Aparticle of charge q is fixed at the origin of an xy coordinate system. at t = 0 a particle (m = 0.923 g, q = 4.52 µc is located on the x axis at x = 22.6 cm, moving with a speed of 45.7 m/s in the positive y direction. for what value of q will the moving particle execute circular motion? (neglect the gravitational force on the particle.)

Explanation:

Given data:

particle mass =  0.923 g

particle charge is 4.52 micro C

speed of particle 45.7 m/s

In this particular case, coulomb attraction will cause centrifugal force and taken as +ve and Q is taken as -ve

solving for Q WE GET

where

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.