What is Law of Conservation of Momentum? | Simple Explanation for Class 10

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What is the Law of Conservation of Momentum?

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

The Law of Conservation of Momentum states that for a closed system, the total momentum before an interaction (like a collision or explosion) is equal to the total momentum after the interaction. This means that momentum is neither lost nor gained, only transferred between objects within the system.

Simple Example

Quick Example

Imagine two auto-rickshaws, one empty and one full of passengers, colliding on a street. Before the collision, each auto has some momentum. Right after they hit each other, the total momentum of both autos combined remains the same as their total momentum just before they collided, assuming no outside forces like friction from the road are acting significantly.

Worked Example

Step-by-Step

PROBLEM: A 2 kg cricket ball travelling at 10 m/s hits a stationary 0.5 kg wooden block. After the collision, the ball moves at 6 m/s in the same direction. What is the velocity of the wooden block after the collision?

Step 1: Identify the given values.
Mass of ball (m1) = 2 kg
Initial velocity of ball (u1) = 10 m/s
Mass of block (m2) = 0.5 kg
Initial velocity of block (u2) = 0 m/s (stationary)
Final velocity of ball (v1) = 6 m/s
Final velocity of block (v2) = ?

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Step 2: Apply the Law of Conservation of Momentum formula: m1u1 + m2u2 = m1v1 + m2v2.

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Step 3: Substitute the known values into the formula.
(2 kg * 10 m/s) + (0.5 kg * 0 m/s) = (2 kg * 6 m/s) + (0.5 kg * v2)

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Step 4: Calculate the momentum before collision.
20 kg m/s + 0 kg m/s = 20 kg m/s

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Step 5: Calculate the known momentum after collision.
12 kg m/s + 0.5 kg * v2

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Step 6: Set total initial momentum equal to total final momentum.
20 = 12 + 0.5 * v2

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Step 7: Solve for v2.
20 - 12 = 0.5 * v2
8 = 0.5 * v2
v2 = 8 / 0.5
v2 = 16 m/s

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Answer: The velocity of the wooden block after the collision is 16 m/s.

Why It Matters

This law is super important for understanding how things move and interact, from launching rockets into space (ISRO uses this!) to designing safer cars. Engineers use it to build robust structures, and even game developers use it for realistic physics in video games.

Common Mistakes

MISTAKE: Forgetting that momentum is a vector quantity and ignoring directions (positive/negative) | CORRECTION: Always assign positive and negative signs to velocities based on a chosen direction (e.g., right is positive, left is negative).

MISTAKE: Applying the law when external forces like friction or air resistance are significant | CORRECTION: Remember the law applies strictly to a 'closed system' where no net external force acts. If external forces are present, the total momentum changes.

MISTAKE: Mixing up units or not converting them to SI units (kg and m/s) | CORRECTION: Always ensure all masses are in kilograms (kg) and all velocities are in meters per second (m/s) before applying the formula.

Practice Questions

Try It Yourself

QUESTION: A 5 kg object moving at 8 m/s collides with a 3 kg object moving at 4 m/s in the same direction. If they stick together after the collision, what is their combined velocity? | ANSWER: 7 m/s

QUESTION: A 1000 kg car travelling at 20 m/s collides head-on with a 1500 kg truck travelling at 10 m/s in the opposite direction. If the car bounces back at 5 m/s, what is the velocity of the truck after the collision? | ANSWER: 3.33 m/s (in the original direction of the truck)

QUESTION: A bullet of mass 0.02 kg is fired from a rifle of mass 5 kg. If the bullet leaves the rifle with a velocity of 300 m/s, calculate the recoil velocity of the rifle. | ANSWER: -1.2 m/s (The negative sign indicates the rifle moves in the opposite direction to the bullet).

MCQ

Quick Quiz

Which of the following scenarios best demonstrates the Law of Conservation of Momentum?

A ball rolling down a hill and speeding up.

A rocket launching into space by expelling hot gases.

A car slowing down due to friction from the road.

A person pushing a wall and the wall not moving.

The Correct Answer Is:

Option B is correct because the rocket and the expelled gases form a closed system. The backward momentum of the gases equals the forward momentum of the rocket. Options A and C involve external forces (gravity, friction) acting on the system, and Option D describes forces without a change in momentum for the wall.

Real World Connection

In the Real World

You see this law in action every time ISRO launches a rocket from Sriharikota! The rocket expels hot gases downwards, gaining momentum upwards. It's also crucial for designing safety features in cars, like crumple zones, to manage the momentum transfer during a collision and keep passengers safe.

Key Vocabulary

Key Terms

MOMENTUM: The product of an object's mass and its velocity (p = mv) | CLOSED SYSTEM: A system where no external forces act on it, and no matter enters or leaves | COLLISION: An event where two or more objects exert forces on each other for a short time | RECOIL: The backward movement of a gun when a bullet is fired, due to conservation of momentum.

What's Next

What to Learn Next

Great job understanding momentum! Next, you should explore Newton's Laws of Motion, especially the third law (action-reaction). You'll see how it's closely related to the conservation of momentum and helps explain why objects exert forces on each other during interactions.