A cable stretches by an amount d as it supports a crate of mass M. The cable is cut in half. What is the mass of the load that can be supported by either half of the cable if the cable stretches by an amount d?

Explanation:

For the same stress as the full cable, the new cable would stretch by only .

Since it has stretched by d, the stress must now be two times the original. Therefore, the mass must also be two times the original which is

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2M

Explanation:

Let's say the initial length of the cable is L.

Now, if it is cut in two, it will have two lengths of L/2 each.

We are told that the cable stretches by d.

Now, young's modulus is;

E = stress/strain.

Stress = Force/Area = Mg/A

Strain = change in length/original length = d/(L/2)

Since g, A and L are constant, thus;

E α M/(L/2)

E α 2M/L

Thus, mass of the load that can be supported by either half of the cable if the cable stretches by an amount d is 2M

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.

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form