An electric cannon, such as shown in (Figure 1), consists of a 16-kg metal ball

Question

An electric cannon, such as shown in (Figure 1), consists of a 16-kg metal ball with charge 1.3 times 10^-44 C compressed into a plastic barrel so that it is 0.10 m from an equally charged object at the closed end of the barrel. The barrel is oriented at 37 degree 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

a) change in gravitational potential energy = 16 * 9.8 * (3 - 0.10) * sin37

                                                                   = 273.65 J

b) change in electric potential energy = 8.98 * 109 * 1.3 * 10-4 * 1.3 * 10-4 * (1/0.12 - 1/32)

                                                           = 15159.33 J

c) Final speed of charge = sqrt(2 * 14885.68/16)

                                          = 43.13 m/s

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