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

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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.
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