An electric cannon, such as shown in (Figure 1) , consists of a 10-kg metal ball

Question

An electric cannon, such as shown in (Figure 1) , consists of a 10-kg metal ball with charge 1×104 Ccompressed into a plastic barrel so that it is 0.10 mfrom an equally charged object at the closed end of the barrel. The barrel is oriented at 37 with respect to the horizontal. When the ball is released, it shoots 3.0 m along the barrel from its starting position because of the repulsive force between the two charged objects.

Find the change in gravitational potential energy.

Express your answer to two significant figures and include the appropriate units.

Find the change in electric potential energy.

Express your answer to two significant figures and include the appropriate units.

Find the final speed of the charge as it leaves the barrel.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given,

mass of the object = 10 kg

charge on both the objects = 1 * 10^-4 C

distance between both the objects = 0.1 m

angle = 37 degree

length of the barrel = 3 m

initial gravitational potential energy Uo = 0 J

final height = 3 * sin(37)

final gravitational potential energy Uf = 10 * 9.8 * 3 * sin(37)

final gravitational potential energy Uf = 176.934 J

change in gravitational potential energy = 176.934 - 0

change in gravitational potential energy = 176.934 J

electric potential energy = kQq / r

initial electric potential energy = 9 * 10^9 * 1 * 10^-4 * 1 * 10^-4 / 0.1

initial electric potential energy = 900 J

final electric potential energy =  9 * 10^9 * 1 * 10^-4 * 1 * 10^-4 / 3

final electric potential energy = 30 J

change in electric potential energy = 30 - 900

change in electric potential energy = -870 J

initial kinetic energy = 0

by conservation of energy

initial energy = final energy

initial gravitational potential energy + initial electric potential energy + initial kinetic energy = final gravitational potential energy + final electric potential energy + final kinetic energy

0 + 900 + 0 = 176.934 + 30 + 0.5 * 10 * v^2

v = 11.77 m/s

speed of the charge = 11.77 m/s

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