Newton’s Third Law of Motion: Exploring Action and Reaction
Newton’s Third Law is one of the most famous principles in physics, often summarized by the statement: “For every action, there is an equal and opposite reaction.” Despite its simplicity, the Third Law is fundamental to understanding the interactions between objects in our universe.
This comprehensive guide will dive deep into Newton’s Third Law, its applications, and how to approach problems involving action-reaction force pairs, with insights into concepts like Atwood machines and practical examples. Let’s explore the core of classical mechanics!
Understanding Newton’s Third Law
The Law Defined
Newton’s Third Law states:
“For every action, there is an equal and opposite reaction.”
Key Concepts
Force Pairs: Forces always occur in pairs. When one object exerts a force on another, the second object exerts an equal and opposite force back on the first.
Equal Magnitude, Opposite Direction: Action and reaction forces are equal in magnitude but act in opposite directions.
Interacting Objects: The two forces in the action-reaction pair act on different objects, which is why they don’t cancel each other out.
Types of Forces: The Third Law applies universally to all forces, whether gravitational, electromagnetic, or frictional.
Everyday Examples
Walking: When you push the ground backward with your feet, the ground pushes you forward with an equal force.
Swimming: As you push water backward, the water pushes you forward.
Launching a Rocket: Exhaust gases push downward, and the rocket is pushed upward with an equal force.
Action-Reaction Force Pairs
How to Identify Force Pairs:
Identify the two objects interacting.
Determine the direction of the force each object exerts on the other.
Recognize that these forces are equal in magnitude and opposite in direction.
Common Force Pairs in Physics
Frictional Force: The force of friction between two surfaces in contact is an example of an action-reaction pair.
Action: Object A applies frictional force to Object B.
Reaction: Object B applies frictional force to Object A.
Tension Force: Forces in a rope or cable also form a pair.
Action: The object pulls the rope.
Reaction: The rope pulls the object.
Gravitational Force: The force of gravity acts as an action-reaction pair between two masses.
Action: Earth exerts a gravitational pull on the moon.
Reaction: The moon exerts an equal gravitational pull on Earth.
Applications of Newton’s Third Law
Atwood Machines
An Atwood machine consists of two masses connected by a string over a pulley. It’s a classic problem in physics that demonstrates Newton’s Third Law.
Key Characteristics:
Forces acting on the masses are tension and gravity.
Tension in the string provides an action-reaction pair.
The acceleration of the system depends on the difference in masses.
Deriving Acceleration
Assume:
Mass 1 =
Mass 2 =
Gravitational acceleration =
Acceleration of the system =
For :
For :
Adding these equations to eliminate :
Solving for acceleration:
Key Insights
The tension in the string provides the equal and opposite forces acting on both masses.
Acceleration is directly proportional to the mass difference and inversely proportional to the total mass.
Vertical Motion and Tension
In vertical systems, such as elevators or pendulums, tension and gravitational forces interact as action-reaction pairs.
At the top of a vertical loop, the forces acting are tension and gravity. Their combination provides the centripetal force necessary for circular motion.
At the bottom, tension exceeds gravity due to the increased centripetal force requirement.
Common Misconceptions
Forces Cancel Out:
Forces in a pair act on different objects, so they don’t cancel each other.
Only Applies to Contact Forces:
The Third Law applies universally, including forces like gravity and magnetism.
Magnitude Differences:
Action and reaction forces are always equal in magnitude, regardless of object size or mass.
Practice Problems
Problem 1: Rocket Propulsion
A rocket expels exhaust gases downward at a rate of 500 kg/s with a velocity of 2000 m/s. What is the upward force exerted on the rocket?
Solution:
Using momentum principles:
Where:
= rate of mass ejection = 500 kg/s
= velocity of ejected gases = 2000 m/s
The rocket experiences an upward force of 1,000,000 N.
Problem 2: Tension in a Rope
Two people pull on opposite ends of a rope with forces of 100 N and 120 N. What is the tension in the rope?
Solution:
The tension in the rope is determined by the smaller force (assuming no acceleration):
The tension remains uniform due to the equal and opposite reaction forces within the rope.
Key Takeaways
Newton’s Third Law is foundational for understanding interactions between objects.
Action-reaction pairs occur universally, from gravitational forces to friction.
Practical applications like Atwood machines and vertical loops highlight the significance of this law in solving real-world problems.
Always identify force pairs and their respective objects in systems to correctly apply the Third Law.
Newton’s Third Law simplifies the complexities of motion by showing the balance of forces in every interaction, making it a cornerstone of classical mechanics and an essential principle for physics students and enthusiasts alike.
Newton’s Laws of Motion: Third Law FAQs
1. What is Newton’s Third Law of Motion?
Newton’s Third Law states, “For every action, there is an equal and opposite reaction.” This means that forces always occur in pairs, and when one object exerts a force on another, the second object exerts an equal and opposite force on the first.
2. What is the significance of Newton’s Third Law?
The Third Law explains the interaction between objects and the forces they exert on each other. It is fundamental in understanding motion, equilibrium, and the dynamics of systems.
3. Can you give an example of Newton’s Third Law in everyday life?
A common example is walking. When you push backward on the ground with your foot, the ground pushes you forward with an equal and opposite force, enabling you to move.
4. How does Newton’s Third Law apply to a rocket launch?
In a rocket launch, the rocket expels gases downward (action), and the gases exert an equal and opposite force upward on the rocket (reaction), propelling it into the air.
5. What are action and reaction forces?
Action and reaction forces are the pair of forces described in Newton’s Third Law. They are:
Equal in magnitude.
Opposite in direction.
Act on different objects.
6. How does Newton’s Third Law explain swimming?
When a swimmer pushes water backward with their hands and feet (action), the water pushes them forward with an equal and opposite force (reaction).
7. What is the relationship between action and reaction forces?
Action and reaction forces are always equal in magnitude and opposite in direction. They act on different objects and never cancel each other out.
8. How does the Third Law apply to jumping?
When you jump, you exert a downward force on the ground (action). The ground exerts an equal and opposite upward force on you (reaction), allowing you to lift off.
9. How does Newton’s Third Law relate to momentum conservation?
In a system where no external forces act, action and reaction forces ensure the total momentum of the system remains conserved.
10. What is the role of Newton’s Third Law in collisions?
During a collision, the force one object exerts on another is matched by an equal and opposite force from the second object. This interaction determines the post-collision motion of both objects.
11. Can action and reaction forces cause acceleration?
Yes, action and reaction forces can cause acceleration. For example, a boat accelerates forward when its propeller pushes water backward (action-reaction pair).
12. Why don’t action and reaction forces cancel each other?
Action and reaction forces act on different objects, so they cannot cancel each other out. Only forces acting on the same object can balance each other.
13. How does Newton’s Third Law apply to bird flight?
When a bird flaps its wings downward (action), the air pushes back upward and forward (reaction), allowing the bird to lift and move.
14. How does the Third Law work in tug-of-war?
In tug-of-war, each team pulls the rope (action), and the rope exerts an equal and opposite force (reaction). The team with the greater net force on the ground usually wins.
15. How does the Third Law explain a bouncing ball?
When a ball hits the ground, it exerts a downward force on the surface (action). The surface exerts an equal and opposite upward force on the ball (reaction), causing it to bounce.
16. How does the Third Law relate to static equilibrium?
In static equilibrium, the action and reaction forces are equal and opposite, ensuring no net force acts on the object, keeping it stationary.
17. How does Newton’s Third Law explain rowing a boat?
When a rower pushes water backward with an oar (action), the water pushes the boat forward with an equal and opposite force (reaction).
18. How does the Third Law apply to firing a gun?
When a bullet is fired, the gun exerts a force on the bullet (action), and the bullet exerts an equal and opposite force on the gun (reaction), causing recoil.
19. How does Newton’s Third Law apply to friction?
When an object exerts a force on a surface, the surface exerts an equal and opposite frictional force on the object, resisting motion.
20. How does the Third Law work in car propulsion?
In a car, the tires push backward on the road (action), and the road pushes forward on the tires (reaction), propelling the car forward.
21. How does Newton’s Third Law apply to magnetism?
When two magnets interact, the force one magnet exerts on the other is matched by an equal and opposite force from the second magnet.
22. How does the Third Law explain trampoline jumps?
When you push down on a trampoline (action), the trampoline pushes you upward with an equal and opposite force (reaction), causing you to bounce.
23. How does the Third Law relate to elevators?
When an elevator cable pulls upward on the elevator (action), the elevator pulls downward on the cable with an equal and opposite force (reaction).
24. How does the Third Law explain the motion of fish?
Fish push water backward with their fins (action), and the water pushes the fish forward with an equal and opposite force (reaction).
25. How does the Third Law work in cycling?
A cyclist pushes down on the pedals (action), and the pedals push back on the cyclist’s feet (reaction), transferring energy to the wheels.
26. How does Newton’s Third Law explain a hammer striking a nail?
When a hammer strikes a nail (action), the nail exerts an equal and opposite force on the hammer (reaction), causing it to rebound slightly.
27. How does the Third Law apply to space exploration?
In space, a spacecraft expels gas backward (action), and the gas exerts an equal and opposite force on the spacecraft (reaction), propelling it forward.
28. How does the Third Law explain pendulum motion?
When a pendulum bob pushes against the air (action), the air pushes back with an equal and opposite force (reaction), causing slight resistance.
29. How does the Third Law explain slingshots?
When you pull back on a slingshot (action), the elastic band exerts an equal and opposite force (reaction), storing potential energy.
30. How does the Third Law apply to jet engines?
In jet engines, hot gases are expelled backward (action), and the jet moves forward with an equal and opposite force (reaction).
31. How does Newton’s Third Law apply to pressure?
When a fluid exerts pressure on a surface (action), the surface exerts an equal and opposite force back on the fluid (reaction).
32. How does the Third Law explain walking on ice?
On ice, when you push backward on the surface (action), the surface pushes you forward (reaction). Reduced friction makes walking challenging.
33. How does the Third Law relate to buoyancy?
When an object pushes down on a fluid (action), the fluid exerts an equal and opposite buoyant force upward (reaction).
34. How does the Third Law apply to spinning tops?
A spinning top exerts force on the surface (action), and the surface exerts an equal and opposite force on the top (reaction), maintaining its motion.
35. How does Newton’s Third Law explain earthquakes?
Tectonic plates push against each other (action), and the plates exert equal and opposite forces (reaction), leading to seismic activity.
36. How does the Third Law apply to drones?
Drone propellers push air downward (action), and the air pushes the drone upward (reaction), enabling it to hover.
37. How does the Third Law explain the motion of balloons?
When air escapes from a balloon (action), the balloon moves in the opposite direction (reaction).
38. How does Newton’s Third Law relate to lifting weights?
When you pull upward on a weight (action), the weight pulls downward with an equal and opposite force (reaction).
39. How does the Third Law explain jumping into water?
When you push down on the water with your legs (action), the water pushes you upward (reaction), propelling you into the air.
40. How does the Third Law work in kayaking?
When you paddle water backward (action), the water pushes the kayak forward (reaction).
41. How does Newton’s Third Law explain the operation of seesaws?
When one person pushes down on a seesaw (action), the seesaw pushes up with an equal and opposite force (reaction).
42. How does the Third Law apply to car collisions?
In a collision, the force one car exerts on the other is matched by an equal and opposite force from the second car.
43. How does the Third Law explain shooting arrows?
When the bowstring pushes the arrow forward (action), the arrow exerts an equal and opposite force on the string (reaction).
44. How does the Third Law relate to electric forces?
Two charged particles exert equal and opposite electric forces on each other, following Newton’s Third Law.
45. How does Newton’s Third Law apply to mechanical springs?
When a spring is compressed or stretched (action), it exerts an equal and opposite restoring force (reaction).
46. How does the Third Law work in magnetic interactions?
Two magnets exert equal and opposite magnetic forces on each other, illustrating the Third Law.
47. How does the Third Law explain surfing?
A surfer pushes water backward with the board (action), and the water pushes the board forward (reaction).
48. How does the Third Law apply to parachutes?
A parachute pushes air downward (action), and the air pushes upward on the parachute (reaction), slowing descent.
49. How does Newton’s Third Law apply to cranes?
When a crane lifts a load upward (action), the load pulls downward on the crane with an equal and opposite force (reaction).
50. Why is Newton’s Third Law important?
Newton’s Third Law is crucial for understanding interactions in mechanical systems, explaining motion, equilibrium, and conservation laws in various real-world applications.
2.3 Newton's Laws of Motion: Third Law
2.1 Newton's Laws of Motion: First and Second Law
Unit 2 Overview: Newton’s Laws of Motion
9.2 Crafting an argument through stylistic choices like word choice and description
9.1 Strategically conceding, rebutting, or refuting information
Unit 9 Overview: Developing a Complex Argument
