2. A small, just barely visible dust particle has a mass of about 10^-8 g It fal

Question

2. A small, just barely visible dust particle has a mass of about 10^-8 g It falls onto a glass of water at 300K where it is supported by the surface tension and moves freely in only two dimensions. What is the root-mean-square speed there? Answer: v rma = 288x10^-5 m/s 3. A spring of mass m = 0.5 kg rests on a horizontal frictionless table attached to a spring of spring constant k spring = 2 N/m. The other end of the spring is attached to a wall. The mass has been lying there untouched for years and is seemingly at rest. The ambient temperature is 500K. a. What is the mean thermal energy of the mass? Answer: E = kT = 4.14 x 10^-21 J b. What is the mean horizontal amplitude of the thermally induced oscillations? Answer: A = 6.44 x 10^-11 m

Explanation / Answer

apply the formula for Vrms = sqrt(2KT/m)

where k is boltszmann constant = 1.38 e -23

T = 300 K

m = 10^-8 gms = 10^-11 kgs

Vrms = sqrt(2 * 1.38 e-23 * 300/1e-3)

Vrms = sqrt(1.38e-23*2*300/1e-11)

Vrms = 2.877 *10^-5 m/s

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use formula for eenrgy E = kt

K is boltzman constant = 1.38 e -23

so

E = 1.38 e -23 * 300

E = 4.14 e -21 Joules

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so   apply Eenergy U = 0.5 kA2

A^2   = 2U/K

A^2 = 2 * 4.14 e -21/2

A = sqrt (41.4 e -22)

A =   6.44 e -11 m

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