Compressed Springs

Energy can be stored in springs and released as the spring uncoils. This mechanism is commonly found in mechanical clocks that are wound. The more the spring is compressed, the more energy it holds; however, due to the nature of springs, it takes more effort (or force) the further the spring is to be compressed (See table below). The units for force are Newtons (N) where 1 Newton is the amount of force needed to accelerate a mass of 1 kilogram 1 meter per second per second. The energy stored inside the spring is represented by the area beneath the curve on a graph of the compressional force versus the distance compressed. For the following data, plot the points with the x-axis denoting the distance compressed and the y-axis denoting the force, or the effort used to compress the spring.

Displacement versus compressional force

Connect these points with the curve you think is best.

To find how much energy is stored inside the spring when it is compressed to 1 meter, you need to find the area under the curve from x = 0 to x = 1. Using this idea, find the amount of energy stored inside the spring when it is compressed 1 meter, 2 meters, and 4 meters. Explain how you calculated the area and make sure to express your answers in the correct units.