Question

In an elastic collision:

• A. Total kinetic energy is conserved
• B. Total Momentum is conserved
• C. Momentum and kinetic energy are conserved
• D. None of the above

Answer 1

Answer:

C. Momentum and kinetic energy are conserved

• An elastic collision is a type of collision where both momentum and kinetic energy are conserved.

• This means that the total momentum of the system of interacting bodies before the collision is equal to the total momentum after the collision.

• Similarly, the total kinetic energy of the system remains unchanged throughout the collision.

Conservation of Momentum

• Momentum is defined as the product of an object's mass and its velocity (p = mv).

• In any collision, whether elastic or inelastic, momentum is always conserved due to the principle of conservation of linear momentum, which states that the total momentum of an isolated system remains constant.

• Mathematically, for a system of two bodies colliding:

  m1*u1 + m2*u2 = m1*v1 + m2*v2

  Where:

  • m1 and m2 are the masses of the two bodies.

  • u1 and u2 are their initial velocities before collision.

  • v1 and v2 are their final velocities after collision.

Conservation of Kinetic Energy

• Kinetic energy is the energy an object possesses due to its motion, calculated as KE = 1/2 * mv².

• In an elastic collision, the sum of the kinetic energies of all bodies involved is the same before and after the collision.

• Mathematically:

  1/2*m1*u1² + 1/2*m2*u2² = 1/2*m1*v1² + 1/2*m2*v2²

• This is a distinguishing feature of elastic collisions, differentiating them from inelastic collisions where kinetic energy is not conserved (often converted into heat, sound, or deformation).