How many seconds are there in 27.5 days?

The ball will oscillate along the z axis between z=dz=d and z=−dz=−d in simple harmonic motion. What will be the angular frequen

Eddi Din [679]

Answer:

$\omega = \sqrt{\dfrac{kq_0Q}{ma^3} }$

Explanation:

Additional information:

The ball has charge $-q_0$ , and the ring has positive charge $+Q$ distributed uniformly along its circumference.

The electric field at distance $z$ along the z-axis due to the charged ring is

$E_z= \dfrac{kQz}{(z^2+a^2)^{3/2}}.$

Therefore, the force on the ball with charge $-q_0$ is

$F=-q_oE_z$

$F=- \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}$

and according to Newton's second law

$F=ma=m\dfrac{d^2z}{dz^2}$

substituting $F$ we get:

$- \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}=m\dfrac{d^2z}{dz^2}$

rearranging we get:

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{(z^2+a^2)^{3/2}}=0$

Now we use the approximation that

$z^2+a^2\approx a^2$ (we use this approximation instead of the original $d^2+a^2\approx a^2$ since $z$ , our assumption still holds )

and get

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{(a^2)^{3/2}}=0$

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Qz}{a^{3}}=0$

Now the last equation looks like a Simple Harmonic Equation

$m\dfrac{d^2z}{dz^2}+kz=0$

where

$\omega=\sqrt{ \dfrac{k}{m} }$

is the frequency of oscillation. Applying this to our equation we get:

$m\dfrac{d^2z}{dz^2}+ \dfrac{kq_0Q}{a^{3}}z=0\\\\m=m\\\\k= \dfrac{kq_0Q}{a^{3}}$

$\boxed{\omega = \sqrt{\dfrac{kq_0Q}{ma^3} }}$

5 0

4 years ago

What type of charge do individual hair strands have when standing on end due to static electricity?

aalyn [17]

Answer:

C. I think

Explanation:

C. permanent positive charges

8 0

3 years ago

Explain why sugar was used in this experiment. How does the experiment relate to a baker adding yeast to bread to make it rise?

tia_tia [17]

Answer:

Yeast can use oxygen to release the energy from sugar (like you can) in the process called "respiration". ... So, the more sugar there is, the more active the yeast will be and the faster its growth (up to a certain point - even yeast cannot grow in very strong sugar - such as honey).

7 0

2 years ago

PLEASE HELP ME VERY IMPORTANT

saul85 [17]

Answer: let's see, so it's a 1/4 chance of getting it right, hope your odds are good, have a wonderful day

Explanation:

:D

6 0

3 years ago

A ray diagram is shown. what does the letter x represent?

kobusy [5.1K]

Answer: Letter X in the diagram represent the angle of incidence

Explanation: One of the properties of wave is reflection. But before reflection can occur, there must have been a directed motion of wave particle towards a plane surface. The angle of incidence is the angle between the direction of motion of the wave particle ( for example; light) and the normal to the plane surface.

8 0

4 years ago

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