9. A stainless steel tube having an outside diameter of 0.6 cm and a wall thickness of 0.05 cm is to be insulated with a material having a thermal conductivity of 0.065 W/mK. If the inner and outer convective heat transfer coefficients are 5.9 W/m²K. what will be the heat loss per meter of length for insulation thicknesses of 0, 0.25, 0.5, 0.75, 1.00, and 1.25 cm if the inside temperature is 95 C and the outside temperature is 10 C? Plot heat loss per meter versus insulation thickness. Also, plot the surface and interface temperatures as a function of insulation thickness.

a) DERIVE the equation for the change in the free energy of a CYLINDRICAL nucleus heterogeneously forming from an existing phase. The nucleus grows with its circular base on

the mold wall and the axis of the cylinder normal to the wall. ASSUME that the height of the cylinder can be written as h = a * r, where a is a constant, and r is the cylinder radius.

b) Find the critical radius and the energy barrier to nucleation for this shape of precipitate.

c) We can vary the shape of the nucleating phase by changing the constant a. Make a log- log plot of the size of the energy barrier versus the parameter a over a range from a

= 0.01 (disk shaped) to a = 100 (needle shaped). Explain your results.

Dark matter; C&O 24.22.

(a) Assume that the density of dark matter in our Galaxy is given by ρ(r) = ρ0/(1+(r/a) ^2) . Show that the amount of dark matter interior to a radius r is given by: Mr = 4πρ0a^2 [ r − a tan^−1 ( r/a )].

(b) If 5.4 × 10^11 M⊙ of dark matter is located within 50 kpc of the Galactic centre, determine ρ0 in units of M⊙ kpc−1 . Repeat your calculation if 1.9 × 10^12 M⊙ is located within 230 kpc of the Galactic centre. Assume that a = 2.8 kpc.

Suppose that you decided to send a spacecraft to Neptune using a Hohmann transfer. The craft starts in a circular orbit close to the Earth (1 AU) and is to end up in a circular orbit near   Neptune (about 30 AU).   (a) How long would the transfer take?   (b) How could you shorten this time, without increasing the amount of fuel required?   (c) What change in velocity is needed to enter the transfer orbit?   (d)   What is the change in velocity needed to enter the circular orbit near Neptune?

SCENERIO: You are working for a humanitarian aid agency that plans to air-drop supplies into a war-torn region. The political landscape is such that in order to reach the civilians in need – and not fall into the wrong hands – the supplies must land in a very precise location. The agency’s helicopters are equipped with a ramp down which bundles of supplies can be rolled as a means of launching them. The bundles of supplies are spherical and cylindrical, and come in a variety of sizes and masses. Enough friction is present on the ramp that all bundles are certain to roll without slipping as they are launched. It is up to you to determine from where on the ramp each bundle of supplies should be launched, assuming the helicopter hovers at a constant height.

QUESTION: Now assume that conditions in the war-torn region have deteriorated to the point that it is no longer safe for a helicopter to hover stationary above the ground for a supply drop. How would your answers about where to drop supplies change if they are instead released from an aircraft moving with constant velocity? With constant acceleration?

Compare the green house effect on Earth to Venus then discuss two similarities and two differences in the green house effect between Earth and Venus.

Indicate whether each quantity increases, decreases, or remains the same for the situation being described: The number of particles and volume are held constant and the gas is cooled

• How many possible directions are there for the frictional force?

• Physicists categorize the frictional force according to the relative motion between the two surfaces. What are some of the categories?

• One category of frictional forces is the static frictional force. What is the relative motion between the surfaces for this category? Describe a theory of static frictional forces.

• Another category of frictional forces is the kinetic frictional force. What is the relative motion between the surfaces for this category? Describe a theory of kinetic frictional forces.

In an experiment, 426 g of water is in a copper calorimeter cup of mass 205 g. The cup and the water are at an initial temperature of 10.9 oC. An unknown material with a mass of 361 g at a temperature of 296.1 oC is placed in the water. The system reaches thermal equilibrium at 36.1 oC. What is the specific heat of the unknown material? units = J/kg-C

Discuss the general design of light and heavy water reactors

Three children are riding on the edge of a merry-go-round that is 122 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The children have masses of 19.9, 29.5, and 40.8 kg. If the child who has a mass of 29.5 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

A 425 kg satellite is in a circular orbit at an altitude of 400 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 2.00 km/s. How much energy was transformed to internal energy by means of friction?
J

1-What is the expression for the thin lens equation? Define all the terms in the expression.

2-Describe the three properties that determine the focal length of a lens.

3-Define the following:
i. Converging lens______

ii. Diverging lens_______

iii. Focal length___________

iv. Focalpoint____________

v. Object distance_______

vi. Imagedistance___

vii. Real image___

viii. Virtual image