Springs：練習問題

Two identical springs, each with a force constant \(k\), are connected in parallel to support a load \(W\). What is the total extension of the system compared to a single spring supporting the same load?

Two identical springs, each with a force constant of \(400 \text{ N m}^{-1}\), are connected in series. A 2.0 kg mass is suspended from the bottom of the combination. What is the total elastic potential energy stored in the system of two springs?

A student hangs a mass of 250 g from a vertical spring. The spring extends by 1.5 cm and remains within its limit of proportionality. Calculate the force constant \(k\) of the spring.

A spring with a force constant \(k\) is used in a testing rig. When a force \(F\) is applied, the spring stores a certain amount of elastic potential energy \(E\). If the applied force is doubled to \(2F\) and the spring still obeys Hooke's law, what is the new elastic potential energy stored in the spring?

A student hangs a weight of \(4.0\text{ N}\) from a spring, causing it to extend by \(0.05\text{ m}\). Calculate the force constant \(k\) of the spring, assuming it obeys Hooke's law.

A spring has a force constant of \(120\text{ N m}^{-1}\). Calculate the work done in stretching the spring from an initial extension of \(0.02\text{ m}\) to a final extension of \(0.05\text{ m}\).

A load-extension graph is plotted for a copper wire until it breaks. Describe how the graph can be used to distinguish between the elastic region and the plastic region of the deformation, and explain what happens to the energy supplied during plastic deformation.

A metal spring has an unstretched length of 0.150 m. When a mass of 450 g is suspended from the spring, its length increases to 0.185 m. Assume the spring obeys Hooke’s law.

(a) Calculate the force constant \( k \) of the spring. [2]
(b) Calculate the elastic potential energy stored in the spring when the 450 g mass is attached. [2]
(c) A second identical spring is connected in parallel with the first. The same 450 g mass is now suspended from the center of a bar connecting the two springs. Calculate the new total extension of the system. [1]

A student investigates a spring system composed of three identical springs, each with a force constant \(k = 250\text{ N m}^{-1}\) and an original length of \(12.0\text{ cm}\). The student connects two of these springs in parallel, and then connects the third spring in series with this parallel pair. The entire combination is suspended vertically from a fixed support, and a mass of \(0.60\text{ kg}\) is hung from the bottom of the system.