Electric Charge — Question 5

Question 5

Equal interaction forces do not imply equal accelerations

Two isolated charged particles A and B repel. Their masses are $m_A=2.0$ g and $m_B=5.0$ g. At an instant the electrostatic force on A is $-12$ mN along the line joining them, with B to the right. Other forces are negligible.

1. Find the force on B and both accelerations.

2. Find the acceleration of their separation $x_B-x_A$ and the acceleration of the center of mass. Explain the different results.

Question 5 - Solution

Equal interaction forces do not imply equal accelerations

(a) Method and calculation

$$F_{B,x}=-F_{A,x}=+12\,\mathrm{mN}.$$$$a_A=-.012/.002=-6.0\,\mathrm{m/s^2},\quad a_B=.012/.005=+2.4\,\mathrm{m/s^2}.$$

(b) Interpretation and further calculation

$$\ddot{(x_B-x_A)}=a_B-a_A=8.4\,\mathrm{m/s^2}.$$$$a_{\mathrm{CM}}=\frac{m_Aa_A+m_Ba_B}{m_A+m_B}=0.$$Internal forces separate the particles while their mass-weighted position continues with constant velocity.

Physical check

Newton third-law equality concerns force, whereas acceleration also depends on the mass of the object receiving the force.