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What is the Elastic Collision?
Grade Level:
Class 8
Space Technology, EVs, Climate Change, Biotechnology, HealthTech, Robotics, Chemistry, Physics
Definition
What is it?
An elastic collision is a type of collision where both the total kinetic energy and the total momentum of the objects remain unchanged before and after the collision. Imagine two billiard balls hitting each other perfectly; they bounce off without losing any energy to heat or sound.
Simple Example
Quick Example
Think about two marbles of the same size rolling towards each other on a smooth floor. When they collide and bounce back perfectly, without any sound or heat being generated, that's close to an elastic collision. Their speed changes, but the total 'energy of motion' and 'pushing power' (momentum) of the system stays the same.
Worked Example
Step-by-Step
Let's say a small toy car (Car A) of mass 1 kg is moving at 2 m/s and collides head-on with another identical toy car (Car B) of mass 1 kg, which is initially at rest (0 m/s). They have an elastic collision. What are their velocities after the collision?
Step 1: Understand the given values. Mass of Car A (m1) = 1 kg, Initial velocity of Car A (u1) = 2 m/s. Mass of Car B (m2) = 1 kg, Initial velocity of Car B (u2) = 0 m/s.
---Step 2: Apply the Law of Conservation of Momentum. Total momentum before = Total momentum after. (m1*u1) + (m2*u2) = (m1*v1) + (m2*v2). So, (1*2) + (1*0) = (1*v1) + (1*v2), which simplifies to 2 = v1 + v2 (Equation 1).
---Step 3: Apply the Law of Conservation of Kinetic Energy. Total KE before = Total KE after. (0.5*m1*u1^2) + (0.5*m2*u2^2) = (0.5*m1*v1^2) + (0.5*m2*v2^2). So, (0.5*1*2^2) + (0.5*1*0^2) = (0.5*1*v1^2) + (0.5*1*v2^2). This simplifies to 2 = 0.5*v1^2 + 0.5*v2^2, or 4 = v1^2 + v2^2 (Equation 2).
---Step 4: From elastic collision properties, for identical masses, the velocities are often exchanged. Let's solve using the equations. From Equation 1, v1 = 2 - v2. Substitute this into Equation 2.
---Step 5: 4 = (2 - v2)^2 + v2^2. So, 4 = (4 - 4*v2 + v2^2) + v2^2. This gives 0 = 2*v2^2 - 4*v2. Factor out 2*v2: 0 = 2*v2*(v2 - 2).
---Step 6: This gives two possible solutions for v2: v2 = 0 or v2 = 2. If v2 = 0, then from Equation 1, v1 = 2. This means no collision happened, which is not what we're looking for.
---Step 7: So, the other solution is v2 = 2 m/s. If v2 = 2 m/s, then from Equation 1, v1 = 2 - 2 = 0 m/s.
---Step 8: Therefore, after the collision, Car A stops (v1 = 0 m/s) and Car B moves with the initial velocity of Car A (v2 = 2 m/s).
Answer: After the collision, Car A's velocity is 0 m/s and Car B's velocity is 2 m/s.
Why It Matters
Understanding elastic collisions is crucial for designing efficient machines and vehicles. Engineers use this concept in robotics to ensure robots move smoothly and in space technology to calculate rocket trajectories accurately. It also helps in understanding how atoms interact in chemistry and how energy is transferred in various physical systems.
Common Mistakes
MISTAKE: Thinking that kinetic energy is always conserved in ALL collisions. | CORRECTION: Kinetic energy is only conserved in elastic collisions. In most real-world collisions (like a car crash), some kinetic energy is lost as heat, sound, or deformation.
MISTAKE: Confusing elastic collisions with inelastic collisions. | CORRECTION: In elastic collisions, both kinetic energy and momentum are conserved. In inelastic collisions, only momentum is conserved, while kinetic energy is not.
MISTAKE: Forgetting that momentum is a vector quantity and direction matters. | CORRECTION: When calculating momentum, always consider the direction of velocity. If objects move in opposite directions, one velocity should be taken as negative.
Practice Questions
Try It Yourself
QUESTION: In an elastic collision, if a 2 kg ball moving at 5 m/s hits a stationary 2 kg ball, what will be the velocity of the first ball after the collision? | ANSWER: 0 m/s
QUESTION: A 4 kg object moving at 3 m/s has an elastic collision with a 2 kg object moving in the same direction at 1 m/s. If the 4 kg object slows down to 2 m/s, what is the velocity of the 2 kg object after the collision? (Hint: Use conservation of momentum and then conservation of kinetic energy.) | ANSWER: 5 m/s
QUESTION: Two identical balls, each with mass 'm', undergo a head-on elastic collision. Ball 1 is moving at 'u' m/s, and Ball 2 is at rest. What are the final velocities of Ball 1 and Ball 2 in terms of 'u'? | ANSWER: Ball 1's final velocity = 0 m/s, Ball 2's final velocity = u m/s
MCQ
Quick Quiz
Which of the following quantities is conserved in an elastic collision?
Only kinetic energy
Only momentum
Both kinetic energy and momentum
Neither kinetic energy nor momentum
The Correct Answer Is:
C
In an elastic collision, by definition, both the total kinetic energy and the total momentum of the system are conserved. They remain the same before and after the collision.
Real World Connection
In the Real World
You see elastic collision principles in action when you play billiards or carrom. The way the striker hits the coins, and how they scatter or pocket, involves energy and momentum transfer. Even the design of shock absorbers in cars and bikes, though often involving inelastic collisions, builds on the fundamental understanding of how objects interact during impact to manage energy.
Key Vocabulary
Key Terms
COLLISION: An event where two or more bodies exert forces on each other for a short time | KINETIC ENERGY: The energy an object possesses due to its motion | MOMENTUM: A measure of the mass and velocity of an object, indicating its 'quantity of motion' | CONSERVATION: The principle that a physical quantity remains constant over time
What's Next
What to Learn Next
Great job understanding elastic collisions! Next, you should explore 'Inelastic Collisions'. This will help you understand collisions where some energy is lost, which is more common in our everyday world, and how it differs from what you just learned.
