Equivalent Electri Force, Find the charge.

[pmd28]

Homework Statement

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.3 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 2.3 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object? (Note: there are two possible pairs of answers, but assume q1 to be the larger number.)

Homework Equations

F=kq1q2/r²

The Attempt at a Solution

So I know that since force is equal Fr²/k is a constant. Also since the charge in the 2nd case is equally shared I can re-write the equation for force as F=kq²/r². Solving for q gets me 4.8e-6.


From here since the charge was shared equally between q1 and q2, q=q1+q2/2. Using substitution to solve for q2, I came up with the following quadratic:

-q1²+9.6e-6(q1)-9.6e-6. This results in an invalid quadratic equation because b₂-4ac gives me a negative number. I think I made math errors or I'm missing a step, but the underlying concept makes sense.

 

[SammyS]

Homework Statement

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.3 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 2.3 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object? (Note: there are two possible pairs of answers, but assume q1 to be the larger number.)

Homework Equations

F=kq1q2/r²

The Attempt at a Solution

So I know that since force is equal Fr²/k is a constant. Also since the charge in the 2nd case is equally shared I can re-write the equation for force as F=kq²/r². Solving for q gets me 4.8e-6.

From here since the charge was shared equally between q1 and q2, q=q1+q2/2. Using substitution to solve for q2, I came up with the following quadratic:

Be careful with parentheses. That should be written,

q = (q₁+q₂)/2​

-q1²+9.6e-6(q1)-9.6e-6. This results in an invalid quadratic equation because b₂-4ac gives me a negative number. I think I made math errors or I'm missing a step, but the underlying concept makes sense.

It's likely that the signs of the charges is what's causing your problems.

The magnitude of the force is the same for both situations, so

|q₁q₂| = q²​

but because q₁q₂ is negative,

|q₁q₂| = -q₁q₂ .​

 

[pmd28]

ok now I just got a completely wrong answer. My new quadratic equation is q2²-9.59e-6+4.8e-6. I got answer of like .00348

 

[SammyS]

ok now I just got a completely wrong answer. My new quadratic equation is q2²-9.59e-6+4.8e-6. I got answer of like .00348

Coulombs?

What equations are you putting together to get your answers ?

 

[Nickie]

Your approach is correct, but there is an error in your calculation. The correct equation for the initial force is F=kq1q2/r^2, where r is the distance between the two objects. Since the objects are brought into contact and then returned to their initial positions, the distance between them remains the same. Therefore, the initial force is still 2.3 N.

Using this information, we can set up the following equations:

For the initial attractive force: 2.3 N = kq1q2/(0.3 m)^2

For the repulsive force after the objects are brought into contact: 2.3 N = k(q1/2)(q2/2)/(0.3 m)^2

Solving for q1 and q2 in terms of k and the initial force, we get:

q1 = (2.3 N)(0.3 m)^2/kq2

q2 = (2.3 N)(0.3 m)^2/kq1

Substituting these values into the equation q=q1+q2/2 and simplifying, we get:

q = (2.3 N)(0.3 m)^2/k(1+q1/q2)

Since we know that the initial force is equal to the repulsive force after the objects are brought into contact, we can equate the two equations and solve for q1:

(2.3 N)(0.3 m)^2/kq2 = (2.3 N)(0.3 m)^2/k(1+q1/q2)

Solving for q1, we get:

q1 = q2(1+q1/q2) - 1

q1 = q2 + q1 - q2

q1 = q1

This means that q1 and q2 are equal. Substituting this into the equation for the initial attractive force, we get:

2.3 N = kq^2/(0.3 m)^2

Solving for q, we get:

q = √(2.3 N)(0.3 m)^2/k

Since there are two possible pairs of answers, we can assume that q1 is the larger number, which means that q2 is equal to q1. Therefore, the initial charge on each object is √(2.3 N)(0.3 m)^