Consider a spherical shell with radius R and surface charge density σ. By integrating the electric field, find the potential outside and inside the shell. You should find that the potential is constant inside the shell. Why?

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t, at which time the fuel is exhausted and it becomes a freely "falling" body. 1919 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to −16 ft/s in 5 s. The rocket then "floats" to the ground at that rate.

(a) Determine the position function s and the velocity function v(for all times t).

(b) At what time does the rocket reach its maximum height? (Round your answer to two decimal places.)

What is that height? (Round your answer to the nearest integer.)

(c) At what time does the rocket land? (Round your answer to one decimal place.)

The Moon orbits Earth in an average of p = 27.3 days at an average distance of a =384,000 kilometers. Using Newton’s version of Kepler’s third law determine the mass of Earth. You may neglect the mass of the Moon in comparison to the mass of Earth.

Please no pictures or handwriting, it is always difficult to read.

Hello, please if you were to learn and teach these topics

Counted systems and integers

Fractions, decimals and percentages

Powers and laws of indices

Counting using the product rule

what kind of difficulties you might face when learning these

what kind of difficulties student might face when learning these topics

How would you explain and teach these topics  classroom practice

how would you teach it,

why do you think it would be hard for students to learn.

Please answer this in essay-based format

I want this to be about 300 words, please

1. At high noon, a sinusoidal electromagnetic wave is heading straight toward San Diego. At a 12:00 sharp, the electric field at a certain location is 700 N/C directed South. a) What is the magnitude and direction of the magnetic field at this location at this instant? b) If it takes 1.0 x 10^-15 seconds for the fields at this location to return to the values described above, what is the wavelength of this wave? c) Does this wave fall within the visible range? d) At what rate does this wave deliver energy to a patch of Earth of area 2 m², assuming all is absorbed?

Normal seeds can be separated from discoloured ones and from foreign objects by means of an electrostatic seed-sorting machine that operates as follows. The seeds are observed by a pair of photocells as they fall one by one inside a tube. If the colour is not right, a voltage is applied to a needle that deposits a charge on the seed. The seeds then fall between a pair of electrically charged plates that deflects the undesired ones into a separate bin. One such machine can sort dry seeds at the rate of 100 per second, or about 2000 kg per 24 hour day.

i) over what distance must they fall if they must be separated by 20 mm when they pass between the photo-cells? Neglect air resistance.

ii) Assuming that the seeds acquire a charge of 1.5 10-9 C, that the deflecting plates (large enough to consider negligible the side distortions of the field) are parallel and 50 mm apart, and that the potential difference between them is 25 kV, how far should the plates extend below the charging needle if the charged seeds must be deflected by 40 mm on leaving the plates? Assume that the charging needle and the top of the deflecting plates are close to the photocell.

A sphere of radius R has a radius dependent charge density ρ = B · r3 in terms of R and B.

Calculate the potential as a function of r from the center of the sphere.

Topic:Physics statistics

Give definition of chemical potential. Calculate the canonical partition function and chemical potential of a classic N-particle ideal gas

Patch-Clamp instruments allow researchers to measure the opening and closing of a single channel in a membrane. A typical acetylcholine receptor channel passes about 5 pA (picoamperers) of ionic current over a period of 5 msec at -60mV. Given that an electric current of 1 A is about 6.2x10^18 electrical charges per second, how many ions (potassium or sodium) pass through the channel during the time that it is open?

A stone with a mass of 525 g in air is found to have an apparent mass of 377 g when submerged in water. a. What mass of liquid is displaced? b. What is the volume of the stone? c. What is the average density of the stone?

Question 1
a) Continuing concerns about the ‘sustainability’ of both fossil and nuclear fuel use
have been a major catalyst of renewed interest in the renewable energy sources
in recent decades. One of the criteria of renewable energy source is it does
not entail significant pollutant emission or other environmental problems.
i) Based on this criterion and solar photovoltaic panel life cycle (from raw
material extraction, manufacturing to disposal), discuss the sustainability of
solar photovoltaic panels.
ii) On a large scale, compare the sustainability between wind energy and solar
energy (PV panels).

b) Consider a horizontal axis aero-generator that designed to develop 100 W
(electrical power) at a wind speed of 7 m/s. NACA 4412 airfoil is used for the wind
rotor blade and the design power coefficient is close to the maximum value of
commercial small wind turbine. The combined drive train and generator efficiency
is 0.9. Assume the air density to be 1.224 kg/m3.
i) Suggest the number of rotor blade. Provide the reasons for the blade
number selected.
ii) Estimate the power coefficient. Calculate the wind rotor radius.

c) One of the elements considered in energy efficient buildings is high performing building envelope. Determine 2 parts of building envelope that applicable to a single-storey house in Malaysia.

A household’s daily energy usage is 800 Wh. The operating voltage is set at 24 V. Day of autonomy required is 4 days and the manufacturer only allows the battery to have a minimum state of charge of 50%. Calculate the minimum sized battery bank in Ah that would meet the household’s load requirements?

Due to a recession, expected inflation this year is only 2.75%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2.75%. Assume that the expectations theory holds and the real risk-free rate (r*) is 1.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 1.0%, what inflation rate is expected after Year 1?

Madsen Motors's bonds have 24 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 6%, and the yield to maturity is 8%. What is the bond's current market price?

<Basic Physics (Conceptual)>

1. Look up the distance to the nearby star Alpha Centauri. And look up the distance to the center of the Milky Way. Convert (or get) both of those distances in light years. Now imagine traveling to both of those places in a spaceship that can travel at half the speed of light. To answer these questions, you might want to look up “length contraction”. In the frame of reference of that spaceship, traveling to Alpha Centauri, how far away is Alpha Centauri? In the frame of reference of another spaceship, traveling to the Galactic Center, how far away is the Galactic Center? How long does it take to get to those two locations? Give two answers: One for the reference frame of the Earth (essentially at rest in the Galaxy), and one for the reference frame of the astronauts on the spaceship.

2. Look up the “twin paradox” and answer the following questions: Imagine one of your friends is a flight attendant and spends five years flying around in jet planes. By how much will your friend’s age be different than it would have been if the friend had spent that time hanging out at home. Older or younger? Now imagine the same but for a friend who is on the International Space Station for five years? (In detail this question is weird because flights and space stations go around the Earth, not out and back. But just do the calculation as if your friend just went out and back. The answer you get is close to the true answer.) Now imagine the same but for a friend who spends five years on a journey to a distant star, traveling at 0.2 c. Now the same but 0.99 c. Here you might want to say how much has your friend aged, instead of the correction to the age.

A basketball is dropped from 140 meters height with back spin. It goes straight down and then it gains speed as it curves 70 meters horizontally away from where it is dropped. That is a spectacular example of the Magnus effect. A paper cylinder is dropped down the inclined plane and rolls backward. This is another example of Magnus affect. Why is the example of the basketball more extreme than that of the paper cylinder ?