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5 May, 21:38

Two particles, with identical positive charges and a separation of 3.41 * 10-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 3.68 * 103 m/s2, while particle 2 has an acceleration a2 whose magnitude is 10.8 * 103 m/s2. Particle 1 has a mass of 4.66 * 10-6 kg. Find (a) the charge on each particle and (b) the mass of particle 2.

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  1. 5 May, 23:18
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    (a) the charge on each particle is 4.71 x 10⁻⁸ C

    (b) the mass of particle 2 is 1.59 x 10⁻⁶ kg

    Explanation:

    given information:

    distance of both particle, r = 3.41 * 10⁻² m

    acceleration of the particle 1, a₁ = 3.68 * 10³ m/s²

    acceleration of the particle 1, a₂ = 10.8 * 10³ m/s²

    the mass of particle 1, m₁ = 4.66 * 10⁻⁶ kg

    (a) the charge on each particle

    the both particle has positive identical charge, thus q₁=q₂=q. to find the charge we can use the electrostatic force equation

    F = k q₁q₂/r²

    where

    F = electrostatic force (N)

    k = coulomb's constant (8.99 x 10⁹ N. m²/C²)

    q = the charge (C)

    r = then distance of the charge (m)

    F = k q₁q₂/r²

    = k q²/r²

    = 8.99 x 10⁹ q² / (3.41 * 10⁻²) ²

    = 7.73 x 10¹² q² N

    according to newton's second law

    F = ma

    F = m₁a₁

    7.73 x 10¹² q² = (4.66 * 10⁻⁶) (3.68 * 10³)

    q² = (4.66 * 10⁻⁶) (3.68 * 10³) / 7.73 x 10¹²

    q = 4.71 x 10⁻⁸ C

    (b) the mass of particle 2

    F₁=F₂, the force of both particle is the same

    m₁a₁ = m₂a₂

    m₂ = m₁a₁/a₂

    = (4.66 * 10⁻⁶) (3.68 * 10³) / (10.8 x 10³)

    = 1.59 x 10⁻⁶ kg
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