Question

Newton's third law of motion leads to the law of conservation of (A) Angular momentum (B) Energy (C) mass (D) momentum

Short answer

The correct answer is (D) momentum. The conservation of momentum is a direct consequence of Newton's third law of motion, as the equal and opposite forces between two interacting objects leads to equal and opposite changes in their momentum, thus conserving total momentum in a closed system.

Step-by-step solution

Option A: Angular momentum

Newton's third law of motion is primarily concerned with linear forces acting upon objects. While angular momentum can be conserved in certain scenarios, it is not a direct consequence of Newton's third law. This option is incorrect.

Option B: Energy

Conservation of energy refers to the principle that both kinetic and potential energy in a closed system remains constant. While energy conservation is an essential principle in physics, it is not a direct result of Newton's third law of motion. So this option is incorrect.

Option C: Mass

Conservation of mass refers to the principle that the total mass of substances in a closed system remains constant. While it is a fundamental concept in chemistry and thermodynamics, it is not a direct outcome of Newton's third law of motion. This option is incorrect.

Option D: Momentum

Momentum is the product of mass and velocity. According to Newton's third law, the forces between two objects are equal and opposite; therefore, when the objects interact with each other, their momentum change is also equal and opposite. This leads to the conservation of total momentum in a closed system of interacting objects. So the consequence of Newton's third law of motion is the conservation of momentum. Thus, the correct answer is (D) momentum.

Key concepts

Law of Conservation of Momentum

The law of conservation of momentum is a fundamental principle in physics. It states that the total momentum of a closed system remains constant, provided no external forces are acting on it. Momentum is defined as the product of an object's mass and its velocity, represented by the equation: \[ p = mv \] where \(p\) is momentum, \(m\) is mass, and \(v\) is velocity. In any interaction between two or more objects, such as a collision, the total system momentum before and after the event remains the same. This is because the forces they exert on each other are internal to the system. Newton's third law plays a crucial role here as it states that for every action, there is an equal and opposite reaction. When two objects interact, they apply forces to each other that are equal in magnitude and opposite in direction. This mutual interaction results in the transfer of momentum between the objects, without changing the total momentum, leading to its conservation.

Linear Forces

Linear forces are those that occur along a straight line, affecting the linear motion of objects. These forces influence the velocity and direction of an object's motion. Examples of linear forces include gravitational force, frictional force, and tension. In the context of Newton's laws, linear forces are crucial because they determine how forces interact with objects in a linear direction. Newton's third law of motion is often linked with linear forces. When an object experiences a force, it exerts an equal force in the opposite direction on the source of the initial force. This concept explains why, when you push on a wall, the wall pushes back with equal force (even though it does not move). Understanding linear forces helps in the analysis of motion in a straight line, such as vehicles moving on a road or objects being lifted vertically. By recognizing how linear forces act, one can predict the movement of objects under various force conditions.

Newton's Laws of Motion

Newton's laws of motion consist of three key principles that govern the behavior of objects in motion. These laws are foundational to classical mechanics and explain how forces affect an object's movement.

• The first law, or the law of inertia, states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by a net external force.
• The second law establishes the relationship between force, mass, and acceleration: \( F = ma \). This law quantifies how forces cause an object to accelerate.
• The third law states, for every action, there is an equal and opposite reaction, which is critical in understanding interactions between objects.

These laws collectively describe how objects interact through forces, clarifying that the movement of objects is predictable and quantifiable. They also provide the basis for more complex concepts, such as momentum and energy conservation.

Closed System in Physics

A closed system in physics is one that is isolated from any external influences that might affect its internal conditions. This means no outside forces or energies are added or removed from the system. In such a system, the laws of conservation, such as conservation of momentum and energy, are especially pertinent. When considering momentum, a closed system allows the total momentum before and after any interactions within the system to remain constant because external forces do not disturb it. This makes closed systems particularly useful in experimental physics, where variables need to be controlled to study specific interactions. Additionally, closed systems are not influenced by external heat exchanges or mass transfer, meaning internal energy states remain unchanged unless internal reactions occur. This concept is essential in thermodynamics and mechanics, helping physicists and engineers predict how systems behave under isolation.