A force parallel to the x-axis acts on a particle moving along the x-axis. The force produces a potential energy U (x) given by U (x) = ↵x4, where ↵ = 0.630 J/m4. What is the force (magnitude and direction) when the particle is at x = 0.800 m?

The force acting on the particle at x = -0.800 has magnitude of 1.29 N and directed toward the origin

Explanation:

First we write the potential energy produced by the force

where α = 0.630

therefore

For motion along a straight line, a conservative force is the negative derivative of its associated potential energy function U(x):

therefore

At  x = -0.80 the force equals

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

waves moving from a fast medium to a slow medium will experience a reflection as light travels more slowly than red light. total internal reflection occurs when the critical angle is.