Free Fall
Item
1.
Aim
To determine the acceleration due to gravity on Earth.
2.
Learning
Objectives
By the end of this experiment, the student should be
able to:
1. Describe the phenomena of free fall.
2. Setup an experiment to study the phenomena of
free fall.
3. Determine the value of the acceleration due gravity
3.
Tools
1. Electromagnet.
2. Vertical mount with a movable photogate.
3. Steel ball.
4. on/off switch.
5. Timer.
Figure 1: Free Full apparatus.
4.
Theoretical The term free fall refers to the situation in which a
Background body is falling towards the earth’s surface under the
effect of gravitational field of the earth only.
Based on Galileo’s experiments, he was able to
show that, an object falling freely in a uniform
gravitational field is constantly accelerated. The
force that causes the acceleration is the result of the
mutual attraction between the mass of the falling
object and the Earth.
The acceleration with which a freely falling body
approaches the earth’s surface is approximately
constant and has an average value of 9.78 m/s2 at
the equator and its values increases as we move
towards the poles to 9.832 m/s2, as it is affected by
the rotation of earth. This acceleration is a denoted
by g and is called the acceleration due to gravity.
Now we consider a body of mass m, starting from
rest is falling freely from height y towards the earth’s
surface. Applying the conditions,
ay = -g = -9.8 m/s2
vi = 0 ,
to the equation of motion
y - yo =vi t + 1/2 ay t2
we get
y=1/2g t2
yi = y ,
yf = 0 ,
5.
Procedure
1. Adjust the distance y between the ball and the
photogate sensor to some distance (say10 cm).
2. Press the red on/off button to release the ball.
3. The timer starts when the ball is released and
stops when the ball crosses the photogate.
4. The time shown on the timer screen is the time
taken by the ball to fall freely through the
distance y.
5. Press the record button to record the fall time t.
6. Repeat the above steps for different distances
(e.g., 90, 80, 70, 60, 50 cm).
7. An EXCEL sheet will be downloaded containing
the data you have recorded.
6.
Data
Analysis
1. The EXCEL sheet will look like that shown in
figure below (values gives may not be actual)
A
B
∆y(cm) t (s)
42.33 0.28
72.33 0.38
77.67
0.4
100
0.45
C
m
2. In col. C, calculate the square of the fall time
(in col. B)
3. In col. D, convert the values of y (in col. B) from
cm into m (dividing by 100)
A
∆y(cm)
42.33
72.33
77.67
100
B
t (s)
0.28
0.38
0.4
0.45
C
D
2
y(m) m
t (s)
0.0784 0.4233
0.1444 0.7233
0.16 0.7767
0.2025
1
2
4. Plot y (col. D) vs t2 (col. C) which should yield a
straight line that passes through the origin.
5. Using the slope of the line, calculate the
acceleration due to gravity g from g = 2 × slope