#### miniake

1. The problem statement, all variables and given/known data
A point charge $q_{1}=15.00\mu C$ is held fixed in space. From a horizontal distance of $3.00cm$ , a small sphere with mass $4.00*10^{-3}kg$ and charge $q_{2}=+2.00\mu$C is fired toward the fixed charge with an initial speed of $38.0m/s$ . Gravity can be neglected.
What is the acceleration of the sphere at the instant when its speed is $20.0m/s$ ?

2. Relevant equations

$a = \frac{k*q_{1}*q_{2}}{m*r^{2}}$

3. The attempt at a solution

$a = \frac{9*10^{9}*15*10^{-6}*2*10^{-6}}{4*10^{-3}*r^{2}}$

$a = 67.5 * \frac{1}{r^{2}}$

By integration,

$v = -67.5 * \frac{1}{r} + C$

Initial conditions: $v = 38 m/s, r = 0.03m$

$38 = -67.5 * \frac{1}{0.03} + C$

$C = 2288$

$v = -67.5 * \frac{1}{r} + 2288$

When $v = 20m/s$,

$20 = -67.5 * \frac{1}{r} + 2288$

$r = 0.029761904$

$a = 67.5 * \frac{1}{0.029761904^{2}}$

$a ≈ 76200 m/s^{2}$

Since both charges are +ve,

$a = -76200 m/s^{2}$

However, the solution is not correct.

May anyone pointing out the errors? Thank you very much.

Last edited:
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#### gneill

Mentor
1. The problem statement, all variables and given/known data
A point charge $q_{1}=15.00\mu C$ is held fixed in space. From a horizontal distance of $3.00cm$ , a small sphere with mass $4.00*10^{-3}kg$ and charge $q_{2}=+2.00\mu$C is fired toward the fixed charge with an initial speed of $38.0m/s$ . Gravity can be neglected.
What is the acceleration of the sphere at the instant when its speed is $20.0m/s$ ?

2. Relevant equations

$a = \frac{k*q_{1}*q_{2}}{m*r^{2}}$

3. The attempt at a solution

$a = \frac{9*10^{9}*15*10^{-6}*2*10^{-6}}{4*10^{-3}*r^{2}}$

$a = 67.5 * \frac{1}{r^{2}}$

By integration,

$v = -67.5 * \frac{1}{r} + C$

Initial conditions: $v = 38 m/s, r = 0.03m$

$38 = -67.5 * \frac{1}{0.03} + C$

$C = 2288$

$v = -67.5 * \frac{1}{r} + 2288$

When $v = 20m/s$,

$20 = -67.5 * \frac{1}{r} + 2288$

$r = 0.029761904$

$a = 67.5 * \frac{1}{0.029761904^{2}}$

$a ≈ 76200 m/s^{2}$

Since both charges are +ve,

$a = -76200 m/s^{2}$

However, the solution is not correct.

May anyone pointing out the errors? Thank you very much.
Hi miniake, Welcome to Physics Forums.

I think the problem lies with your assumption that you can integrate the acceleration with respect to distance to yield velocity. Velocity is the integral of acceleration with respect to time.

Have you considered using a conservation of energy approach to find the separation for v = 20.0 m/s ?

#### Tanya Sharma

Hello miniake

What is the correct answer ?

Edit :Conservation of energy is the correct way to approach the problem.

Last edited:

#### miniake

Hi miniake, Welcome to Physics Forums.

I think the problem lies with your assumption that you can integrate the acceleration with respect to distance to yield velocity. Velocity is the integral of acceleration with respect to time.

Have you considered using a conservation of energy approach to find the separation for v = 20.0 m/s ?
Thank you gneill.

It works, using the formula $U_{1}+KE_{1} = U_{2}+KE_{2}$.

Thanks again.

Hello miniake

What is the correct answer ?
Using the above approach will work.

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