Ametal ball with diameter of a half a centimeter and hanging from an insulating thread is charged up with 1010 excess electrons. an initially uncharged identical metal ball hanging from an insulating thread is brought in contact with the first ball, then moved away, and they hang so that the distance between their centers is 20 cm. (a) calculate the electric force one ball exerts on the other, and state whether it is attractive or repulsive. (enter the magnitude of the force.) entry field with correct answer 1.44e-7 n this force is entry field with correct answer attractive repulsive (b) now the balls are moved so that as they hang, the distance between their centers is only 5 cm. naively one would expect the force that one ball exerts on the other to increase by a factor of 42

a)   F = 1.44 10⁻⁷ N, the charges are of the same sign the force is repulsive

b)    F₂ / F₁ = 16

Explanation:

a) When the balls are touched the load is distributed evenly between the two balls, therefore when separating each ball has a load of

          q₁ = q₂ = ½ 10¹⁰ 1.6 10⁻¹⁹ C

          q₁ = q₂ = 0.8 10⁻⁹ C

As the charges are of the same sign the force is repulsive

To calculate the force let's use Coulomb's law

        F = k q₁ q₂ / r²

        F = 8.99 10⁹  0.8 10⁻⁹  0.8 10⁻⁹ / 0.20²

        F = 1.44 10⁻⁷ N

b) Let us seek strength for the distress of

              r₂ = 0.05 m

             F₂ = 8.99  10⁹ 0.8 0.8 10⁻¹⁸ / 0.05²

             F₂ = 2,301 10⁻⁶ N

b) The relationship between these two forces is

            F₂ / F₁ = 23.01 10⁻⁷ / 1.44 10⁻⁷

            F₂ / F₁ = 16

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.