# PHYS 17200 Lecture Notes - Lecture 18: Kinetic Energy, Electronvolt

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6 Apr 2015

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PHYS 17200 - Modern Mechanics - Lecture 18_Collisions

Collisions

● A collision is a brief interaction between objects involving large forces.

● Remember that we can use both the energy and momentum principles when predicting

and explaining systems’ behavior.

● When analyzing a collision it is useful to apply these principles to the system consisting

of all the colliding objects. Because external forces are small compared to those that act

between objects during the collision we can neglect them. So,

○ the system’s total momentum is constant.

○ the system’s total energy is constant.

● When colliding objects’ internal energies do not change we say the collision is “elastic”.

When one or more objects’ internal energy does change the collision is “inelastic”.

● Working in a coordinate system in which the center of mass of the system of colliding

objects is at rest can simplify analysis of a collision.

Formulas

● Elastic, Head-on Collision

○ Kinetic energy AND momentum is conserved

○ m1v1,i + m2v2,i = m1v1,f + m2v2,f

● Inelastic, Head-on Collision

○ ONLY momentum is conserved

○ m1v1,i + m2v2,i = (m1+m2)vf

Quantum Collisions

● An electron (Kelectron = 1eV) is heading straight toward atom A, which is at rest and in its

ground state.

● Can the collision be inelastic?

○ No

● Inelastic means Eint ≠ 0. Only possibility is for atom to get excited.

● But the necessary (threshold) energy to excite the atom is 4 eV.

● The incident electron isn’t energetic enough to excite the atom. Further, U = 0 before

and after (since atom will be far away from electron).

● Hence, Eint ≠ 0 isn’t possible here.