Third Law of Motion

Newton's Third Law of Motion

Newton's Third Law of Motion states that:

"To every action, there is an equal and opposite reaction."

This means that if object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude but in the opposite direction on object A.

Application: recoil of a gun

When a bullet is fired from a gun, the bullet moves forward (action), and the gun moves backward (reaction). This backward motion of the gun is known as recoil.

Assume the following:

Mass of the gun = $m_g$

Mass of the bullet = $m_b$

Velocity of the bullet after firing = $v_b$

Recoil velocity of the gun = $v_g$

Before firing:

The total momentum of the system (gun + bullet) is zero since both are at rest:

$\text{Total initial momentum} = 0$

After firing:

The bullet moves forward, and the gun recoils backward. According to the principle of conservation of momentum:

$\text{Total final momentum} = \text{momentum of bullet} + \text{momentum of gun}$

$m_b v_b + m_g (-v_g) = 0$

The negative sign for $v_g$ is because the gun moves in the opposite direction to the bullet.

Step 1: Rearranging the equation

$m_b v_b = m_g v_g$

Step 2: Solving for the recoil velocity of the gun

$v_g = \frac{m_b v_b}{m_g}$

Therefore:

The recoil velocity of the gun is given by:

$v_g = \frac{m_b v_b}{m_g}$

This shows that the gun's recoil velocity depends on the mass and velocity of the bullet and is inversely proportional to the mass of the gun.

The recoil of a gun after firing a bullet is an example of Newton's Third Law of Motion. The bullet moves forward (action), and the gun moves backward (reaction), conserving the total momentum of the system.

Applications of Newton's Third Law of Motion

Firing a gun

1. Action: When a bullet is fired from a gun, the gun applies a forward force on the bullet, propelling it out of the barrel.
2. Reaction: The bullet applies an equal and opposite force on the gun, causing it to recoil backward. This backward motion of the gun is called recoil.

Example: A person firing a gun experiences a backward push (recoil) as the bullet is propelled forward.

Walking

1. Action: When we walk, our feet push backward against the ground.
2. Reaction: The ground exerts an equal and opposite forward force on our feet, propelling us forward.

Example: When you push backward with your feet while walking, the ground pushes you forward, allowing you to move.

Swimming

1. Action: A swimmer pushes the water backward using their hands and feet.
2. Reaction: The water pushes the swimmer forward, allowing them to move in the opposite direction.

Example: When a swimmer strokes the water, the water pushes them forward with the same force.

Rocket propulsion

1. Action: A rocket expels exhaust gases downward with high speed.
2. Reaction: The rocket experiences an upward force equal in magnitude and opposite in direction, propelling it upward.

Example: When a rocket launches, the expulsion of gas pushes the rocket up due to the reaction force.

Jumping off a boat

1. Action: When a person jumps off a boat, they push against the boat with their legs.
2. Reaction: The boat moves in the opposite direction (backward) as a result of the force exerted by the person.

Example: If you jump off a stationary boat into the water, the boat will move backward as you move forward.

Bird flying

1. Action: A bird pushes air downwards using its wings.
2. Reaction: The air pushes the bird upwards with an equal force, allowing the bird to fly.

Example: As a bird flaps its wings downward, the equal and opposite reaction lifts it off the ground.

Balloon releasing air

1. Action: When air is released from a balloon, the air moves downward (or outward) from the nozzle.
2. Reaction: The balloon moves in the opposite direction to the expelled air due to the reaction force.

Example: When a balloon is released with the air flowing out, it moves in the opposite direction of the airflow.