Collision – Detailed Notes for B.Sc. 1st Year Physics Students

Collision – Detailed Notes for B.Sc. 1st Year Physics Students

🔹 Introduction

In the realm of classical mechanics, the concept of collision is crucial for understanding how objects interact when they come into contact or exert forces on each other. Whether it’s billiard balls hitting one another or vehicles colliding on the road, the study of collisions helps us predict the resulting motion based on the initial conditions.

This comprehensive note is tailored for B.Sc. 1st Year Physics students to understand the types, principles, equations, and applications of collisions in a clear and exam-friendly way. Mastering this topic will also help you score better in both theory and numerical problems in university exams.

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🔹 What is a Collision?

A collision is an event in which two or more bodies exert forces on each other in a relatively short time. These forces may cause the objects to change their direction, speed, or even get deformed.

In physics, the focus is on momentum and energy conservation during and after the collision.

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🔹 Types of Collisions

There are mainly three types of collisions:

1. Elastic Collision:

   • Both momentum and kinetic energy are conserved.

   • There is no loss of energy in the form of sound, heat, or deformation.

   • Common in idealized systems and microscopic particle interactions.

2. Inelastic Collision:

   • Momentum is conserved.

   • Kinetic energy is not conserved.

   • Some energy is transformed into other forms like heat, sound, or internal energy.

3. Perfectly Inelastic Collision:

   • A special case of inelastic collision.

   • The colliding bodies stick together after the collision.

   • Maximum possible kinetic energy is lost.

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🔹 Laws Applicable to Collisions

1. Law of Conservation of Momentum:

   • Total momentum before collision = Total momentum after collision

   • $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

2. Law of Conservation of Kinetic Energy (Only in elastic collisions):

   • $\frac{1}{2}m_1 u_1^2 + \frac{1}{2}m_2 u_2^2 = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2$

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🔹 One-Dimensional (Head-On) Collision

Elastic Head-On Collision Equations (for two bodies):

Let:

• $m_1, m_2$: masses of the two bodies

• $u_1, u_2$: initial velocities

• $v_1, v_2$: final velocities

Final velocities:
$v_1 = \frac{(m_1 - m_2)u_1 + 2m_2 u_2}{m_1 + m_2}$
$v_2 = \frac{(m_2 - m_1)u_2 + 2m_1 u_1}{m_1 + m_2}$

In Perfectly Inelastic Collision (bodies stick together):
$v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}$

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🔹 Two-Dimensional Collisions

In two-dimensional collisions, we apply conservation of momentum along both x and y axes.

• Along x-axis:
  $\sum p_x^{\text{initial}} = \sum p_x^{\text{final}}$

• Along y-axis:
  $\sum p_y^{\text{initial}} = \sum p_y^{\text{final}}$

Use vector diagrams and trigonometry to resolve velocities and solve problems.

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🔹 Coefficient of Restitution (e)

The coefficient of restitution is a measure of how elastic a collision is.

$e = \frac{\text{Relative velocity after collision}}{\text{Relative velocity before collision}}$
$e = \frac{v_2 - v_1}{u_1 - u_2}$

• $e = 1$: perfectly elastic

• $0 < e < 1$: inelastic

• $e = 0$: perfectly inelastic

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🔹 Important Concepts

1. Impulse:

   • Change in momentum = Force × time

   • $J = F \cdot \Delta t = \Delta p$

2. Newton’s Third Law:

   • Action and reaction forces are equal and opposite

3. External Forces:

   • Must be negligible or absent for conservation laws to apply

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🔹 Real-Life Examples

1. Billiard Balls – Approximate elastic collisions

2. Car Accidents – Usually inelastic; energy lost in deformation

3. Rocket Exhaust Particles – Apply momentum conservation

4. Meteor Collisions – Inelastic; cause craters

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🔹 Sample Numerical Questions

Q1: Two masses 4 kg and 2 kg collide elastically. Initial velocities are 6 m/s and 3 m/s respectively. Find final velocities.

Solution:
Use:
$v_1 = \frac{(m_1 - m_2)u_1 + 2m_2 u_2}{m_1 + m_2}$
$v_1 = \frac{(4 - 2)6 + 2\cdot2\cdot3}{6} = 5 \text{ m/s}$

$v_2 = \frac{(2 - 4)3 + 2\cdot4\cdot6}{6} = 7 \text{ m/s}$

Q2: Two blocks stick together after collision. m1 = 1 kg, u1 = 5 m/s; m2 = 1 kg, u2 = 0. Find final velocity.

$v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2} = \frac{5}{2} = 2.5 \text{ m/s}$

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🔹 Experimental Verification

You can verify conservation laws using:

• Air track experiments (frictionless)

• Ballistic pendulums

• Momentum trolleys

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🔹 Applications of Collision Theory

• Astronomy: Understanding cosmic events and asteroid impacts

• Sports Physics: Predict ball trajectories

• Nuclear Physics: Particle collision analysis

• Automobile Safety: Crash simulations and design

• Engineering: Impact testing in materials science

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🔹 Summary and Key Takeaways

• Collision involves force interactions in a short time span

• Momentum is always conserved if external forces are negligible

• Kinetic energy conservation depends on the type of collision

• Coefficient of restitution tells us how bouncy a collision is

• Understand and apply both 1D and 2D collision formulas

• Mastering collisions improves problem-solving and practical application skills

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🔹 Final Words

The study of collisions gives you insight into how forces, momentum, and energy interact in the physical world. Whether you’re aiming to solve theoretical problems or understand real-world scenarios like vehicle crashes, mastering this topic is a must for all physics students.

If this note helped clarify your concepts, be sure to revisit and revise it regularly before your exams. Also, feel free to share it with your classmates and contribute to collective learning.

Keep learning, stay curious, and let physics continue to amaze you!

Important notes for BSC Physics students.

In this page you can find BSC Physics Handwritten notes for TU 1st year students.You can download pdf file below.