Experimental study on the application of spring to investigate the external force of liquid phase

Make a note of the product of the upper end of the spring and the number of turns of the platform lowering knob and the pitch, ie s, then the elongation of the spring is s-s0, the spring is replaced by an elongated metal rod, and the operation of pulling the water film is the same as above. The difference between the two readings is the height of the liquid film h=sc-sc0, and the measurement formula of the surface tension coefficient of water is: a=k(s-s0)-LdhQg2(L+d) (1) where k The spring constant of the spring; L is the length of the wire; d is the diameter of the wire; h is the height before the water film is broken; Q is the density of water; g is the acceleration of gravity; LdhQg is the weight of the water film, One is not big and can be ignored.

The surface tension coefficient of the spring is measured by five springs with different elastic coefficients, data recording and processing. Because of the dnL in the experiment, the obtained data is substituted into A=k(s-s0)2L, and the obtained theoretical value of A is subtracted from the actual value of A, which is $A.

3 Theoretical analysis In the case of ignoring the gravity of the water film, the formula (1) can be changed to: A = k(s - s0) 2 (L + d) (2) Since A is based on the direct measured value k, s, s0, L, d calculated, namely: A = f (k, s, s0, L, d), and each direct measurement in the equation is measured several times under the same conditions, so its synthesis uncertainty For: uc(A)=Au2(k)+u2(s)+u2(s0)+u2(L)+u2(d)(3) In this experimental theory, suppose u(s), u(s0), u(L) and u(d) are constant, such that equation (3) becomes uc(A)WAu2(k)+c(4) where c is a constant.

According to Hooke's law, f=kx can be obtained, from which k=f/x can be solved. Since uc(f)=u2A(f)+u2B(f), uc(x)=x2A(x)+u2B (f) Thus, the synthetic uncertainty is: uc(k)=u2c(f)+u2c(x)(5) Assuming uf(f) and uc(x) are the same when measured with springs of different elastic coefficients The value of (5) is larger by equation (5), and uc(k) is larger, and then equation (4) shows that Au2(k)+c is also larger.

In addition: It can be obtained from experiments that the larger k is, the larger uA(s) and uA(s0) are. In summary, the greater the spring coefficient, the greater the uncertainty caused by the spring, that is, the greater the error.

Results Discussion The k-$A curve was calculated from the experimental data. As shown, it can be seen that as the elastic coefficient k increases, $A gradually decreases. When the experimental allowable error is 5%, that is, the actual value of A is allowed to be maintained in the A (1-0105), during the entire lifting process of the spring, whether it is always maintained/three-line aligned 0, etc., in addition, with spring pairs of different elastic coefficients The measurement results will also have a large impact. In order to avoid excessive errors caused by the selection of the spring coefficient of elasticity is unreasonable, a spring with a small spring constant should be used. Therefore, by mastering the more accurate experimental methods and understanding the reasons for the error, the accuracy of the measurement can be improved.

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