GT4605SP single pendulum experiment instrument manual

Studying the movement characteristics of the pendulum. The single pendulum experiment has a long history. When Galileo observed the chandelier swing in the church of Pisa, it was found that the pendulum has a certain pendulum and its swing period does not change due to the swing angle, so it can be used for timing. Huygens used the observations of Galileo to invent the pendulum clock.

This experiment uses the classical single pendulum formula to measure the gravitational acceleration g, analyzes the factors affecting the measurement accuracy, and learns how to improve the measurement method to further improve the measurement accuracy.

[Objective requirements]

1. Measuring the dynamic acceleration with a single pendulum;

2. Learn to use timing instruments (stopwatch, photoelectric timer);

3. Learn to correctly map and process data on Cartesian coordinates paper;

4. Learn to use the least squares method for straight line fitting.

[Instrument]

Single pendulum device, meter ruler with bayonet, vernier caliper, electronic stopwatch, photoelectric timer.

[Experimental principle]

Placing a metal ball on a slender line, as shown in Figure 1. If the mass of the wire is much smaller than the mass of the ball, and the diameter of the ball is much smaller than the length of the wire, the device Can be seen as a thin wire without quality, tied to a quality

figure 1

Point, this is the pendulum. Slightly the air resistance and buoyancy and the elongation of the line are not counted. When the swing angle is very small, the single pendulum can be considered as a simple harmonic vibration, and its vibration period T is

(1)

Where l is the pendulum length of the pendulum, which is the distance from the hanging point O to the ball center, and g is the gravitational acceleration. Therefore, the pendulum period T is only related to the pendulum length l and the gravitational acceleration g. If we measure the order The l and T of the pendulum can calculate the gravitational acceleration g.

[Experimental content]

First, fixed pendulum length, measure g

(1) Determine the length of the pendulum (the length of the pendulum l is about 100cm)

1 First measure the distance l1 from the point of suspension O to the lowest point A of the ball with a meter with a knife edge (see Figure 1), as listed below:

Position of the hanging point O /cm

The position of the lowest point A of the ball /cm

L1=∣x1-x2∣/cm

Re-estimate the limit uncertainty l of l1 and calculate the standard uncertainty .

2 First measure the diameter d of the ball along the length of the pendulum with a vernier caliper (see Figure 4-1), as listed below:

frequency

1

2

3

average

Caliper zero

Correct the average after zero point

d/cm

Find again with

3 swing length is

Find

Swing for:

(2) Measuring the pendulum period.

Let the pendulum swing as a small angle. It can be seen from the calculation that when the amplitude of the ball is less than 1/12 of the pendulum length, the swing angle θ<5°. The amplitude of the ball is determined by the position of the bar in the horizontal direction. The rod is smoothly released from the ball and starts to swing freely. After the swing is stabilized, it is measured with a photoelectric timer.

How to use the photoelectric timer: After the power is turned on, the default number of times is 30 times. Connect the photoelectric door and the timer's cable. Press the “Execute” button to prepare the timing. When the ball passes through the photoelectric door to block the light, Timing is performed. Since the photoelectric timer records the value of the gear light time every time, the light block is blocked twice in one cycle, and the time is stopped in the 61st light block. Other times, the analogy. If you want to change the number of times, After pressing the “Reset” button, press the “Up” and “Down” buttons to change the number of times. Press the “Execute” button to time.

The time required to oscillate 30 times is measured 30T (accumulation method), and the measurement is repeated several times, and the average value is listed as follows:

frequency

1

2

3

4

5

average

30T/s

Find

with

Then 30T = ± S

(3) by

(2)

Calculate the standard uncertainty of g (You can use 30T as a number when calculating, without having to find T).

g= ± 〔〕 (write unit symbol)

Second, change the pendulum length, measure G

Let l be 50, 60, 70, 80, 90cm, and measure 30T under different pendulum lengths.

(1) Use a rectangular coordinate paper for the l-(30T)2 diagram. If it is a straight line, what does it mean? Find the slope from the straight line

(2) Using l and the corresponding (30T)2 data, the least squares method is used for straight line fitting, and the slope is obtained, and g.

Third, fixed pendulum length, change the swing angle θ, measurement cycle

Let θ be 10°, 20°, 30°, measure the swing period T with a photoelectric timer, and then compare them, as listed in Table 1.

(1) The second approximation of the period T with the swing angle θ

(3)

Calculate the period values ​​of the above corresponding angles and compare them (where g takes the local standard value).

(2) Calculate the value of period T using equation (1) and compare it (where g takes the local standard value).

From the above comparison, the importance of the condition that the swing angle θ is small is required, and the necessity of correcting by the formula (3) when the swing angle θ is slightly larger is realized.

Table 1 Fixed pendulum length, measuring the oscillation period T with photoelectric timer

Swing angle

frequency

10°

20°

30°

1

2

3

Experimental value

Calculate T/s from equation (3)

/(%)

Calculate T/s from equation (1)

/(%)

Fourth, other system error considerations

In addition to the influence of the swing angle, due to the errors in theory and method, it is necessary to analyze and correct the measurement results from the following aspects.

(1) Correction of the complex pendulum

In the simple pendulum formula (1), we assume that the ball is a mass point and does not count the cycloidal quality. In fact, from the perspective of accurate measurement, the cycloidal mass μ is not equal to zero, and the radius r of the ball is not equal to zero, ie, A rational pendulum, but a complex pendulum that oscillates around a fixed axis. Its period can be expressed as:

m is the mass of the ball, μ is the quality of the cycloid, l is the length of the cycloid, and r is the radius of the ball.

The second and third items are corrections, and the order of magnitude is about 10-4.

(2) Correction of air buoyancy and resistance

Taking into account the buoyancy and resistance of the air, the cycle will increase.

Ρ0 and ρ are the density of air and small balls, and the order of magnitude is about 10-4. The second and third terms are correction items, and the order of magnitude is about 10-4.

Five, matters needing attention

(1) If the cycle is measured with a stopwatch, the ball should be selected to pass the lowest position and start and stop at a fixed position. Or use the difference calculation to reduce the human response error, such as 40 times. And the difference of 10 times.

(2) Pay attention to the experimental conditions of the small swing angle, such as controlling the swing angle θ<5°.

(3) Pay attention to keep the ball swinging in the same vertical plane to prevent the formation of a "cone pendulum".

(4) The instrument provides the diameter of the iron pellet: 20mm.

(5) The light-shielding needle is a hollow plastic cylinder with a length of 15mm and a diameter of 2.7mm. It is inserted into the bottom hole of the ball during the experiment.

[thinking questions]

1. Please think of a method of making a "single pendulum" with a pendulum that is an irregularly shaped heavy object (such as a padlock) and measuring the gravitational acceleration g.

2. Suppose that the swing of a single pendulum is not in the vertical plane, but is used in a conical shape (ie, "cone pendulum"). If no correction is made, the measured g value will be larger or biased under the same swing angle condition. small? why?

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