Thank you, Mr. Wang Sihui from Nanjing University, for sharing two home experiments with us. The two experiments were published in the 5th issue of physical experiments in 2007.
Experiment 1: measure the moment of inertia and acceleration of gravity of hanger: bracket, hanger, stopwatch, ruler, weight (small weight is enough), tape, line, white paper, scissors principle: the cycle formula of compound pendulum is
(1) In the formula, t is the period of the compound pendulum, X is the distance from the center of mass of the compound pendulum to the axis of rotation, a is the radius of rotation, G is the acceleration of gravity, l = x + X 'is the effective length of the pendulum, X' = A2 / X is the conjugate point of X: if the distance from the axis of rotation to the center of mass is x, the corresponding period is t, and if the axis of rotation passes through the point X 'on the compound pendulum, the period is still T, then x and X' points are conjugate points.
In general, there are two methods to measure the acceleration of gravity with a compound pendulum. Method 1: using the property that the period of conjugate point of compound pendulum is equal, the conjugate point X and X 'can be obtained by measuring the relationship between T and X, so as to determine a and G. Method 2: another property of the compound pendulum is that when x = a, the period of the compound pendulum has a minimum value. It is also a common method to find the minimum value by measuring the relationship between T and X. However, due to the simple structure of the hanger compound pendulum, it is unable to adjust the turning radius, and there are not enough measuring fulcrum on the hanger, the above two methods are generally not feasible. The reference scheme of hanger compound pendulum is as follows: 1) make heavy hammer with weight and line, and determine the position of hanger center of mass with heavy hammer. Hang the different positions of the hanger on the horizontal axis (knife edge, thin rod, nail, etc.), fasten the heavy hammer line on the axis, hang the lower end, draw the outline of the hanger and the heavy hammer line on the white paper, and the intersection of the two lines is the centroid position. Draw the hanger and center of mass on white paper. 2) Fix another weight (the mass is M0, if there is no balance, the one yuan coin can be used as the reference mass) on the clothes rack far away from the center of mass, determine the position of the center of mass again, and draw it on the white paper. Using the definition of center of mass to calculate the mass of hanger.
3) Using different positions of the hanger as fulcrum, it is suspended on the shaft to make it swing at a small angle in a plane. Measure the time of 20-30 cycles, calculate the corresponding cycle T, measure the distance X between the fulcrum and the center of mass, measure as many sets of X and T values at different positions as possible, and list the results. 4) The method of data processing is to deform (1), in which. The values corresponding to y are calculated and plotted by using the measurement results, and G sum is given by slope and intercept.
Experiment 2: Pencil compound pendulum experiment pencil compound pendulum experiment uses a property of strike Center: the distance from strike center to suspension point on rigid body is exactly the effective pendulum length of compound pendulum, that is, strike center and suspension point are just a pair of conjugate points mentioned above, so the following simple experiment is designed.
Equipment: pencil, automatic lead core, bracket, transparent tape, stopwatch, ruler experiment scheme: 1) place the automatic lead core horizontally, one end is fixed on the bracket with transparent tape, the other end is managed to support (no need to fix). The lead core is used as a rotating shaft, and the hook of the pencil cap is hung on the lead core. The pencil can swing with the lead core as the shaft. 2) Use another pen to tap the lower end of the pen along the direction of the lead core, and observe the movement direction of the hanging end of the lead core at the moment of knocking. Change the striking point many times, and find out the striking point which makes the hanging end (the hanging point of the pen cap) almost have no displacement. Measure the distance L from the point to the suspended lead core. 3) Measure the value of swing period T of pencil on the device. The acceleration of gravity can be obtained by using. This experiment doesn't even need the special equipment in the laboratory. The usual student stationery is enough.
Practice and Thinking:
(1) Can the moment of inertia of pencil be determined from the above data? How to determine? (2) The relation curve between the period of the compound pendulum and the distance x from the center of mass to the rotating axis is qualitatively described, and the minimum value of the period is proved to be. (3) The relationship between the strike center and the effective swing length is proved.
Excerpt from: Wang Sihui, Su Weining, Zhou Jin. Simplification and deepening of college physics experiment [J]. Physics experiment, 2007,27 (5): 27
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