- #1

lorenz0

- 148

- 28

- Homework Statement
- Consider two small charged sphere of mass ##m=1g## and radius ##r=50\mu m##. One has charge ##q_1=6\mu C## and the other ##q_2=-6\mu C ##. They are released from rest at a distance of ##r_0=1mm##. Find the speed with which they hit each other.

- Relevant Equations
- ##E=k\frac{q_1q_2}{r}-G\frac{m^2}{r} ##

Since the forces involved (gravity and electric force) are conservative we can use conservation of energy.

The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get ##v=\sqrt{\left(kq_1q_2\left(\frac{1}{r_0}-\frac{1}{2r}\right)+Gm^2\left( \frac{1}{2r}-\frac{1}{r_0} \right) \right)}\frac{1}{m}=1000\cdot\sqrt{ 9\cdot 10^9 \cdot(-36\cdot 10^{-12})\cdot( 10^3 -10^4 ) +6.67\cdot 10^{-11}\cdot 10^{-6}\cdot (10^4 -10^3) }m/s\approx 54,000 m/s ## but the solution to this problem says that the naswer should be ##\approx 1700 m/s ## and I don't see what I am doing wrong so I would appreciate some feedback on my solution, thanks.

The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get ##v=\sqrt{\left(kq_1q_2\left(\frac{1}{r_0}-\frac{1}{2r}\right)+Gm^2\left( \frac{1}{2r}-\frac{1}{r_0} \right) \right)}\frac{1}{m}=1000\cdot\sqrt{ 9\cdot 10^9 \cdot(-36\cdot 10^{-12})\cdot( 10^3 -10^4 ) +6.67\cdot 10^{-11}\cdot 10^{-6}\cdot (10^4 -10^3) }m/s\approx 54,000 m/s ## but the solution to this problem says that the naswer should be ##\approx 1700 m/s ## and I don't see what I am doing wrong so I would appreciate some feedback on my solution, thanks.

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