The doctor is trying to decide what type of “feather” material to give his creations so that they keep warm while sleeping in the winter. Given the following data calculate the conductive heat flux (W) for the different “feather” materials. Material “A” has a K of 0.036 W/mK and increases the bird’s x by 2.769 x 10^-3 m. Material “B” has a K of 0.17 W/mK and increases the bird’s x by 1.308 x 10^-2 m. The bird’s internal temperature is 311.0 K (we are assuming that they are endothermic) and the temperature of the ground is 260.0 K. The distance from the exterior of the bird’s skin to its core is 0.75 m. When the animal is sleeping the surface area of the bird that touches the ground is 1.76 m². Which of these materials results in the smallest loss of heat due to conduction?     

Please include detailed work for answers

A piston contains 770 moles of an ideal monatomic gas that initally has a pressure of 1.23 × 10⁵ Pa and a volume of 4.2 m³. The piston is connected to a hot and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir and exhausting energy into the cold reservoir.

1. The pressure of the gas is increased to 4.23 × 10⁵ Pa while maintaining a constant volume.
2. The volume of the gas is increased to 11.2 m³ while maintaining a constant pressure.
3. The pressure of the gas is decreased to 1.23 × 10⁵ Pa while maintaining a constant volume.
4. The volume of the gas is decreased to 4.2 m³ while maintaining a constant pressure.

It may help you to recall that CVCV = 12.47 J/K/mole and CPCP = 20.79 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 10²³) times the number of moles of the gas.

1)How much energy is transferred into the gas from the hot reservoir? ___J

2)How much energy is transferred out of the gas into the cold reservoir? ___J

3)How much work is done by the gas? ___J

How do you perform the mechanical advantage equation and howto find the f required to move a lever based on the resistance load, resistance arm, and the force arm

While a roofer is working on a roof that slants at 45.0 ∘∘ above the horizontal, he accidentally nudges his 90.0 NN toolboxes, causing it to start sliding downward, starting from rest.

a)If it starts 4.70 mm from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 19.0 NN ?

calculate the conductive heat flux (W) for the different “feather” materials. Material “A” has a K of 0.036 W/mK and increases the bird’s x by 2.769 x 10^-3 m. Material “B” has a K of 0.17 W/mK and increases the bird’s x by 1.308 x 10^-2 m. The bird’s internal temperature is 311.0 K (we are assuming that they are endothermic) and the temperature of the ground is 260.0 K. The distance from the exterior of the bird’s skin to its core is 0.75 m. When the animal is sleeping the surface area of the bird that touches the ground is 1.76 m². Which of these materials results in the smallest loss of heat due to conduction?     

Inflation

(a) What is the cosmic epoch of inflation in the early universe? How is this different from the usual expansion of the universe?

(b) What similarities and differences are there between inflation and dark energy?

Inflation

(a) Why is it puzzling that the observed CMB temperature is almost exactly the same on opposite sides of the sky? How would this result be explained in cosmology theories that do not include inflation?

(b) How does inflation answer the puzzle from part (a)? What other properties of the homogeneous universe does inflation explain?

Please use any of the methods to prove whether each of the following arguments is valid or invalid. For each problem, please identify the method that you have decided to employ and make sure to show your work.

1. It is obvious that nuclear energy is needed. Nuclear energy is needed if and only if solar energy cannot be harnessed. And it is also true both that solar energy can be harnessed only if funds to do so are available, and that funds are not available.

Please include detailed work for answers.

A window air conditioner uses 1272 W of electricity and has a coefficient of performance of 3.64. For simplicity, let's assume that all of that electrical energy is transformed into work done by the air conditioner to cool a room with dimensions of 7 m x 7 m x 3 m. The air inside this room will initially have the same temperature as the air outside (318 K) and the air conditioner will attempt to cool the room to 295 K. For the purposes of estimation, assume that the air in this room will be cooled at constant volume, that the specific heat of the air at constant volume is 720 J/kg-K, and that the density of the air is 1.2 kg/m³.

1)How much energy must be transferred out of this room in order to decrease the temperature of the air from 318 K to 295 K? ___J

2)How much work will be done by the air conditioner during the process of cooling the room? ___J

3)How much time in minutes will it take for the room to cool using this air conditioner? ___minutes

4)How much time in minutes would the cooling process take if instead we used an air conditioner that uses a Carnot cycle that operates between 318 K and 295 K? ___minutes

A capacitor C1 =1F is connected to a 1V battery using a wire with a total resistance R = 1Ohm

Suppose after the charging is complete the capacitor C1 is connected to another capacitor C2 = 2 F using a wire with a total resistance of R =0.3 Ohm. Now the first capacitor discharges while the second one charges.

2.8 [1pt] How much charge was transferred through the resistor R during the discharge?

ANSWER

2.9 [1pt] How much energy was dissipated in the resistor R during the discharge

ANSWER

Let’s derive the differential equation describing the discharge in this 2-capacitor circuit. Let’s label the charge on the capacitor C1 as q1(t) and the charge on the capacitor C2 as q2(t).

2.10 [1pt] Sketch the circuit diagram, label the charges and their signs at the capacitors plate, and link q1(t) and q2(t).

Hint, what is q1(t=0) and q2(t=0) (t=0 is the instant the connection was made)?

ANSWER

2.11 [1pt] Express the current through the resistor in terms of the charge derivative and write down the voltages across both capacitors and the resistor add up to zero. From the resulting equation, deduce the characteristic charging time without solving it.

ANSWER

In a lava lamp, a waxy fluid (say ρ= 1225[kg/m3]) is surrounded by another fluid

(say ρ= 1200[kg/m3]), they are mutually insoluble, and they are heated by a lamp in the

bottom of the apparatus. The densities of these materials are very similar, where the

waxy one is greater at normal room temperature. As the liquids are heated, the waxy

density becomes less than the surrounding fluid and it rises. What is the buoyant force on

a spherical waxy blob, with radius 0.10[m] in the surrounding fluid? What is the force

due to gravity on this blob? When the blob heats and its density becomes 1100[kg/m3],

how much of its volume is submerged? How do the buoyant force and the force due to

gravity compare now?

1. Special Relativity (a) An observer sees a πon moving past with momentum ~p. In the rest frame of the πon, it decays into a µon and a νtrino in perpendicular directions to the direction in which the observer is moving. Find the velocity of the µon in the rest frame of the πon.

(b) Find the velocity of the µon in the frame of the observer. What angle does it make with the direction of the πon's motion? Repeat for the νtrino (which may be assumed to be massless).

(c) If the µon's average lifetime is τµ, then what is the average time taken it to decay relative to the observer?

A “U” shaped tube (with a constant radius) is filled with water and oil as shown. The water is a height h₁ = 0.36 m above the bottom of the tube on the left side of the tube and a height h₂ = 0.1 m above the bottom of the tube on the right side of the tube. The oil is a height h₃ = 0.33 m above the water. Around the tube the atmospheric pressure is P_A = 101300 Pa. Water has a density of 10³ kg/m³.

A)What is the absolute pressure in the water at the bottom of the tube?
B)What is the absolute pressure in the water right at the oil-water interface?
C)What is the density of the oil?
D)Now the oil is replaced with a height h₃ = 0.33 m of glycerin which has a density of 1261 kg/m³. Assume the glycerin does not mix with the water and the total volume of water is the same as before.

Now what is the absolute pressure in the water at the interface between the water and glycerin?
E)How much higher is the top of the water in the tube compared to the glycerin? (labeled d in the diagram)
F)What is the absolute pressure in the water at the very bottom of the tube?

A block with mass m =6.7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.29 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.7 m/s. The block oscillates on the spring without friction.

A)What is the spring constant of the spring?

B)What is the oscillation frequency?

C)

After t = 0.32 s what is the speed of the block?
D)What is the magnitude of the maximum acceleration of the block?
E)At t = 0.32 s what is the magnitude of the net force on the block?