Speed of two charged particles repelling each other

In summary, the two particles, A and B, with masses m and charges Q and 5Q respectively, are released from rest with a distance of 1.0 m between them. The kinetic energy of particle B at the instant when the particles are 3.0 m apart, given that Q = 12 μC, is 4.3 J. The calculation for this is based on the principle of conservation of energy, where the initial potential energy is divided between the two particles, resulting in 0.7192 J for particle A and 3.596 J for particle B. Therefore, the correct answer is d.
  • #1
fight_club_alum
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1

Homework Statement


28. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest

with the distance between them equal to 1.0 m. If Q = 12 μC, what is the kinetic energy of

particle B at the instant when the particles are 3.0 m apart?

a . 8.6 J

b. 3.8 J

c. 6.0 J

d. 2.2 J

e. 4.3 J

Homework Equations


(delta (u) = delta ke

The Attempt at a Solution


(k*(Q*10^-6)*(5Q*10^-6))/1) - (k*(Q*10^-6)*(5Q*10^-6))/3) = 4.3152
4.3152 = u1 + u2 <-- I want u2 alone since the initial kinetic energy is zero
5u1 = u2
4.3152 = u1 + 5u1
4.3152 = 6u1
u1 = 0.7192
(5*0.7192) = 3.596 ~ 3.6 <-- not the right answer, it should be d

Any help, please?
 
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  • #2
fight_club_alum said:
5u1 = u2
Why?
 
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  • #3
I think because particle two will have a bigger share of the total potential; I am not sure
 
  • #4
fight_club_alum said:
I think because particle two will have a bigger share of the total potential; I am not sure

What about Newton's second and third laws?
 
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  • #5
fight_club_alum said:
I think because particle two will have a bigger share of the total potential; I am not sure
Maybe, but why in that ratio? Use conservation laws.
 
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  • #6
PeroK said:
What about Newton's second and third laws?
Can you please just tell me how to correctly understand this problem because if I could understand it on my own I wouldn't have posted it in the first place?
Thank you
 
  • #7
fight_club_alum said:
Can you please just tell me how to correctly understand this problem because if I could understand it on my own I wouldn't have posted it in the first place?
Thank you

##F = ma##

Is the force on each particle the same? Is the mass the same? What about acceleration? What about KE?
 
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  • #8
PeroK said:
##F = ma##

Is the force on each particle the same? Is the mass the same? What about acceleration? What about KE?
Yes the forces should be the same
They both have the same mass
So They both should have the same acceleration and the same KE
I think I see the issue by now, so the total u should be divided by two
Thank you so much
 

FAQ: Speed of two charged particles repelling each other

What is the speed of two charged particles repelling each other?

The speed of two charged particles repelling each other depends on several factors, including the magnitude of the charges, the distance between the particles, and the direction of their motion. It is typically described using the formula for Coulomb's Law, which states that the force of repulsion is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

How does the speed of two charged particles repelling each other change over time?

The speed of two charged particles repelling each other can change over time due to various factors, such as changes in their charges or the distance between them. For example, if the charges of the particles increase, the force of repulsion will increase, causing the particles to accelerate and increase their speed. Similarly, if the distance between the particles decreases, the force of repulsion will also increase, leading to an increase in speed.

Can the speed of two charged particles repelling each other ever reach the speed of light?

No, the speed of two charged particles repelling each other cannot reach the speed of light. According to Einstein's theory of relativity, as an object approaches the speed of light, its mass and energy increase infinitely. Therefore, it would require an infinite amount of energy to accelerate a charged particle to the speed of light, making it impossible for two particles to repel each other at that speed.

How does the direction of motion affect the speed of two charged particles repelling each other?

The direction of motion can affect the speed of two charged particles repelling each other. If the particles are moving directly towards each other, the force of repulsion will slow them down, causing a decrease in speed. On the other hand, if the particles are moving in parallel directions, the force of repulsion will accelerate them, resulting in an increase in speed.

What is the role of the medium in determining the speed of two charged particles repelling each other?

The medium in which the particles are located can affect the speed of two charged particles repelling each other. In a vacuum, the particles will experience no resistance and will maintain a constant speed. However, in a medium with other particles, such as air or water, there will be some resistance, causing the speed of the particles to decrease over time.

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