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 (B)

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 _____.

<p>pairs</p> Signup and view all the answers

Match the following laws of motion with their descriptions:

<p>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.</p> Signup and view all the answers

What does Newton's Second Law of Motion express?

<p>The relationship between force, mass, and acceleration (D)</p> Signup and view all the answers

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

<p>True (A)</p> Signup and view all the answers

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

<p>F = ma</p> Signup and view all the answers

In an isolated system, the total momentum remains _____ .

<p>constant</p> Signup and view all the answers

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

<p>The forces are equal and opposite. (B)</p> Signup and view all the answers

Match the following laws or principles to their descriptions:

<p>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</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

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

<p>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.</p> Signup and view all the answers

Flashcards

Newton's Third Law

Newton's Third Law describes how forces act in pairs between interacting objects. It states that for every force exerted by one object on another, there's an equal and opposite force exerted back by the other object.

Forces Act on Different Objects

The forces described by Newton's Third Law always act on different objects. They never act on the same object.

Force Direction

The forces described by Newton's Third Law always act along the same line, but in opposite directions.

Equal and Opposite Forces

The force exerted by object A on object B is equal in magnitude but opposite in direction to the force exerted by object B on object A.

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Newton's Third Law Derivation

Newton's Third Law is derived from the Second Law when applied to interacting bodies.

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Newton's First Law of Motion (Inertia)

Newton's First Law states that an object at rest will remain at rest, and an object in motion will stay in motion at a constant velocity unless acted upon by an external force. This means the object will maintain its state of motion without changing speed or direction.

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Newton's Second Law of Motion

Newton's Second Law describes how the motion of an object changes when subjected to a force. It states that the force applied to an object is directly proportional to its mass and the acceleration it experiences.

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Newton's Third Law of Motion

Newton's Third Law explains that for every action, there is an equal and opposite reaction. This means that when two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction.

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Conservation of Momentum

The total momentum of a system remains constant in the absence of external forces. Momentum is the product of an object's mass and velocity.

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Action-Reaction Forces

The force exerted by object A on object B is equal in magnitude but opposite in direction to the force exerted by object B on object A.

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Force as Rate of Change of Momentum

The rate of change of momentum of an object is equal to the net force acting on it. This is a restatement of Newton's Second Law.

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Forces and Interactions

A force is the result of an interaction between two or more objects. These interactions can be contact interactions, like pushing a box, or non-contact interactions, like gravity.

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Direction of Force and Acceleration

The direction of force is the same as the direction of acceleration.

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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 FAB is the force A exerts on B.
  • Force FBA is the force B exerts on A.
  • FAB = mBaB and FBA = mAaA

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 (ΔpA + ΔpB = 0).

Step 3: Forces and Momentum Change

  • Force is the rate of change of momentum. FAB = ΔpB/Δt, FBA = ΔpA/Δt
  • Substituting the momentum relationship: FBA = -FAB

Step 4: Newton's Third Law

  • The equation FBA = -FAB 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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