pisa, next to the leaning tower, people will point to you the
swinging lamp, in the church, Galileo used to do his experiment. He used his pulse to count the period of a cycle. Some say he was attending a very boring sermon and had nothing else to do but to count the period of the lamp.
Here is the mathematical formula for the period of a pendulum:
A pendulum has a string with a length 1.2m.
What is the period of the pendulum on the surface of the EArth ? Tearth = ________ s
What is the period of the pendulum on the surface of the moon ? (gravity on Moon = 1/6 (Earth's gravity) = 6 times less )
Tmoon = ______________s
Which one is greater ? find the ratio Tmoon / Tearth =___________. So Tmoon is _________ times larger than Tearth.
Now find the square root of 6 sqrt(6) = _________. If you are in Algebra II, this should not be surprising.
(given the formula for the period)
Can you prove it mathematically ? extra credits if you do ? you need to play with the formula above.
4) A pendulum has a period of 4.0 seconds. What is its frequency? easy
5) You swing a rope over your head in a circle with a speed of 15.0m/s and radius of 2.0m.
A) What is the period of the motion? (hint: you need to find the time for the tip of the rope to cover a circle. you have the distance and the speed.)
B) What is the frequency of the motion?
6) What is the frequency of a pendulum with a length of 0.20m on earth?
7) To make a good clock, a pendulum should have a period of 1.0 second.
How long must a pendulum on earth be to have this period? (use formula above)