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 21.5 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 29.0 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

energy is conserved in all three given situation:

Let, v be the speed of particle in first sitaution, v+ be when its given positive charge and v- be when its negatively charged.

for the first situation

1/2 m v^2 = m g h (1)

In second case

1/2 m v+^2 = m g h + q V

q V = 1/2 m v+^2 - m g h (2)

for third situation,

1/2 m v-^2 = m g h - q V (3)

putting the values from 1 and 2 into 3 we get

1/2 m v-^2 = 1/2 m v^2 - (1/2 m v+^2 - m g h)

1/2 m v-^2 = m (1/2 v^2 - 1/2 v+^2 + 1/2 v^2 )

m gets cancelled

1/2 v-^2 = v^2 - 1/2 v+^2

v- = sqrt (2v^2 - v+^2)

v- = sqrt (2 x 21.5^2 - 29^2) = 9.14 m/s

Hence, v- = 9.14 m/s

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