Mechanics
1.3.03-11/15
Dynamics
Newton’s second law with Cobra3 / Air track or Demonstration track
What you can learn about …
Linear motion
Velocity
Acceleration
Conservation of energy
Principle:
According to Newton’s 2nd law of
motion for a mass point, the relationship between mass, acceleration
and force are investigated.
Set-up of experiment P2130315 with demo track
What you need:
Experiment P2130311 with air track
Experiment P2130315 with demo track
Cobra3 Basic-Unit, USB
12150.50
1
1
Power supply 12V/2A
12151.99
1
1
Software Cobra3, Translation/ Rotation
14512.61
1
1
Light barrier, compact
11207.20
1
Air track rail
11202.17
1
Blower 230V/50Hz
13770.97
1
Pressure tube, l = 1.5 m
11205.01
1
1
Glider for air track
11202.02
Slotted weights, 1 g, polished
03916.00
20
9
Slotted weights, 10 g, coated black
02205.01
4
4
Slotted weights, 50 g, silver bronzing
02206.02
4
4
Stop, adjustable
11202.19
1
Starter system, mechanical with release
11202.13
1
Tasks:
Magnet with plug for starter system
11202.14
1
Tube with plug
11202.05
1
1
Plasticine, 10 sticks
03935.03
1
1
Hook with plug
11202.07
The distance-time law, the velocitytime law and the relationship between mass, acceleration and force
are determined. The conservation of
energy can be investigated.
Pulley, movable, d = 40 mm, with hook
Silk thread on spool, l = 200 mm
03970.00
02412.00
1
1
Weight holder, 1 g, silver bronzing
02407.00
1
Bench clamp -PASS-
02010.00
1
Bosshead
02043.00
2
Support rod, stainless steel 18/8,
l = 250 mm, d = 10 mm
02031.00
1
Connecting cable, 4 mm plug, 32 A, red, l = 100 cm
07363.01
1
Support rod, stainless steel 18/8, l = 100 mm
02030.00
1
Connecting cable, 4 mm plug, 32 A, blue, l = 100 cm
07363.04
1
Measuring tape, l = 2 m
09936.00
1
1
Connecting cable, 4 mm plug, 32 A, yellow, l = 100 cm 07363.02
Needle with plug
11202.06
2
1
Connecting cable, 4 mm plug, 32 A, black, l = 100 cm 07363.05
1
Demonstration Track, Aluminium, l = 1.5 m
11305.00
1
Connecting plug, pack of 2
07278.05
1
1
Cart, low friction sapphire bearings
11306.00
1
Crocodile clips, black, plastic insulation, pack of 10
07276.15
1
1
Holder for pulley
11305.11
1
PC, Windows® XP or higher
Weight for low friction cart, 400 g
11306.10
1
End holder for demonstration track
11305.12
2
Portable balance, OHAUS CS2000
48917.93
1
Complete Equipment Set, Manual on CD-ROM included
Newton’s second law with Cobra3 /
Air track or Demonstration track
P21303 11/15
20 Laboratory Experiments Physics
1
Path-time law.
1
1
1
1
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
1
1
1
LEP
1.3.03
-11
Newton’s 2nd Law / Air track with Cobra3
Related topics
Linear motion, velocity, acceleration, conservation of energy.
Principle
According to Newton’s 2nd law of motion for a mass point, the
relationship between mass, acceleration and force are investigated.
Tasks
The distance-time law, the velocity-time law and the relationship between mass, acceleration and force are determined.
The conservation of energy can be investigated.
Equipment
Cobra3 Basic Unit
Power supply, 12 VRS232 cable
Cobra3 Translation/Rotation Software
Light barrier, compact
Air track
Blower
Pressure tube, l = 1.5 m
Glider for air track
Slotted weight, 1 g, polished
Slotted weight, 10 g, black
Slotted weight, 50 g, silver bronze
Stop, adjustable
Starter system, mechanical, with trigger
Magnet with plug for starter system
Tube with plug
Plasticine, 10 sticks
Hook with plug
Silk thread, l = 200 m
Weight holder, 1 g
Bench clamp -PASSRight-angle clamp
Support rod, l = 250 mm
Support rod, l = 10 cm
Measuring tape, l = 2 m
12150.00
12151.99
14602.00
14512.61
11207.20
11202.17
13770.97
11205.01
11202.02
03916.00
02205.01
02206.02
11202.19
11202.13
11202.14
11202.05
03935.03
11202.07
02412.00
02407.00
02010.00
02043.00
02031.00
02030.00
09936.00
Portable balance, CS2000
Connecting cord, l = 100 cm, red
Connecting cord, l = 100 cm, blue
Connecting cord, l = 100 cm, yellow
48892.00
07363.01
07363.04
07363.02
1
1
1
1
PC, WINDOWS® 95 or higher
Fig. 2. Connection of the compact light barrier with the
Cobra3 BASIC UNIT
1
1
1
1
1
1
1
1
1
9
4
4
1
1
1
1
1
1
1
1
1
2
1
1
1
yellow
blue red
Fig.1: Experimental set-up to measure linear accelerated movements.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2130311
1
LEP
1.3.03
-11
Newton’s 2nd Law / Air track with Cobra3
Alternative experimental set-ups are located at the end of this
experimental description.
Before beginning with the measurements, it is advisable to
check the track`s adjustement.
Set-up
In accordance with Figs. 1 and 2.
Ensure that the thread runs parallel to the track.
Remarks
If the values (50 ms) in the ”Get value every (50) ms” dialog
box are too high or too low, noisy or non-uniform measurements can occur. In this case, adjust the measurement sampling rate appropriately. At excessively low velocities and
exceedingly high sampling rates (short ms times) the velocity
0 m/s can be intermittently measured at irregular intervals. In
this case increase the sampling time.
Procedure
Set the measuring parameters in accordance with Fig. 3.
Place the glider in the starting position and affix it to the starter
system with the magnet. The weight holder has to be located
directly adjacent to the light barrier’s wheel.
Release the glider; it starts accelerated motion. At the end of
the movtion it collides with the stopper. Recording of the measured values begins as soon as the value of the measured
velocity exceeds 0.01 m/s. During the course of the motion,
the glider’s velocity is continuously actualized. At the end of
the measurement recording, the velocity again falls below
0.01 m/s and the recording process ends.
The mass of the glider can be altered by adding slotted
weights. Always place weights having the same mass on the
glider’s weight-bearing pins, as optimum gliding properties are
provided only with symmetrically loading. The accelerating
force acting on the glider can be varied by changing the number of weights (on the weight holder) acting via the silk thread
and the precision pulley. Determine the mass of the glider
without the supplementary slotted weights by weighing it.
Position the adjustable stop on the track in such a manner that
the glider is gently braked just before the accelerating weight
touches the floor.
To determine the acceleration as a function of the mass,
increase the mass of the glider progressively by 20 g increments (10 g on each side).
In determining the acceleration as a function of force, the total
mass remains constant. Successively transfer 2 g (1 g from
each side) from the glider to the weight holder.
The accelerated mass must not exceed 20 g.
Fig. 3. Measurement parameters (Light barrier)
Theory and evaluation
Newton’s equation of motion for a mass point of mass m to
S
which a force F is applied is given by the following:
S
S
m· a F ,
where
S
d2 r
S
a dt2
is the acceleration.
The velocity v obtained by application of a constant force is
given as a function of the time t by the expression
S
F
S
v 1t 2 t
m
for
S
v 10 2 0.
Assuming that
S
S
v 102 0; r 102 0
S
the position of r of the mass point is
S
1 F
S
r 1t 2 · t2 .
2 m
(0)
In the present case the motion is onedimensional and the
force produce by a weight of m1 is
S
S
0 F 0 m1 · 0 g 0 m1 · g
where g is the acceleration of gravity. If the total mass of the
glider is m2 the equation of motion is given by
S
1m2 m1 2 · 0 a 0 m1 · g;
(1)
The velocity is
m1 · g
S
0 v 1t 2 0 v ·t
m1 m2
(2)
and the position is
1 m1 · g
S
· t2 .
0 r 1t 2 0 s 1t2 2 m1 m2
2
P2130311
(3)
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.3.03
-11
Newton’s 2nd Law / Air track with Cobra3
Typical measurement data are displayed in a v-t (or s-t) diagram (Fig. 4). In addition to the measured points of interest
(the rising branch of the v (t) curve), the collision phase of the
glider with the stopper is also recorded. These latter measured
points must be deleted before continuing with the evaluation.
At the left image margin, at low velocities, the velocities have
been only inadequately registered due to the slow rotation of
the light barrier’s wheel and show a nearly constant velocity
course.
Fig. 5 shows the velocity-time curve, a straight line, which
conforms to the relationship v = a · t. A regression line has
been fitted to the measured points; the slope m supplies the
acceleration a, in this case 0.229 m/s2.
Fig. 4. Measurement data before the deletion of the unnecessary measured points
Fig. 7. Path-time law
Fig. 5. Velocity-time law with linear regression curve
Fig. 8. Path-time law with the square of time on the x axis
Fig. 6. Acceleration-time law
Fig. 9. Kinetic energy
The time course of acceleration a (t) is shown in Fig. 6. Initially,
the acceleration increases. This is due to the light barrier’s
measurement principle. The light beam interruptions by the
spoked wheel are counted for equal time intervals, in this case
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2130311
3
LEP
1.3.03
-11
Newton’s 2nd Law / Air track with Cobra3
50 ms. At very low velocities even with accelerated movement
only one interruption per time interval occurs, i.e. the velocity
is measured as a constant value. Subsequently, measured
points of constant acceleration are recorded. Ultimately, the
acceleration again decreases, i.e. when the glider reaches the
end of the track or the stop. If the ”Measure” icon is chosen,
a horizontal cursor line can be positioned. It approximately
passes through the centres of the points that represent constant acceleration. The measured average acceleration value
a agrees well with the value determined using regression in
Fig. 5. Now the acceleration of gravity can be calculated. The
following relationship applies (see equation (1)).
(m1 + m2) a = m2 g
and thus
(m1 + m2) a / m2 = g
Fig. 10. Potential energy
Since m1 (the mass of the glider) and m2 (the accelerated
mass) are known (their weights can be checked), the acceleration of gravity g can be calculated with the calculator in
Utilities in WINDOWS® when a has been measured. For a typical measurement, where m1 = 200.2 g, m2 = 5 g and a =
0.229 m/s2 are measured, it follows that g = 9.4 m/s2.
According to equation (3) the curve of the path-time law
exhibits a parabolic course (Fig. 7).
This fact can be verified as follows: The time axis is squared
to obtain a linearized curve course (Fig. 8).
Using the Measurement / Channel Manager, the time is placed
on both the x and the y axes. This is necessary because only
the y axes can be mathematically reworked.
Using Analysis / Channel modification, the operation x := x * x
is performed on the y axis. This new channel is exported into
the original measurement (Export Measurement / Measuring
Channel).
Fig. 11. Sum of the respective kinetic and potential energies
Fig. 12. Experimental set-up for measurement of the linear, accelerated movement (with movement sensor)
4
P2130311
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.3.03
-11
Newton’s 2nd Law / Air track with Cobra3
Finally, using Measurement / Channel Manager, the new
squared time is assigned to the x axis and the path s (t), to the
y axis. The regression line in Fig. 8 proves that the curve
course is now linear and thus also the original quadratic
dependence of the path on the time.
The law of conservation on energy states that the sum of
kinetic and potential energy in this closed system must be
constant. This statement can easily be checked by the addition of potential and kinetic energy (Fig. 11).
In a very similar manner, other measured channels can also be
mathematically transformed. To verify the energy balance, the
kinetic and potential energy has to be calculated and displayed.
Kinetic energy (Fig. 9): Ekin (t) = 0.5 (m1 + m2) v2, where m1 +
m2 = 205.2 g. Conversion using: Analysis / Channel modification / Operation
x:= 0.5 * 205.2 * x * x, where x = v (t).
Potential energy (Fig. 10): Epot (t) = m2 g (h – s (t)), where h =
0.932 m.
Conversion using: Analysis / Channel modification / Operation
x:= 5 * 9.81 * (0.932 – x ), where x = s (t).
Remarks
In order to achieve a higher path resolution, the movement
sensor (12004.10) can be used instead of the compact light
barrier (11207.20) (cf. Fig. 12 and Fig. 13).
Please ask for this alternative set-up.
Fig. 13: Connection of the movement sensor to the Cobra3
Basic Unit
Fig.14: Measurement parameters (movement sensor)
Mount the movement sensor in such a manner that its housing is to the right of the track when the car moves toward the
sensor. If the movement sensor is mounted the other way
round, negative velocities will be measured. Pass the thread
across the larger of the movement sensor’s two cord grooves.
Set the measurement parameters according to Fig. 14.
red
black
yellow
BNC1
BNC2
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2130311
5
LEP
1.3.03
-11
6
Newton’s 2nd Law / Air track with Cobra3
P2130311
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen