Question

Suppose that one sphere is held in place; the other sphere, with mass 1.40 g, is shot away from it. What minimum initial speed would the moving sphere need to escape completely from the attraction of the fixed sphere?

Answer 1

Answer:

The minimum initial speed is 20.0 m/s.

Explanation:

Given that,

Mass of sphere = 1.40 g

Suppose a system of two small spheres, one carrying a charge of 1.70 μC and the other a charge of -4.40 μC , with their centers separated by a distance of 0.240 m .

We need to calculate the potential energy

Using formula of potential energy

$P.E=\dfrac{kq_{1}q_{2}}{d}$

Put the value into the formula

$P.E=\dfrac{9\times10^{9}\times1.70\times10^{-6}\times4.40\times10^{-6}}{0.240}$

$P.E=-280.5\times10^{-3}\ J$

We need to calculate the minimum initial speed

Using formula of energy

$K.E=-P.E$

$\dfrac{1}{2}mv^2=-280.5\times10^{-3}$

Put the value into the formula

$\dfrac{1}{2}\times1.40\times10^{-3}\times v^2=280.5\times10^{-3}$

$v=\sqrt{\dfrac{2\times280.5\times10^{-3}}{1.40\times10^{-3}}}$

$v=20.0\ m/s$

Hence, The minimum initial speed is 20.0 m/s.