Newton's third law, known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction back on the first object. For example, if person A pushes block B with a force of 50 newtons (denoted as \( F_{AB} = 50 \, \text{N} \)), block B exerts a force back on person A, represented as \( F_{BA} = -50 \, \text{N} \). It is crucial to understand that these forces act on different objects, preventing them from canceling each other out and allowing for movement.
In practical terms, consider the normal force, which is the force exerted by a surface to support the weight of an object resting on it. If block A exerts a downward force due to its weight, the floor exerts an equal upward normal force in response. Another example is gravitational force; while the Earth pulls you down with a force of \( mg \) (where \( m \) is mass and \( g \) is the acceleration due to gravity), you also pull on the Earth with an equal force, though the Earth's massive size results in negligible acceleration.
To illustrate these concepts, consider a scenario where an 80 kg person (A) stands on a frozen lake and pushes a 40 kg ice block (B) with a force of 20 newtons. The force exerted by the person on the block is \( F_{AB} = 20 \, \text{N} \). According to Newton's third law, the block exerts an equal and opposite force on the person, \( F_{BA} = -20 \, \text{N} \). To analyze the motion, free body diagrams for both objects must be drawn, identifying all forces acting on them.
For block B, the only horizontal force is \( F_{AB} \), while for person A, the only horizontal force is the reaction force \( F_{BA} \). Using the equation \( F = ma \), we can calculate the acceleration of each object. For block B, the equation becomes:
\[ F_{AB} = m_B \cdot a_B \Rightarrow 20 \, \text{N} = 40 \, \text{kg} \cdot a_B \Rightarrow a_B = 0.5 \, \text{m/s}^2 \]
For person A, the equation is:
\[ -F_{BA} = m_A \cdot a_A \Rightarrow -20 \, \text{N} = 80 \, \text{kg} \cdot a_A \Rightarrow a_A = -0.25 \, \text{m/s}^2 \]
This example highlights that even though the forces are equal, the resulting accelerations differ due to the mass of each object. The acceleration is inversely proportional to mass, meaning that objects with different masses will accelerate differently when subjected to the same force.