A particle is uncharged and is thrown vertically upward from ground level with a

Question

A particle is uncharged and is thrown vertically upward from ground level with a speed of 25.6 m/s. As a result, it attains a maximum height h. The particle is then given a positive charge +q and reaches the same maximum height h when thrown vertically upward with a speed of 29.3 m/s. The electric potential at the height h exceeds the electric potential at ground level. Finally, the particle is given a negative charge -q. Ignoring air resistance, determine the speed with which the negatively charged particle must be thrown vertically upward, so that it attains exactly the maximum height h. In all three situations, be sure to include the effect of gravity.

Explanation / Answer

1/2 m v^2 = m g h h = v^2/2g = 25.6^2/(2*9.81)=33.4 m now if + q 1/2 m v^2 = m g h + q V 0.5*m*29.3^2 = m*9.81*33.4 + q V now if -q 0.5*m * v^2 = m*9.81*33.4 - q V add two equations ms cancel 0.5*29.3^2 + 0.5*v^2 = 2*9.81*33.4 v=21.26 m/s

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