Consider a perfectly reflecting mirror oriented so that solar radiation of intensity i is incident upon, and perpendicular to, the reflective surface of the mirror. if the mirror has surface area a, what is frad, the magnitude of the average force due to the radiation pressure of the sunlight on the mirror

To solve this problem we need to know the following:

the mass of the sun, Msun, 2.0 * 10^30 kg

the intensity of sunlight as a function of the distance R from the sun,

Isun(R) = 3.2 * 10^25 * 1/R2 (W/m2), and

the gravitational constant G = 6.67 * 10^-11 m3/(kg⋅s2)

Suppose that the mirror described in Part A is initially at rest a distance R away from the sun.

What is the critical value of area density for the mirror at which the radiation pressure exactly cancels out the gravitational attraction from the sun?

Using the formula from Part A, find the force due to solar radiation:

Fr = 2IA/c

And compare to the force due to gravity:

Fg = G * m1 * m2 / R2

Fr = Fg

2IA/c = G * m1 * m2 / R2

Substitute in for I and the mass of the sun:

2 * (3.2 * 10^25 * 1/R2) * A / c = G * (2.0*10^30) * m2 / R2

The R2s cancel:

2 * (3.2 * 10^25) * A / c = G * (2.0 * 10^30) * m2

Now solve for m/A (where m = m2, the mass of the solar sail):

m/A = 2 * (3.2 * 10^25) / (c * G * (2.0*10^30))

m/A = 2 * (3.2 * 10^25) / ((3.0 * 10^8) * (6.67 * 10^-11) * (2.0 * 10^30))

mass/area = 0.00160 kg/m2

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:

0.19 m/s and 0.45 m/s