The equivalent method sets the spring's gravity to G, the stiffness coefficient to k, and the horizontal placement to a length of l0. When suspended vertically, the deformation effect of gravity on the whole spring is equivalent to the deformation effect of gravity acting only on the half of the center of gravity. The stiffness coefficient of the spring is 2k, and the resulting deformation is x=G/ 2k. When the force F is applied to the lower end of the entire spring to produce a large deformation such as the action of gravity G, F = kx = G/2, which is not the F = G in the answer.
However, because the spring is suspended vertically, the influence of gravity on different parts of the spring is different, and the spring as a whole is sparsely dense, and it is impossible to determine whether the equivalent method is correct. The calculus method is used to analyze the influence of spring weight on the shape variable.
The gravity of the spring is G, the stiffness coefficient is k, and the length is l0 when placed horizontally, then the spring stiffness coefficient of part l is k'=l0lk, and the gravity of part dl is dG=Gl0dl. When the spring is vertically suspended, The deformation force of the spring part of the dl part is dx, then dx=dGk'=Gll20kdl, and the total shape variable generated by the total gravity of the spring is x, then x=∫l0Gll20kdl=G2k.
From this point of view, the shape variable generated by the gravity of the spring itself is x=G/2k, which is correct by the previous equivalent method.
The experiment verifies that the spring itself exerts the gravitational force to generate the shape variable x, and the shape variable generated by the heavy object at the lower end of the spring is x'. If the above conclusion is true, x=G/2k, x'=G/k, x=x'/2 should be observed in the experiment. For the convenience of experiment, use white paint on one soft spring to mark two white points on one end and the middle of the spring, so that one long spring is divided into two springs of the same mass (the same number of turns), with 2 white points The spring is used as the research object (called white spring for convenience), and the length of the white spring when it is placed horizontally is l0=8.90cm; when the white spring is suspended vertically at the lower end, the length of the white spring is l1= 9.00cm, as shown; when the white spring is suspended vertically at the upper end, the length of the white spring is l2 = 9.20cm.
Then the white spring itself exerts a shape variable of x=l1-l0=0.1cm, and a force F equal to the gravity is applied to the lower end of the white spring to generate a shape variable x'=l2-l1=0. 2cm, thereby obtaining x=x'/2, the above conclusion is completely correct.
Note to the experiment: 1) No need for the quality of the balance spring. If the balance is used to measure 2 the natural length of the white spring 3 the length of the white spring at the lower end 4 the length of the white spring at the upper end is the specific mass of the spring, it is not convenient to find a heavy object such as a spring to suspend the operation, using the weight of the measurement quality It is not easy to add upstream code quality for operation when hanging.
2) The spring of the experimental spring is not measured by a spring balance. The spring force of the experimental soft spring is small, the reading error is large when the spring balance is measured, and the gravity of the spring scale itself has a great influence on the reading when the spring balance is pulled vertically.
3) Do not use dense springs without gaps. When such springs are placed horizontally, the inner springs are in close contact with each other due to the inherently strong contraction elastic force. The internal contraction elastic force will cancel the effect of a part of the spring gravity when the spring is vertically suspended, resulting in a large experimental error.
Correction From the above investigation, the constant C=G/2 in the equation of the linear equation F=kx-C is known. In the physics, the specific influence of the spring's own gravity on the deformation is not studied in depth. Therefore, the specific calculation of the spring's own weight should not be discussed in the experimental exercises to verify Hooke's law. The most reason for analyzing the F2x image is that the origin is: horizontally placed in the experiment. The natural length of the time is the original length, in fact, the natural length of the spring when it is vertically suspended is the original length; or the spring weight has an influence on the shape variable.
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