1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
TiliK225 [7]
3 years ago
10

Several years from now you have graduated with an engineering/physics degree and have been hired by a nanoengineering firm as an

intern. You have been assigned to work under a top engineer from the company. Their current project is to design a microscopic oscillator as a time keeping device. The engineering design involves placing a negative charge at the center of a very small positively charged metal ring. Your boss claims that the negative charge will undergo simple harmonic motion if displaced away from the center of the ring. Furthermore, they claim they can change the period (timing) of oscillation by adjusting the amount of charge on the ring. The first task they give you is to check the validity of their design.
a. Consider a charge −???? located a small distance z above the center of a positively charged ring with total charge +Q and radius R. Write an expression for the net force exerted on the charge −???? due to the ring of charge. What is the magnitude of the force on the charge −???? if it is at the location z = 0?

b. Use the binomial expansion as a mathematical tool to understand the motion of the charged particle under the assumption that it is only displaced a small distance z ≪ ???? away from the center of the ring. Using the binomial approximation, simplify your expression from part (a). You should have two terms in your expression for the net force.

c. Suppose that z =1.0 nanometer and R = 1.0 millimeter. Using these values, determine the relative strength of the force that each term in your expression contributes to the total force (calculate the ratio of z/R that appears in each term). Is one term negligible (i.e. is the value of one term very close to zero)?

d. Using results from part (c) show that the relevant force on charge −???? simplifies to a Hook’s law restoring force: ???? = −????x, where k is now a more complicated constant made up of several constants from this problem. What is k?

e. Using Newton’s 2nd Law, write down the differential equation of motion for the particle as it undergoes oscillations due to this Hook’s law force. Determine the period T of oscillations charge −???? makes about the equilibrium point z = 0 (this should not involve any calculations, see equations 15.32 and 15.37 from your book). Asses the validity of your solution by analyzing the physical units to make sure that your solution has units of time.
Physics
1 answer:
nadya68 [22]3 years ago
5 0

Answer:

See attached handwritten document for answer

Explanation:

You might be interested in
Define efficiency. class -8 ​
Finger [1]

the state or quality of being efficient.

"greater energy efficiency"

Answer

Efficiency is the ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result.

8 0
2 years ago
Read 2 more answers
Which letter explains why no machine is 100 percent efficient.
kondaur [170]

Answer:

A

Explanation:

Think about rubbing your hands together- the friciton produces heat

4 0
2 years ago
Compared to all other forms of energy, wind power is most similar to tidal wave power because _____.
SOVA2 [1]
It is because they are both renewable sources of energy
5 0
3 years ago
Read 2 more answers
Which property of sound waves decreases as the square of the distance from the source increases?
Vitek1552 [10]

Answer:

Intensity

Explanation:

The intensity of a sound wave is equal to the ratio between to the power emitted by the source divided by the area of the spherical surface through which the wave propagates:

I=\frac{P}{4\pi r^2}

where

P is the power

4\pi r^2 is the area of the spherical surface

r is the distance from the source

As we see from the formula, the intensity is inversely proportional to the square of the distance from the source:

I\propto \frac{1}{r^2}

so, intensity is the correct answer.

3 0
3 years ago
The_______ of an object is given relative to an origin
Setler79 [48]
The slope of an object is given relative to an origin.
8 0
3 years ago
Other questions:
  • Which waves are longitude waves? Check all that apply.
    12·1 answer
  • How does the electric force between two charged particles change if particle's charge is reduced by a factor of 3?
    14·2 answers
  • Carlos runs with velocity \vec{v}v →= (5.6 m/s, 29o north of east) for 10 minutes. How far to the north of his starting position
    10·1 answer
  • Because the snow suddenly gets too slushy, you decide to carry your 100-n sled the rest of the way home. How much work do you do
    6·1 answer
  • Can you have constant speed with zero net force?
    11·1 answer
  • Give me a copy and pasted bible lol
    9·1 answer
  • A machine used an input force of 200 N to produce an output force of 800N. What is the mechanical advantage of this machine?
    7·2 answers
  • Freeeeeeee points!!!
    13·2 answers
  • PLEASE HELP MEE I REALLY NEED IT
    15·1 answer
  • State Newton's second law of motion in terms of momentum<br>​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!