Mechanics
Dynamics
Free fall 1.3.07-01
What you can learn about …
Linear motion due to constant
acceleration
Laws of falling bodies
Gravitational acceleration
Principle:
A sphere falling freely covers certain
distances. The falling time is measured and evaluated from diagrams.
The acceleration due to gravity can
be determined.
Tasks:
1. To determine the functional relationship between height of fall
and falling time (h = h(t)=1/2 gt2).
2. To determine the acceleration due
to gravity.
What you need:
Falling sphere apparatus
02502.88
1
Digital counter, 4 decades
13600.93
1
Timer 2-1
13607.99
1
Support base -PASS-
02005.55
1
Right angle clamp -PASS-
02040.55
2
Plate holder, opening width 0...10 mm
02062.00
1
Cursor for scale, 2 pieces, plastic, red
02201.00
1
Meter Scale, l = 1000 x 27 mm
03001.00
1
Support rod -PASS-, square, l = 1000 mm
02028.55
1
Connecting cable, 4 mm plug, 32 A, red, l = 100 cm
07363.01
2
Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm
07363.04
2
Alternatively to 13600.93:
Complete Equipment Set, Manual on CD-ROM included
Free fall
P2130701
Height of fall as a function of falling time.
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
Laboratory Experiments Physics 23
LEP
1.3.07
-01
Free fall
Related topics
Linear motion due to constant acceleration, laws of falling
bodies, gravitational acceleration.
Principle
A sphere falling freely covers certain distances. The falling
time
is measured and evaluated from diagrams. The acceleration
due to gravity can be determined.
Equipment
Falling sphere apparatus
consisting of
Release unit
Impact switch
Digital counter, 4 decades
Support base -PASSRight angle clamp -PASSPlate holder
Cursors, 1 pair
Meter scale, demo, l = 1000 mm
Support rod-PASS-, square, l = 1000 mm
Fig. 1: Experimental set-up for the free fall
02502.88
1
02502.00
02503.00
13600.93
02005.55
02040.55
02062.00
02201.00
03001.00
02028.55
1
1
1
1
2
1
1
1
1
Connecting cord, l = 1000 mm, red
Connecting cord, l = 1000 mm, blue
07363.01
07363.04
2
2
Tasks
1. To determine the functional relationship between height of
fall and falling time (h = h(t)=1/2 gt2).
2. To determine the acceleration due to gravity.
Set-up and procedure
The set up is shown in Fig. 1. An electrically conducting
sphere is gripped in the release mechanism which closes the
start circuit.
The pan is adjusted, using the adjusting screw under the
arrest switch, in such a way that a downward motion of a few
tenths of a millimetre closes the stop circuit. The pan is raised
by hand after each single measurement (initial position).
For the effective determination of the height of fall using the
marking on the release mechanism, the radius of the sphere
must be taken into account (diameter 3/4 inch, approx.
19 mm). The aerodynamic drag of the sphere can be disregarded.
Theory and evaluation
If a body of mass m is accelerated from the state of rest in a
S
constant gravitational field (gravitational force m g , it performs a linear motion. By applying the coordinate system in a
way that the x axis indicates the direction of motion and solving the corresponding one- dimensional equation of motion,
we get:
m
d2h1t 2
dt2
m·g
We obtain, for the initial conditions
h (0) = 0
dh102
dt
0
the coordinate h as a function of time (see Fig.2):
h1t 2 1 2
gt
2
(1)
The height is directly proportional to the square of time.
This can be displayed by a representation of h(t2) as shown in
Fig.3.
From the regression line of the data, we can calculate the
gravitational acceleration because the slopeis equal to 1/2 g
according to equation (1).
For this measurement, we receive:
g = 9.77 m/s2.
(Theoretical value: 9.81 m/s2)
Fig.4 shows the values of the gravitational acceleration for different measurements (heights of fall).
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2130701
1
LEP
1.3.07
-01
Free fall
Fig. 2: Height of fall as a function of falling time
Fig. 4: Measured values of the gravitational acceleration
Fig. 3: Height of fall as a function of the square of falling time
2
P2130701
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen