Question

Two particles, with identical positive charges and a separation of 2.83 × 10^-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 5.56 × 10^3 m/s2, while particle 2 has an acceleration a2 whose magnitude is 11.7 × 10^3 m/s2. Particle 1 has a mass of 8.95 × 10^-6 kg. Find (a) the charge on each particle and (b) the mass of particle 2.

Answer 1

$1.Coulomb's \;law\\F=k\frac{q_1q_2}{r^2};F_1-F_2=0;m_1a_1=m_2a_2=k\frac{q_1q_2}{r^2};\\q_1=q_2=q;m_1a_1=m_2a_2=k\frac{q^2}{r^2}\\8.95 × 10^{-6} ×5.56 × 10^3=\\=4.253 × 10^{-6}×11.7 \times 10^3=k\frac{q^2}{r^2};\\49.762\times10^{-3}=49.762\times10^{-3};\\q=r\sqrt{\frac{F}{k}};\\q=2.83\times10^{-2}\sqrt{\frac{49.762\times10^{-3}}{9\times10^9}}=6.654\times10^{-8}C\\2.F_1-F_2=0;m_1a_1-m_2a_2=0;\\(Newton's \;second\ law)\\m_1a_1=m_2a_2;\\m_2=\frac{m_1a_1}{a_2}\\m_2=\frac{8.95 × 10^{-6} ×5.56 × 10^3}{11.7 \times 10^3}=4.253 × 10^{-6}kg\\Answer:\\1.q=6.654\times10^{-8}C\\2.m_2=4.253 × 10^{-6}kg$