Physics, 20.02.2020 18:38, o10889084

Two electrons, each with mass m and charge q, are released from positions very far from each other. With respect to a certain reference frame, electron A has initial nonzero speed v toward electron B in the positive x direction, and electron B has initial speed 3v toward electron A in the negative x direction. The electrons move directly toward each other along the x axis (very hard to do with real electrons). As the electrons approach each other, they slow due to their electric repulsion. This repulsion eventually pushes them away from each other. What is the minimum separation rmin that the electrons reach? Express your answer in term of q, m, v, and k (where k=14πϵ0)

Answers: 3

Show answers

Answers

answered: elizabethhubbe

The minimum separation reached by the electrons is $\dfrac{ke^{2}}{4mv^{2}}$ .

The given problem is based on the concept of total energy. The system of two electrons is an isolated system, and the internal forces acting on the system are only conservative forces: therefore, the total energy of the system must be constant.

If we assume the electric potential energy to be zero at the beginning (because the electrons are very far from each other), then the initial energy is just the sum of the kinetic energy of the two electrons. So total energy is given as,

$E_{t}=\dfrac{1}{2}m(v^{2}) +\dfrac{1}{2}m((-3v)^{2})\\\\E_{t}=\dfrac{1}{2}mv^{2} +\dfrac{9}{2}mv^{2}\\\\E_{t}=5mv^{2}$ .................................................................(1)

When the two electrons reach the distance of minimum approach, part of the kinetic energy has been converted into electric potential energy, so the total final energy is:

$E'_{t}=\dfrac{1}{2}mv'^{2} +\dfrac{1}{2}mv'^{2} +\dfrac{k(e)(e)}{r}$ ..................................................................(2)

Here,

v' is the final speed of the two electrons.

e is the charge of the electron.

r is distance of minimum approach.

Applying the conservation of linear momentum for the isolated system as,

$mv+m(-3v)=mv'+mv'\\\\mv-3mv=2mv'\\\\-2mv=2mv'\\\\v'=v$

Substituting into (2) we get,

$E'_{t}=\dfrac{1}{2}mv^{2}+ \dfrac{1}{2}mv^{2}+\dfrac{ke^{2}}{r}\\\\E'_{t}=mv^{2}+\dfrac{ke^{2}}{r}$

Equate equation (1) and (2) to find the distance of minimum approach as,

$5mv^{2}=mv^{2}+\dfrac{ke^{2}}{r}\\\\ r=\dfrac{ke^{2}}{4mv^{2}}$

Thus, we can conclude that the minimum separation reached by the electrons is $\dfrac{ke^{2}}{4mv^{2}}$ .

Learn more about the Conservation of momentum here:

link

answered: aislamgomes22

Distance of minimum approach: $r=\frac{ke^2}{4mv^2}$

Explanation:

The system of two electrons is an isolated system, and the internal forces acting on the system are only conservative forces: therefore, the total energy of the system must be constant.

The total energy is the sum of the kinetic energy and the electric potential energy.

$E_i = \frac{1}{2}m(v)^2+\frac{1}{2}m(-3v)^2=\frac{1}{2}mv^2+\frac{9}{2}mv^2=5mv^2$ (1)

where v and (-3v) are the initial velocities of the 2 electrons, while m is the mass of each electron.

Later, when the two electrons reach the distance of minimum approach, part of the kinetic energy has been converted into electric potential energy, so the total final energy is:

$E_f=\frac{1}{2}mv'^2+\frac{1}{2}mv'^2+\frac{k(e)(e)}{r}$ (2)

where

v' is the final speed of the two electrons (at the distance of minimum approach, they have the same speed, because the velocity of the center of mass of the system must be zero)

$\frac{k(e)(e)}{r}$ is the final electric potential energy of the system, with

e = charge of the electron

r = distance of minimum approach

Also, the system is isolated, so we can apply the law of conservation of momentum:

$mv+m(-3v)=mv'+mv'\\mv-3mv=2mv'\\-2mv=2mv'\\v'=-v$

Substituting into (2) we get

$E_f=\frac{1}{2}mv^2+\frac{1}{2}mv^+\frac{ke^2}{r}=mv^2+\frac{ke}{r}$

And now we can finally equate the initial and final energy (1)=(2) to find the distance of minimum approach:

$5mv^2=mv^2+\frac{ke^2}{r}\\\rightarrow r=\frac{ke^2}{4mv^2}$

answered: Guest

1.the balanced chemical equation is as below

cu + 2 ag(no)₃ → cu(no₃)₂ +2 ag

2.the much silver produced is 50.9 g

step 1: find the moles of cu

moles = mass÷ molar mass

from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236 moles

step 2: use the mole ratio to determine the moles of ag

from equation above cu: ag is 1: 2

therefore the moles of ag =0.236 moles x 2/1 =0.472 moles

step 3: find the mass of ag

mass = moles x molar mass

from periodic table the molar mass of ag =107.87 g/mol

mass = 0.472 moles x 107.87 g/mol = 50.9 g

3. the much silver collected worth is 1.797 oz

convert 50.9 g to oz

that is 1 gram = 0.0353 oz

50.9 grams =? oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1 gram} =1.797 oz

answered: Guest

Cis the

Other questions on the subject: Physics

Physics, 22.06.2019 10:00, nayellisoto15

Asap and show ! a 14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earths velocity. earth mass is 6.0 * 10^24 kg. show your work assuming the rock earth system is closed.

Answers: 2

continue

Physics, 22.06.2019 17:00, jenn8055

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons

Answers: 3

continue

Physics, 22.06.2019 17:40, hmontalvo22

Aball horizontally thrown from a cliff at 8m/s

Answers: 1

continue

Physics, 23.06.2019 00:00, elyssa34972

Examine the drawing of a molecule. each ring represents an atom of nitrogen (n). what’s the chemical formula of this substance?

Answers: 2

continue

Do you know the correct answer?

Two electrons, each with mass m and charge q, are released from positions very far from each other....