8.2 estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in.) and having a tip radius of curvature of 1.2 × 10−3 mm (4.7 × 10−5 in.) when a stress of 1200 mpa (174,000 psi) is applied.

34.64Gpa

Explanation:

We can calculate the theoretical fracture strenght by,

Here we have,

Applied stress

Tip radius

lenght of surface crack or half of the lenght of internal crack

Replacing,

Therefore the maximum stress at the crack tip is 34.64Gpa

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.