The suspension point at the upper end of the cycloid should be fixed to prevent the pendulum length from changing.
(2) Measure the pendulum length with a meter ruler and vernier caliper.
Direction: the swing length should be the distance from the suspension point to the center of the ball, that is, L = L+D/2; Where l is the length of the cycloid from the suspension point to the sphere, and d is the diameter of the sphere.
Measure the time t of swinging the pendulum ball for 30 times with a stopwatch, and calculate the period t 。
Direction: In order to reduce the timing error, the countdown method is adopted, that is, when the pendulum ball counts from the open position to the balanced position, "3,2, 1, 0, 1, 2,3 ..." When the button counts to "0", the pendulum ball vibrates for 30 times.
Starting from the balance position is because the swing speed is the highest here, and people judge that the timing error is small when it passes through this position.
In order to reduce the system error, the swing angle A should be less than 5, which can be roughly measured by a protractor or the ratio of its amplitude A to the swing length L can be controlled by a ruler. When A/l 1 m and the deflection angle is not more than 5, let the length of the hanging point on the surface of the metal ball be L, the radius of the ball be r=D/2, and the cycloid length l=L+r can not be ignored.
During the experiment:
What is puzzling is the number of times the pendulum passes through the equilibrium position and the total number of vibrations.
Error-prone: find the value of g by mirror image method, and g≠k is g = 4π 2/k; T=t/n and T=t/(n- 1) are also often misused, (the former means to set the balance position number "0" to start timing, and the latter means to set the number "1" to start timing).
It is easy to forget that the radius of the ball is omitted or increased, and the suspension point is not fixed; I forgot to measure it several times, and g was averaged.
[Experimental conclusion]
Judging from the g calculated in the table, it is about equal to the standard g value found at that time, and its effective figure is at least 3 digits.
3. Experimental flexibility
Flexibility (1): change the equipment, replace the iron platform with the balcony of the teaching building, replace the pendulum ball with a small padlock tied with a few meters of nylon thread, measure only a cycloid with a meter ruler, and measure the local gravity acceleration with a stopwatch during the period t. The brief method is as follows: As shown in Figure 2-46, set the hanging point on the balcony to O, and make a red mark on the pendulum length near the padlock.
T12 = 4π 2 (L1+L2)/g ... ① Relax (or fold) a section of line at the suspension point, and then measure OM = L2, Mo' = l0 unchanged, then T2 = 4π 2 (L2+l0)/g...② 。
According to ① ② formula, g = 4π 2 (L2+L1)/(t 1 2-t22) (where t1,the measurement method of T2 is the same as above).
This experiment can also be solved by T2-l mirror image method.
Change (2): Change equipment and objects. On the surface of the earth, with the help of TV, according to the periodic law, the acceleration of free falling body on the surface of the moon is measured with a mechanical watch.
A physicist watched the astronauts land on the moon on TV. He found a heavy object hanging in the moon landing capsule, and its rope length was almost the height of the astronaut. So he looked at his watch and recorded the number of times the weight passed through the lowest point in a period of time. Even in G months, he knew that he recorded the time from the first time the weight passed through the lowest point to n=30 times. T was 1 minute 12.
T=t/[(n- 1)/2] and T=2π√(L/g).
Change (3): Roughly measure the radius of concave mirror (or concave lens) with stopwatch, caliper and small steel ball. The brief method is as follows:
Place concave mirror horizontally and put a small steel ball on it, as shown in Figure 2-47. If the ball slides, it is not difficult to prove that its vibration is completely similar to the resonance of a simple pendulum with a pendulum length of R-R. 。
R=gT2/4π2+r from T=2π√((R-r)/g) As described in the experimental regulations, R can be measured with calipers.
Variation (4): Measure the density of geology and mineral resources with stopwatch and simple pendulum. The brief method is as follows:
G=4π2l+T2 from T=2π√(L/g) and G = 4/3g π r * * from mg=GMm/R2, ρ=3πl/(GT2R) where L and T can be measured by laboratory methods, and R≈ radius of the earth.
Note: This formula ρ=3πl/(GT2R) should not be confused with ρ=3π/(GT2). The former T is the period of simple pendulum measurement, and the latter T is the period of satellite running on the planet surface.
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