Download EXPERIMENT M2

EXPERIMENT M2
MEASURING THE ACCELERATION DUE TO GRAVITY g BY
THE METHOD OF FREE FALL
Objectives:
• To investigate the motion of a body falling under the influence of gravity
• To understand the use of the equations of motion for this problem
• To gain familiarity with the use of graphs in determining an experimental quantity
• To determine the value of the acceleration due to gravity, g
Background:
You know that when you drop an object it falls towards the Earth’s surface. When you think
about it for a little bit you’ll realise that the object must be accelerating towards the surface of
the earth: otherwise it would be no more dangerous to jump off the top of the Empire State
Building than to jump off a chair! So when you drop an object its velocity increases
continually (i.e. it accelerates). Sir Isaac Newton observed this, as had others before him, but
his achievement was to realise that the acceleration of objects as they fall implies that the earth
is exerting a force on them (the gravitational force you’ll learn about in lectures).
For objects close to the earth, the acceleration due to gravity is independent of the distance to
the earth’s surface (in other words, it is constant) to a high degree of accuracy. It is very
important to note that this acceleration is independent of the mass of the object, because as
the object mass increases so does the gravitational force, and the increased inertia is cancelled
out by the increased gravitational force.
Your task is to measure the acceleration of falling objects. In order to do so you will measure
the distance travelled by a football that you drop as a function of time using a motion sensor.
From this you will be able to use the laws of motion (which you will meet or have met in
lectures) to work out the acceleration. You will also be able to measure a few bounces of the
ball.
Now answer questions A1 and A2 on the answer sheet
Procedure:
This is a Calculator Based Laboratory (CBL) experiment. It will take you some time to get to
know the calculator functions and capabilities, but once you have mastered those, you will
obtain your data within a few minutes.
-3-
Technical note: The motion sensor sends out pulses of ultrasound, and measures how long it
takes to come back when they reflect back off an object. The distance to the object is then
worked out by multiplying this time by the speed of sound in air.
Preparation:
1)
Verify that the motion sensor is connected to the digital input port (labelled
DIG/SONIC) of the CBL.
2)
Switch on the calculator. If there is anything on the screen, ignore it – press the APPS
button and select DATAMATE.
3)
The CBL will now scan all its input ports for detectors, and will detect the motion
sensor after a short while.
4)
Select SETUP, and select DIGITAL MOTION. A screen will appear with a choice of
measuring motion in feet or meters. Select measurements in meters.
5)
Now select MODE, and select TIME GRAPH.
6)
Choose 2 to enter the time between successive measurements of the distance between
the sensor and the ball, and the number of measurements you make (called “number
of samples”). At this point it is not important to get these values “right”: you will
find out by experimenting which settings work best. For a start, try something like
0.05 s and 100 data points. (A maximum of 1024 data points can be recorded and the
time interval should not be less than 0.01 s).
7)
Select OK to enter these data, then select OK again to return to the main screen. You
are now ready to make the measurements!
8)
Fix the motion sensor within the stand so that its position remains fixed while you’re
making measurements.
Making the measurements:
9)
Hold the football close to the motion sensor. When you select START the sensor will
beep – then release the ball.
10) Upon completion a screen will appear with a choice of three graphs. Select DIGDISTANCE. Does the graph look like your prediction under A1? If it does not, either
your prediction was wrong or your measurement didn’t work the way it should have.
It may take a bit of practice to record a few bounces. You may also have to adjust the
time interval and number of data points (step 7).
11) Repeat steps 7-11 until you’re happy with your measurements.
Now answer questions A3 to A5 on the answer sheet
Getting a value for g:
12) Select a region of the graph where the ball is in free fall. To do this, select 2: SELECT
REGION, and follow the instructions on the screen.
13) No go to the main screen, select ANALYZE, then CURVE FIT.
14) Select 7: MORE, and then 5: QUAD (DIST VS TIME). Write the values for A, B and C on
your answer sheet (A6).
15) Again select CURVE FIT, now do 5: LINEAR (VELO VS TIME). Write values for A and B
on your answer sheet (A6).
-4-
Now answer questions A6 to A10 on the answer sheet
You have now successfully completed the prescribed part of the experiment. Feel free to
explore other options that the calculator or the experiment gives you.
Analysis
As you will see or have already seen in lectures, the distance x travelled by a body with initial
velocity v0 and undergoing an acceleration a during a time interval t is given by
while the velocity is given by
x = x0 + v0 t + 12 at 2
(1)
v = v 0 + at
(2)
The units of a are those of acceleration, i.e. m/s2. In free fall experiments, the acceleration is
equal to g, the acceleration due to gravity. The standard or “accepted” value for g on Earth is
9.8 m/s2 (but this varies with position on the surface of the earth).
-5-