A particle is uncharged and is thrown vertically upward from groundlevel with a

Question

A particle is uncharged and is thrown vertically upward from groundlevel with a speed of 50.0 m/s. As aresult, it attains a maximum height h. The particle isthen given a positive charge +q and reaches the samemaximum height h when thrown vertically upward with aspeed of 55.0 m/s. The electricpotential at the height h exceeds the electric potentialat ground level. Finally, the particle is given a negative charge-q. Ignoring air resistance, determine the speed withwhich the negatively charged particle must be thrown verticallyupward, so that it attains exactly the maximum height h.In all three situations, be sure to include the effect ofgravity.

Explanation / Answer

First, when the particle is uncharged, the potential difference isonly caused by the gravity Wg=const in all three situationsbecause h is unchanged. When the particle is charged with q, the potential difference isincrease by We and when it charged with -q, it is-We Energy is conservative. 1st situation: m*50^2/2=Wg 2nd           :m*55^2/2=Wg+We 3rd            m*v^2/2=Wg-We sum the 2nd and 3rd we have. m55^2/2+mv^2/2=2Wg=2m*50^2/2 so 55^2+v^2=2*50^2 so v=sqrt(2*50^2-55^2)=44,44(m/s)

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