Forces Study Guide

Newton's First Law of Motion, often called the Law of Inertia, states that an object will remain at rest, or in uniform motion in a straight line, unless acted upon by a net (resultant) external force. This means that if the net force acting on an object is zero, its velocity will not change. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Therefore, if the net force is zero, the object's speed will remain constant, and its direction of motion will also remain constant. This describes an object moving with uniform velocity.

Conversely, if an object's speed changes, its direction changes, or both its speed and direction change, then its velocity is changing. A change in velocity is known as acceleration. According to Newton's First Law, acceleration can only occur if there is a non-zero net external force acting on the object. This net force is responsible for altering the object's state of motion. For example, if a car speeds up, there is a net forward force; if it slows down, there is a net backward force; and if it turns a corner at constant speed, there is a net centripetal force acting towards the center of the turn, changing its direction. Understanding this law allows us to predict how objects will move based on the forces acting upon them.

When a spring or other elastic object is stretched, a force is applied to it, causing a displacement. Work is done to deform the object. This work done is stored as elastic potential energy within the object. The relationship between the force applied to a spring and its extension is described by Hooke's Law, which states that force (F) is directly proportional to extension (x), provided the elastic limit is not exceeded. So, F = kx, where 'k' is the spring constant.

However, the force needed to stretch a spring is not constant; it increases as the extension increases. Therefore, simply multiplying the maximum force by the extension (F × x) would give an incorrect value for the work done. Instead, we use the average force. Since the force starts at 0 and increases linearly to F (at extension x), the average force is (0 + F) / 2 = F/2. The work done (W) is then given by the average force multiplied by the extension: W = (F/2) × x.

Substituting F = kx into this equation, we get W = (kx/2) × x, which simplifies to W = (1/2)kx². This formula allows us to calculate the work done in stretching or compressing a spring or other elastic object, given its spring constant and the extension or compression. It's crucial to ensure that units are consistent: force in Newtons (N), extension in metres (m), and the spring constant in Newtons per metre (N/m). The work done will then be in Joules (J).