Question

A spring has a spring constant ________. The natural length of the spring is ________ meters long. The work done in compressing it from ________ meters long to ________ meters long is ________ newton-meters (also known as joules). The work done to compress it from ________ meters long to ________ meters long can be expressed as an integral of the form ________.

Answer 1

The force constant of a spring is a measure of its stiffness and can be calculated using the equation W = 1/2k(x2^2 - x1^2). The unloaded length of a spring can be obtained by measuring its length when no external force is applied.

Step-by-step explanation:

The force constant of a spring is a measure of its stiffness and is represented by the symbol k. The natural length of the spring refers to its unstretched length. The work done in compressing the spring can be calculated using the equation W = 1/2k(x2^2 - x1^2), where x1 and x2 are the initial and final displacements of the spring respectively.

For example, in question 38, if it takes 500 J of work to compress a spring by 10 cm, we can use the equation to find the force constant as k = 2W / (x2^2 - x1^2) = 2*500 / (0.1^2 - 0^2) = 10,000 N/m.

Similarly, the unloaded length of the spring can be determined by measuring its length when no external force is applied to it.