If it has enough kinetic energy, a moleculeat the surface of the Earth can escape the Earth’s gravitation. The acceleration of gravity is 9.8 m/s2,and the Boltzmanns’ constant is 1.38066×10−23 J/K. Using energy conservation, a) determine theminimum kinetic energy needed to escape interms of the mass of the molecule m , the free-fall acceleration at the surface g, and the radius of the Earth R

b) Calculate the temperature for which the min- imum escape energy is 11 times the average kinetic energy of an oxygen molecule.

a. mgR b. 483.6 × 10³ K

Explanation:

a. Using the law of conservation of energy,

K₁ + U₁ = K₂ + U₂ where K₁ and K₂ are the initial and final kinetic energies of the molecule and U₁ and U₂ are the initial and final potential energies of the molecule.

K₁ + -GMm/R = 0 + 0

K₁ = GMm/R since GM = gR²,

K₁ = mgR

So its minimum kinetic energy is mgR

b. The average kinetic energy energy of a gas molecule is K = 3/2kT. If K₁ = 11K, then

mgR = 11 ×3/2kT = 33/2kT.

T = 2mgR/k

For oxygen molecule, m = 32 g/6.02 × 10²³ = 5.32 × 10⁻²⁶ kg/molecule

T = 2 × 5.32 × 10⁻²⁶ kg × 9.8 m/s² 6.4 × 10⁶ m/1.38 10⁻²³ J/K = 483.6 × 10³ K

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

15.3 cos 65 degrees trig