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?

Make a table or list of the major similarities & differences between the Moon & Mercury, including three major discoveries about Mercury made by Mariner 10 & three improved results found by MESSENGER. Consider just intrinsic & rotational properties, not orbital properties

A roller-coaster track is being designed so that the roller-coaster car can safely make it around the circular vertical loop of radius R = 24.5 m on the frictionless track. The loop is immediately after the highest point in the track, which is a height h above the bottom of the loop. What is the minimum value of h for which the roller-coaster car will barely make it around the vertical loop?

In each hand you hold a 0.17-kg apple. What is the gravitational force exerted by each apple on the other when their separation is each of the following?

(a) 0.40 m
_______ N

(b) 0.80 m
_______ N

A communications satellite with a mass of 500 kg is in a circular orbit about the Earth. The radius of the orbit is 46,000 km as measured from the center of the Earth.

(a) Calculate the weight of the satellite on the surface of the Earth.
______ kN

(b) Calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.
______ kN

An 8.84-kg block slides with an initial speed of 1.54 m/s down a ramp inclined at an angle of 26.4

a signal is carried by a coaxial cable. The signal is carried by an inner wire with radius R1 while an outer conductor of radius R2 is grounded. An insulating materiel is between the two.

A. Find an expression for the capacitance per meter of the coaxial cable, assuming air is between the two cylinders.

B. Find the Capacitance per meter of a cable with R1= 0.70mm and R2=2.1mm. (answer units are pF/m)

An old piece of wood has a carbon mass of 124 g and an activity of 13 Bq. How old is the song? The radioactive isotope of natural carbon has f = 1.3⋅10−12 parts and has a half life of 5730 years. The average for the year is 3.156⋅107 seconds. Please give your answer in years (ie a).

Four point masses each with a mass of 4.90 kg are positioned at the corners of a rectangle with dimensions 1.80 meters by 3.00 meters. Assume these are the only masses that are gravitationally relevant.

What is the magnitude of the gravitational force on a corner mass due to the other three masses?

A) A henry inductor, a 9 ohm resistor, a .05=1/20 farad capacitor are placed in series and attached to a 9 volt battery to complete the circuit. Find the function for the charge on the circuit at time t if an initial charge of 10 coulombs and an initial response of 10 amps are applied to the circuit at time 0.

b) What is the charge on the capacitor after 1 second?

c) Plot the function for the charge on the capacitor over the first second.

keplers third law states that the square of the period of any planets orbit is proportional to the cube of the semimajor axis of the orbit. for the following, show all your work and dont skip steps

derive the exact expression relating the period (T) and the radius (r) for a planet in circular orbit by applying newtons second law for circular motion.

the orbital period of mars in its revolution around the sun is 1.88 years what average distance from the sun does the keplers thirdlaw predict for mars?

What is the wavelength of the matter wave associated with a proton moving at 381 m/s?

wavelength of proton matter wave: 1.04×10^9 m

What is the wavelength of the matter wave associated with a 151 kg astronaut (including her spacesuit) moving at the same speed?

wavelength of astronaut matter wave: 1.15×10^-38 m

What is the wavelength of the matter wave associated with Earth moving along its orbit around the Sun?

wavelength of Earth matter wave: ??? m

I got the first two answers by my last answer I put 1.34 x 10^-59 and it was wrong.

A squirrel sitting on a peak of a roof which is 1.50 m above the bottom of the roof and 4.50 m above the ground puts an acorn on the roof. It starts from rest at the peak and slides down the sloped roof (coefficient of friction = 0.150) which is angled at 25.0 degrees to the horizontal. After the acorn reaches the edge of the roof it flies off and becomes a projectile. You may ignore air resistance. Part A what is the acorn's acceleration as it slides down the rood? PArt B Find the velocity of the acorn at the edge of the roof? Part C How long after the acorn left the roof does is hit the ground? PArt E How far from the side of the house does the acorn hit the ground?