Answers to Quiz 7

QUIZ 7

Answers:

x = x_o + v_o t + (1/2) a t² where x is the displacement at time t,
x_o is the displacement at time t = 0,
vo is the velocity at time t = 0,
a is the constant acceleration Dimensionally correct. Each term has dimensions of L.

P = where P is pressure,
r is density,
g is gravitational acceleration,
h is height Not dimensionally correct.
[P] = M·L^-1·T^-2
[] = M^1/2·L^-1/2·T^-1

ln N_d/N_a = - [ Vgh_d(r - r_l)] / kT where N_d and N_a are number of
particles, V is volume,
g is gravitational acceleration,
h_d is distance,
r and r_l are densitites,
k is Boltzmann's constant with SI units of joules per kelvin,
T is absolute temperature. Dimensionally correct. Left side of the equation is "dimensionless".
[Vgh_d(r-r_l)] = M·L²/T².
kT has SI units of joules, (which is a unit of energy), and therefore [kT] = M·L²/T².
Right side of the equation is also "dimensionless",
since (M·L²/T²)/(M·L²/T²) =1.

x = x_o + v_o t + (1/2) a t²	where x is the displacement at time t, x_o is the displacement at time t = 0, vo is the velocity at time t = 0, a is the constant acceleration	Dimensionally correct. Each term has dimensions of L.
P =	where P is pressure, r is density, g is gravitational acceleration, h is height	Not dimensionally correct. [P] = M·L^-1·T^-2 [] = M^1/2·L^-1/2·T^-1
ln N_d/N_a = - [ Vgh_d(r - r_l)] / kT	where N_d and N_a are number of particles, V is volume, g is gravitational acceleration, h_d is distance, r and r_l are densitites, k is Boltzmann's constant with SI units of joules per kelvin, T is absolute temperature.	Dimensionally correct. Left side of the equation is "dimensionless". [Vgh_d(r-r_l)] = M·L²/T². kT has SI units of joules, (which is a unit of energy), and therefore [kT] = M·L²/T². Right side of the equation is also "dimensionless", since (M·L²/T²)/(M·L²/T²) =1.

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