Order of work
The device is ready for operation immediately after switching on the voltage and the light does not need heating.
You need:
1. Measure the height h of the pendulum.
2. Squeeze the button "Start" GRM-15 millisekundomera.
3. Wind up on the pendulum axle suspension thread, paying attention to the fact that it wound evenly, one coil to another.
4. Fix the pendulum by an electromagnet, paying attention to the fact that the thread in this position was not too flat.
5. tuck the pendulum in the position of its movement through an angle of 5 and release.
6. Read the measured value of the fall of the pendulum.
7. Press the "Reset".
8. Press the "Start".
9. Repeat steps 3-6.
10. Experiments repeat 5-7 times.
11. Determine the average time of fall of the pendulum
12. Using the expressions (8) and (9), the moment of inertia of the pendulum to count.
13. Calculate the theoretical value of the moment of inertia of the pendulum
I=+I0+Ip+Id (11)
where:
;
and D-outer diameter of the pendulum axis;
where: Dp - the outer diameter of the roller,
where: Dd - the external diameter of the ring.
To measure Dp and Dd is necessary to remove the ring from the roller. Weight, mp md set.
14. Calculate the relative deviation of the experimentally determined value of the moment of inertia of the theoretical
(12)
where: I-moment of inertia obtained from the experiment using the formulas (8) and (9). IT- moment of inertia calculated from the formula (11)
15. Rate error in determining the moment of inertia based on the experimental data, appearing in the expression (8). All measurements must be made with great caution, as the pendulum can be easily damaged. It is necessary to protect the pendulum from the blows.
Control questions
1. In what part of Maxwell pendulum movements?
2. How the experimentally determined moment of inertia of the pendulum?
3. How to calculate theoretically the moment of inertia of the pendulum?
4. What are the moments of inertia units SI?
5. What is the angular acceleration?
6. In what units is measured by the angular acceleration?
7. In what units is measured by linear acceleration?
8. What is the relationship between the linear and angular accelerations?
9. As recorded 2nd Newton's law for rotary motion?
10. Record the forces acting on the pendulum Maxwell.
Literature
1. Savelyev IV The general course of physics. A .: Science, 1977, volume 1.
2. Frisch SE, AV Timoreva General Physics Course Volume 1, A .: Mektep 1971.
3. DV sivukhin The general course of physics. Vol.1, M .: Nauka, 1979.
Job number 5 The study of the laws of the oscillatory motion by means of a physical pendulum
Accessories: universal pendulum FPM-04, supporting prism, caliper,
Objective: To study the vibrational motion of the laws on the example of a physical pendulum, the definition of acceleration of gravity using a pendulum working.
Brief details of the theory. Physical pendulum is called a solid, committed under the influence of gravity fluctuations around the horizontal axis without passing through its center of gravity.
Let solid (Fig. 5.1) mass m revolves freely about a horizontal axis O perpendicular to the plane of the drawing.
Figure 3.1 The physical pendulum.
The distance from the center of mass C to
О about the same axis
.
In the event of the pendulum from the equilibrium position at an
angle
,
a torque which tends to return the pendulum to its equilibrium
position. Attributing,
torque and angular displacement have opposite
signs
(3.1)
Let us write the equation for the pendulum
dynamics of rotational motion. If we denote
the angular acceleration and
torque across the pendulum of inertia about
the axis passing through the point of suspension O by
,
taking into account (3.1), we obtain
(3.2)
At small angles of deviation of the pendulum
;
then
or
(3.3)
Introducing the notation
,
(3.4)
We transform equation (3.3) as follows:
(3.5)
Thus, the small oscillations of a physical pendulum is described by the differential equation (3.5) and its solution has the form:
,
(3.6)
where
- the amplitude of the oscillations, ie, the greatest angle, which
deviates the pendulum:
- phase fluctuations; constant is a phase value at time t = 0 and is
called the initial phase.
Consequently, for small oscillations of the
angular deviation of the pendulum varies with time according to a
harmonic law (the law sine or cosine). The main property of harmonic
oscillations are their frequency, ie, repeatability over the time
interval T to obtain the phase increment
.
This time period is called the period T
(3.7)
value
(3.8)
represents the number of oscillations per unit time is called circular or cyclic frequency.
From equation (3.4.), It follows that for small deviations from the equilibrium position of the frequency of the physical pendulum with respect to the axis of rotation and the distance between the axis of rotation and the center of mass of the pendulum. In accordance with (3.7) during the physical pendulum oscillations with allowance for (3.4) is given by
(3.9)
The value of
(3.10)
called the reduced length of the physical pendulum. By the theorem of Steiner we have:
(3.11)
where
- the moment of inertia about an axis
through the center of gravity (see Figure 3.1...) and parallel to the
swing axis O; l - distance between the axes. Then, the reduced length
of the physical pendulum is equal to
(3.12)
As can be seen from (3.12)
. If postpone along the line segment OS OK
(Fig. 3.1.), Is equal to L, the resulting point K is called the
center of oscillation. Then the pendulum with a mass concentrated at
the point K (this is called a mathematical pendulum) will fluctuate
with the same period as that of the physical pendulum, which is equal
to the period
(3.13)
On the point of suspension and the center of the swing To exhibit the property of reciprocity: if the swing of the pendulum about the point K becomes the new center of oscillation point O, and the period of oscillation of a physical pendulum does not change.
On this property based definition of acceleration of gravity with the help of the so-called revolving pendulum.
Installation and obtain calculation formulas. Revolving pendulum is a steel rod that is rigidly fixed reference prism D and D / (Fig. 5.2.) And the steel weight B. Located between them.
And there is another load at one end of the rod, it can move along the scale rod and secured in position. Watch the pendulum, hanging him on a special stand for supporting the prism alternately. By moving the movable weight and achieve the coincidence of periods of oscillations of a pendulum, when the suspension points are the ribs supporting prisms D and D /.
We write down the value of the periods Т1 and Т2 at the swing on poles О and О/:
(3.14.)
(3.15.)
If we find a position of the load A, in which the pendulum oscillation periods Т1 and Т2 about poles О and О/match, the acceleration of gravity is easily determined from the equation (3.13):
(3.16.)
where Т=Т1=Т2;
those. In this case, the reduced length of
the physical pendulum is equal to the distance between the supports
О and О/.
In fact, the exact equal periods is difficult to achieve. Therefore formula (. 3.14) and (. 3.15) with (. 3.12) can be written as:
(3.17)
(3.18)
From these equations we have:
from whence
(3.19)
Where
(3.20)
The
error can be found from the relation
(3.21)
Where