Spring original length measurement

The original length of the spring is the length of the spring without any external force. It is not easy to create such an environment when doing experiments on the ground. If the spring is hung up, the spring will stretch due to its own gravity. If the spring is placed on the horizontal table, it will cause great error due to the influence of friction. Therefore, we can use the extrapolation method to measure the original length of the spring.

According to Hooke’s law, the spring length L = l0 + F / K

L0 is the original length of the spring, f is the external force on the spring, and K is the stubborn coefficient of the spring. A series of corresponding l0 can be obtained by changing the external force F. Make the L ~ F diagram and extrapolate the diagram line to the case of F = 0 to obtain the original length of the spring.

Experimental equipment

One spring and several weights.

Specific process

Hang the spring to be tested vertically, and hang a small disc with a mass of M0 at the lower end.

Add a weight with mass m into the small disc (to make the spring have an obvious elongation), and measure the length L of the spring.

Increase the weight in the small disc, measure the spring length and repeat it seven times (the spring extension does not exceed its elastic limit).

The abscissa represents f = (M + M0) g, the ordinate represents the spring length L, and the L ~ F diagram is made.
Extrapolate the graph line to f = 0, that is, calculate the intercept of the graph line on the L axis, which is the original length l0 of the spring.

The experimental data are as follows:

M + M0 (g) 80 90 100 120 140 150 160
L (m) 0182 0193 0202 0224 0.242 0.250 0.263
Fit the L ~ F line with a ruler, and calculate the slope of the line from the line, a = 0.100m/n, and the intercept l0 = 0.102m.

The linear regression method is used to calculate the linear slope a = 0.0997 M / N, intercept l0 = 0.103 m, correlation coefficient r = 0.9995, intercept error △ l0 = 0.002 m, so the original length of the spring is 0.103 #0.002 M