Alithium atom starts from rest at a position x = xo and falls toward zinc atom with an acceleration that depends on their separation as a(x) = 4eϵ/m { 12 (σ^12/σ^13) -6 (σ^6/σ^7) where ϵ, m, and σ are positive constants, and the zinc atom stays fixed at position x = 0, assume that xo > 2^(1/6)σ. a. find an expression for how the velocity of the moving lithium atom depends on x. (it will also depend on ϵ, m, xo and σ) b. what is the distance of closest approach of the the two atoms (in terms of σ and xo)?

Please refer to the attachment for answers.

Explanation:

Please refer to the attachment for explanation

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j