The terminals of a 1.30 mF parallel-plate vacuum capacitor is connected to a battery that keeps a voltage of 29.6 V across the plates. Then, without disconnecting the battery, a piece of material with dielectric constant of 3.51 is inserted between the plates. After inserting the dielectric, how much energy (in Joules) is stored in the capacitor?

Energy stored in capacitor with new dielectric is 1.998 joules approximately 2 joules

Explanation:

Detailed explanation and calculation is shown in the image

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.