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Newton's Laws: Third Law Derivation

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Questions and Answers

Which statement best summarizes Newton's Third Law?

For every action, there is no reaction.

For every action, there is an equal and opposite reaction. (correct)

For every action, the resultant force is always zero.

For every action, there is a greater reaction.

According to Newton's Third Law, the forces between two objects act along different lines.

False

What does Newton's Third Law imply about the interaction between two objects?

There is a mutual exchange of forces, where each object exerts an equal and opposite force on the other.

Newton's Third Law emphasizes that forces arise in _____.

pairs Signup and view all the answers

Match the following laws of motion with their descriptions:

Newton's First Law = An object at rest stays at rest unless acted on by a net external force. Newton's Second Law = The acceleration of an object is directly proportional to the net force acting on it. Newton's Third Law = For every action, there is an equal and opposite reaction. Signup and view all the answers

What does Newton's Second Law of Motion express?

The relationship between force, mass, and acceleration Signup and view all the answers

According to Newton's Third Law, for every action, there is an equal and opposite reaction.

True Signup and view all the answers

What is the equation that represents Newton's Second Law of Motion?

F = ma Signup and view all the answers

In an isolated system, the total momentum remains _____ .

constant Signup and view all the answers

Which of the following statements is a direct implication of Newton's Second Law when two bodies interact?

The forces are equal and opposite. Signup and view all the answers

Match the following laws or principles to their descriptions:

Newton's First Law = An object at rest stays at rest unless acted upon by an external force Newton's Second Law = Force equals mass times acceleration Newton's Third Law = For every action, there is an equal and opposite reaction Conservation of Momentum = Total momentum in an isolated system remains constant Signup and view all the answers

Momentum of an object is defined as the product of its mass and acceleration.

False Signup and view all the answers

What do the symbols F_{AB} and F_{BA} represent?

F_{AB} is the force exerted by body A on body B, and F_{BA} is the force exerted by body B on body A. Signup and view all the answers

Study Notes

Newton's Third Law Derivation from Newton's Second Law

Newton's First Law describes motion in the absence of forces (inertia).
Newton's Second Law relates force (F) to mass (m) and acceleration (a): F = ma
Newton's Third Law explains forces as interactions between two objects.

Step 1: Newton's Second Law and Interaction

Newton's Second Law applies to isolated objects, describing how forces change their motion.
Forces arise from interactions between objects.
Consider two interacting objects (A and B).
Force F_AB is the force A exerts on B.
Force F_BA is the force B exerts on A.
F_AB = m_Ba_B and F_BA = m_Aa_A

Step 2: Conservation of Momentum

Conservation of momentum: Total momentum in an isolated system remains constant.
For interacting bodies, change in momentum of A = - change in momentum of B (Δp_A + Δp_B = 0).

Step 3: Forces and Momentum Change

Force is the rate of change of momentum. F_AB = Δp_B/Δt, F_BA = Δp_A/Δt
Substituting the momentum relationship: F_BA = -F_AB

Step 4: Newton's Third Law

The equation F_BA = -F_AB demonstrates Newton's Third Law: For every action, there is an equal and opposite reaction.
This means the forces are equal in magnitude and opposite in direction.
The forces act along the same line.

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Description

Explore the derivation of Newton's Third Law from the framework of Newton's Second Law. This quiz examines how forces are interactions between objects and illustrates the conservation of momentum in isolated systems. Test your understanding of these fundamental principles in physics.