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

Does the resistance torque change as leg position is changed? Explain, based on the average scores for perceived exertion, which leg position is easiest to perform and which is hardest. Why are there differences in perceived exertion for the different leg positions?

What is wave-particle duality of light?

What is energy quantization?

What is ultraviolet catastrophe?

State and describe the Rayleigh-Jeans Law.

A 10-cm-long thin glass rod uniformly charged to 13.0 nC nC and a 10-cm-long thin plastic rod uniformly charged to - 13.0 nC nC are placed side by side, 4.20 cm cm apart. What are the electric field strengths E 1 E1E_1 to E 3 E3E_3 at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods? Specify the electric field strength of E1, E2, E3?

In the experiment: To determine the resistivity of the given semiconductor sample by Four Probe method.

Why are there "four" probes instead of 2? what is the mechanism of that four probe setup in relation with the semiconductor that it touches?

Show that an electron jumping down from the 6^th excited state down to the 5^th excited state in a hydrogen atom emits an infrared photon of 12,367nm.

Show that in a hydrogen atom moving away from a bright star, and its electron jumps up from the 2nd excited state up to the 3^rd excited state and has absorbed a photon with a wavelength of 690 nanometers. How fast is the atom moving? Show your work.

An object with a mass of 4.15 kg undergoes an acceleration of 2.7 m/s2 for a period of 8.0 s. It then undergoes an acceleration of -3.2 m/s2 for a period of 20.0 s If the initial velocity of the object is 6.01 m/s and it first experiences the acceleration when it is at the origin, plot by hand on graph paper (to scale) the force, velocity, and position as functions of time. Explain why your graphs look the way they do. Include all relevant equations. (Each graph 10 pts, each explanation 10 pts, 60 pts total)

A horizontal spring attached to a wall has a force constant of k = 770 N/m. A block of mass m = 2.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below.

(a) The block is pulled to a position xi = 5.80 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 5.80 cm from equilibrium.

J

(b) Find the speed of the block as it passes through the equilibrium position.

m/s

(c) What is the speed of the block when it is at a position xi/2 = 2.90 cm?

m/s

Please Answer the following problem 1 and 2. write clearly.

PROBLEM 1

A 5.96 − kg block is placed against a compress spring on a frictionless 27.0 degrees incline. The spring,

whose force constant is 2.5 N/cm, is compressed 21.3 cm, after which the block is released. How far up

the incline will the block go before coming to rest? Measure the final position of the block with respect

to its position just before being released. Consider two cases:

(a) the block is firmly attached to the spring, and

(b) the block is not attached to the spring and can loosely move up the incline

PROBLEM 2

During a rockslide, a 524 − kg rock slides from the rest down the hill slope that is 488 m long and

292 m high. The speed of the rock when it reaches the bottom of the hill is 62.6 m/s. How much

mechanical energy does the rock lose in the slide due to friction.

A ball of mass m is tied to a string and is rotating in a vertical plane. The string is elastic (it stretches), which causes the path to be elongated vertically rather than perfectly circular. At the top of the path, the speed has the minimum value that still allows the ball to complete its circular path. Find: the length of the string when it makes an angle θ with respect to the horizontal. The following quantities are known: Mass of the ball , m Elastic constant of the string, k Length of the string when the ball is at the top , r0 and angle θ.

PLEASE answer questions 3 , 4 & 5. write clearly

PROBLEM 3

Calculate the magnitude of the gravitational force on a cantaloupe of mass m = 873 g on the surface

of the Earth due to

(a) the Earth

(b) the Moon

(c) the Sun

PROBLEM 4

A hypothetical planet has 1/5 of the diameter of the Earth, and its density is 4 times larger

(compared to the Earth). Find its total mass and the free fall acceleration.

PROBLEM 5

Two planets with masses M1 and M2 are located at a distance D from each other far removed from

any other planets or objects in the outer space. Where should a satellite of mass m be located if we

need to have the two gravitational forces acting on it

(a) to be balanced (equal)

(b) the force from planet M1

to be three times larger compared to that from the planet M2

1. A surgeon inserted a needle in the patient’s vein. The needle was connected to a top-open plastic bag filled with therapeutic fluid and lifted to a height h. Find h , which is just sufficient for the fluid to enter the vein, if the pressure gauge inside the vein was 5980 Pa. The therapeutic fluid density was adjusted to be the same as that of blood, 1060kg/m3.

2. At the next stage of the treatment procedure, the surgeon used a syringe to administer a drug fluid into the same vein as in #1. The syringe was positioned at the same level as the vein. A force of 1.20 N was applied to the plunger of the cross-sectional area 0.81 cm² connected to the needle of the inner radius 0.6 mm. What was pressure difference between the proximal and distal parts of the needle, given that the proximal end opened into the vein? Use the same drug fluid density as in #1.

3. What volume of the drug fluid was injected into the vein in 2.5 s by the pressure difference calculated in #2? [Hint: neglect the fluid speed in the syringe].

Two separate experiments -- double-slit and diffraction grating -- use a 400-nm electromagnetic wave. In both experiments, a long, flat wall where the results are seen is located 2.00-m across from the slits/grating. The slit separation for the double-slit experiment is 0.20mm. The diffraction grating has 1200 lines per mm.

a. Calculate the distance between the first and second bright spots below the center line for each experiment. Compare your answer for each experiment and explain how the pattern created on the screen by the two experiments would differ.

b. If the slit-width is roughly the same for both, which pattern would have a brighter central maximum? Why?

1) A piano tuner hears one beat every 1.3 s when trying to adjust two strings, one of which is sounding 350 Hz. How far off in frequency is the other string?

2) A source emits sound of wavelengths 2.64 m and 2.81 m in air. a) How many beats per second will be heard? (Assume T=20?C.) B)How far apart in space are the regions of maximum intensity?

3) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 3.7 s after shouting. The speed of sound in air is 343 m/s. determine the length of the lake.

4) What is the resultant sound level when an 83 dB sound and an 86 dB sound are heard simultaneously?