What is the acceleration of the elevator?

AI Thread Summary
The discussion revolves around calculating the acceleration of an elevator based on the reading of a bathroom scale when the elevator begins to move. Initially, the scale reads 0.76 of the person's weight, indicating that the elevator is accelerating downwards. The equations of motion are applied, leading to the realization that the weight ratio is crucial for solving the problem. After correcting the approach and recognizing the ratio's significance, the correct acceleration is determined to be 2.5 m/s². This solution highlights the importance of understanding weight ratios in dynamic scenarios.
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Homework Statement



A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.76 of the person's regular weight.

Calculate the magnitude of acceleration of the elevator.

Homework Equations



F=ma
N=ma-mg

The Attempt at a Solution



Ok, so the scale in the elevator shows weight (mg), the elevator accelerates downwards, and the scale shows .76 of the persons weight.

\SigmaF=ma
mg-N=ma
a=(mg-N)/m
a=(m(9.8)-.76)/m

So now I have 2 unknowns in one equation. I need to find A, but I do not know the mass of the person.

I figured that if the weight shown by the person is .76 of his normal, I should be able to figure this out if i just assign a random value to "m"... correct?

so plugging a number in for m i get...
a=((10)(9.8)-.76(10))/(10)
a=9.04

This does not possibly seem correct. if it were true, the elevator would nearly be in freefall, and the scale would be reading something around .2 of the persons weight, right?

What am i doing wrong?
 
Physics news on Phys.org
0.76 is the ratio of the persons weight in the accelerating elevator to his normal weight
m(g-a) / mg
 
payumooli said:
0.76 is the ratio of the persons weight in the accelerating elevator to his normal weight
m(g-a) / mg

Ok, I did not realize that it was a ratio.
so now I solve for a

m(g-a)/mg=.76
m(g-a)=.76mg
g-a=.76g
a=g-.76g
a=9.8-.76(9.8)
a=2.5

Thank you very much, this was the correct answer.
 
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