Forces Study Guide

When a force is applied to an elastic material, such as a spring, it tends to change shape. This change in shape, specifically an increase in length, is called extension. The relationship between the applied force and the resulting extension can be either linear or non-linear. A linear relationship means that the extension of the material is directly proportional to the applied force, as long as the elastic limit of the material is not exceeded. This is often represented by a straight line on a force-extension graph, passing through the origin. For example, if you double the force, the extension also doubles. This proportional relationship is described by Hooke's Law (though the law itself is not part of this objective). Within the linear region, the material will return to its original length once the force is removed.

However, materials have an elastic limit. If the applied force exceeds this limit, the material will enter a non-linear region. In this region, the extension is no longer directly proportional to the force. On a force-extension graph, the line will curve, indicating that further increases in force produce disproportionately larger extensions. Once the elastic limit is surpassed, the material may not return to its original length even after the force is removed; it undergoes permanent deformation. Different materials exhibit these behaviours to varying degrees. For instance, a rubber band will show a non-linear relationship over a much wider range of forces compared to a metal spring, which typically has a more distinct linear region followed by a clear non-linear region when stretched beyond its elastic limit. Understanding these relationships is crucial for designing and using materials effectively in engineering and everyday applications, ensuring they perform as expected without permanent damage.

When an object is in free fall, it is accelerating due to the force of gravity acting upon it. On Earth, this acceleration is approximately 9.8 m/s². This value is often rounded to 10 m/s² for simplicity in many calculations at a Foundation level, but it's important to remember the more precise value. This acceleration means that for every second an object falls, its speed increases by 9.8 meters per second. For example, if an object is dropped from rest, after 1 second its speed will be 9.8 m/s, after 2 seconds its speed will be 19.6 m/s, and so on, assuming no air resistance. This constant acceleration applies to all objects near the Earth's surface, regardless of their mass, in the absence of air resistance. This is a fundamental concept in physics, demonstrated famously by Galileo Galilei, who showed that objects of different masses fall at the same rate. The force responsible for this acceleration is gravity, and it acts towards the center of the Earth.