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
Which means "to study or examine”?
garik1379 [7]
<span>analyze. Analyze means to study or examine something carefully in a methodical way. ... This verb analyze comes from the noun analysis. The noun analysis was in turn borrowed from Greek, from analyein, or "to dissolve."


hope it helps;)
</span>
8 0
3 years ago
Read 2 more answers
Help !!!!!!!!<br>Please its Urgent.<br>​
Wewaii [24]

None can.

A clinical thermometer only measures temperatures above +30°C.

Mercury and alcohol are both frozen solid at -50°C.

6 0
2 years ago
A jetliner, traveling northward, is landing with a speed of 71.9 m/s. Once the jet touches down, it has 675 m of runway in which
Leviafan [203]

Answer:

The value is  a =  -3.7 \  m/s^2

Explanation:

From the question we are told that

   The  landing speed is  u =  71.9 \  m/s

   The  distance traveled is  d =  675 \  m

    The velocity it is reduced to is  v  =  11.3 \  m/s

   

Generally the average acceleration is mathematically represented as

      a =  \frac{ v^2  -  u^2 }{ 2 * d }

=>  a =  \frac{ 11.3^2 - 71.9^2 }{ 2 * 675 }

=>   a =  -3.7 \  m/s^2

5 0
3 years ago
Find the kinetic energy of a bullet weighing 0.10 N if its velocity is<br> 2.0 X 103 m/s?
irina1246 [14]

The kinetic energy of the bullet is 20.4 kJ.

<u>Explanation:</u>

Kinetic energy of a bullet will be equal to the product of mass of the bullet with the square of velocity or speed of the bullet and then the half of that product value.

But here the mass of the bullet is not given, instead the weight of the bullet is given in terms of force. So from this, we have to first find the mass of the bullet.

We know that as per Newton's second law of motion, force is directly proportional to the product of mass and acceleration. So here the acceleration will be equal to the acceleration due to gravity as it is weight of the object.

So F = mg

0.10 N = m × 9.8

So ,the mass of the bullet is 0.0102 kg.

Now, we know the mass and velocity of the bullet is given as 2000 m/s.

So,

kinetic energy = \frac{1}{2} × m × v²

kinetic energy = 0.5 × 0.0102 × 2000 × 2000 = 20.4 kJ

Thus, the kinetic energy of the bullet is 20.4 kJ.

5 0
3 years ago
Which type of radiation produces a wave and a lot of energy?A. GammaB. AlphaC. BetaD. Zeta
Kobotan [32]

The correct answer is option A.

The Gamma waves emitted from radioactive decay have a frequency of around 10¹⁹ Hz, which is much greater compared to the alpha of beta waves.

The frequency is directly proportional to the energy of the waves as given by the equation,

E=hf

Where E is the energy, h is the Planck's constant, and f is the frequency.

Thus the gamma waves have a lot of energy compared to the other options.

Thus the correct answer is option A.

5 0
1 year ago
Other questions:
  • With what minimum speed must you toss a 110 g ball straight up to just touch the 11-m-high roof of the gymnasium if you release
    14·1 answer
  • 1) There are many positive and negative aspects associated with nuclear power. Which is a negative aspect associated with nuclea
    14·1 answer
  • SOME PLEASE HELP ME RN IS AN EMERGENCY
    7·1 answer
  • What are the average velocity and average acceleration of the tip of a 2.4 cm long hour hand of a clock?
    6·1 answer
  • Do you guys know any videos that’ll help understand soh cah toa
    7·1 answer
  • What is Acceleration?
    15·2 answers
  • Why was Democritus considered a philosopher and not a scientist?
    12·1 answer
  • Steve want to catch up to Cami, a girl he likes. If he is jogging at 8 m/s and she is walking at 1 m/s. How long will it take hi
    8·1 answer
  • Which of the following sentences does not contain a type of variation?
    10·2 answers
  • A simple harmonic oscillator has an amplitude of 3. 50 cm and a maximum speed of 26. 0 cm/s. What is its speed when the displace
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!