A small conducting bead of mass and charge is released from rest at a point that is…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

A small conducting bead of mass

4.0\times10^{-3}\,\text{kg}

and charge

+6.0\,\mu\text{C}

is released from rest at a point that is

1.00\,\text{m}

directly above a fixed point charge of

-8.0\,\mu\text{C}

anchored to the ground. The bead is free to move only along the line joining the two charges. Assume the ground is a rigid surface located

0.20\,\text{m}

above the center of the fixed charge, so that the bead cannot approach the fixed charge any closer than

0.20\,\text{m}

. Constants:

k = 8.99\times10^{9}\,\text{N}\cdot\text{m}^2/\text{C}^2

g = 9.8\,\text{m/s}^2

. Neglect air resistance. (a) Compute the change in electric potential energy of the system as the bead moves from its release point to a height of

0.20\,\text{m}

above the fixed charge. (b) Compute the change in gravitational potential energy of the bead over the same displacement. (c) Determine the bead’s speed just before it reaches the height of

0.20\,\text{m}

. (d) If the bead were given an initial downward speed of

3.0\,\text{m/s}

instead of being released from rest, would its speed at

0.20\,\text{m}

be simply

3.0\,\text{m/s}

larger than the value found in part (c)? Explain your reasoning without performing additional calculations.

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