Solved Examples of Action-Reaction Pairs in Mechanics

📚 Quick Study Guide

• 🍎 Newton's Third Law: For every action, there is an equal and opposite reaction. This means that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
• 💪 Action-Reaction Pairs: These forces always act on *different* objects. It's crucial to identify which object is exerting the force and which object is receiving it.
• 📏 Equal in Magnitude: The magnitude (size) of the action force is exactly the same as the magnitude of the reaction force. Mathematically, if $F_{AB}$ is the force of A on B, and $F_{BA}$ is the force of B on A, then $|F_{AB}| = |F_{BA}|$.
• 🧭 Opposite in Direction: The direction of the action force is opposite to the direction of the reaction force. Using the same notation as above, $F_{AB} = -F_{BA}$.
• 💡 Simultaneous: Action and reaction forces occur at the same time. There is no time delay between the action and the reaction.
• 🏋️ Examples: Common examples include a person pushing against a wall (the wall pushes back), a book resting on a table (the table supports the book), and a rocket expelling gas (the gas pushes the rocket forward).

🧮 Practice Quiz

1. Which of the following statements best describes Newton's Third Law?

   1. A) Every action has an equal and opposite reaction.
   2. B) An object in motion stays in motion unless acted upon by a force.
   3. C) Force equals mass times acceleration.
   4. D) Energy cannot be created or destroyed.

2. A book is resting on a table. What is the reaction force to the weight of the book?

   1. A) The weight of the table.
   2. B) The force of the book on the table.
   3. C) The force of the table on the book.
   4. D) The force of gravity on the table.

3. A person pushes against a wall. What is the action-reaction pair?

   1. A) The person pushing on the wall and the friction between their shoes and the floor.
   2. B) The person pushing on the wall and the wall pushing back on the person.
   3. C) The person pushing on the wall and the weight of the wall.
   4. D) The person pushing on the wall and gravity pulling on the person.

4. A rocket expels hot gas downwards. What is the reaction force?

   1. A) The weight of the rocket.
   2. B) The hot gas pushing downwards.
   3. C) The rocket moving upwards.
   4. D) The gas pushing the rocket upwards.

5. A car is accelerating forward. What force propels the car forward?

   1. A) The engine.
   2. B) The force of the tires pushing backward on the road.
   3. C) The force of the road pushing forward on the tires.
   4. D) The air resistance.

6. Two ice skaters push off each other. If skater A has a mass of 50 kg and skater B has a mass of 75 kg, and skater A accelerates at 2 m/s², what is the magnitude of the force that skater B experiences?

   1. A) 50 N
   2. B) 75 N
   3. C) 100 N
   4. D) 150 N

7. A bird is flying through the air. What is the action-reaction pair that allows the bird to fly?

   1. A) The bird flapping its wings and the wind pushing against the bird.
   2. B) The bird pushing air downwards and the air pushing the bird upwards.
   3. C) The bird's weight and the lift force.
   4. D) The bird's forward motion and air resistance.