Springs
From MyMCAT
Introduction
One specific example that is common in the MCAT is the concept of the spring. Springs, like many other objects are capable of producing a force on the object they are attached to, however, this force will change depending on how stretched (or compressed) the spring actually is.
The Force of a Spring
Consider what happens when we are holding a spring attached to the wall. Initially, no resistance is felt because we aren't pulling on the other end, but as we begin to stretch out the spring we feel a stronger and stronger pull backwards, thus the force must increase with the distance we have pulled it outwards. Secondly, this distance is not based on the length of the spring itself (or we would have felt something initially) rather it must be based on only the change in the length we have made. These concepts can easily be expressed in a mathematical expression known as Hooke's Law,
X in this expression is the distance the spring is stetched (or compressed) and thus the change in the total length, not the length of the spring itself. K, is a constant known as the spring constant, and is related entirely on the spring given. The negative sign indicates that the direction of the force F is exactly opposite of the direction that the spring was stretched, thus the spring always tries to resist your pull.
The Spring Constant
If we examine the formula further, one will notice that the units of K must be N/m. Thus knowing K can provide very useful information about the spring in question. Consider two springs of equal length but one is made out of steel and the other rubber. A steel spring would obviously have a stronger force than a rubber spring if they were pulled back the same amount, thus the spring constant K for steel must be much higher than K for rubber.
