A spring is a coiled piece of metal or plastic that has the property of stretching when pulled and compressing when pushed. To study the behavior of springs in the lab, one end is usually attached to a fixed support while the other end is free so that forces can be applied. A force applied to the free end of the spring stretches the spring by an amount, ∆x, measured from the equilibrium position – the position of the free end when no force is applied. With the force applied to the spring, the spring now comes to rest in a new position. If we apply Newton’s Laws to the mass attached to the spring in the figure shown below, it is clear that the gravitational force of the mass on the spring must be balanced by a force from the spring in order for the spring-mass system to remain at rest. This force is called the spring force, Fs. The spring force is an example of a type of force referred to as a restoring force. This name comes from the fact that the spring force tries to restore the spring to its original un-stretched position where it is “comfortable” (the spring doesn’t like to be stretched nor compressed). Robert Hooke was the first to investigate the relationship between the applied force and the extension of the spring and deduced the law for elastic springs called Hooke’s Law in his honor. His law expresses a direct relationship between the applied force and the extension of the spring. Mathematically, Hooke’s law can be stated as Fa=k∆x. Fa stands for the applied force. The actual statement of Hooke’s law is Fs=-k∆x, where Fs is the spring force, the negative sign indicates the restoring nature of the spring force, and k is the constant of proportionality called the spring constant (some call it the force constant) that depend on the material and number of coils of the spring; k indicates the “stiffness” of the spring – the larger the value of k, the stiffer the spring. In this lab, you will determine the spring constant of two different...
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