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Old Feb 25th 2011, 01:46 AM   #1
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Newtons second law

A person stands on a set of bathroom scales in an elevator. The scale reads only 0.75 (i.e, 75%) of the person weight. Calculate the acceleration of the elevator and find the direction of the acceleration.

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Old Feb 25th 2011, 10:04 AM   #2
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The resultant force on the person, the mass of the person and his acceleration is related by F = ma, or more explicitly:

Fnet = ma

What is Fnet? It's the Weight of the person, minus the force of the elevator on the man's feet.

Felevator - Weight = ma

Weight of person = mg
a of elevator = a of person
Now, the bathroom scale will record the force that the elevator exerts on the person.

Felevator - mg = ma

Felevator = ma + mg

Felevator = m(a+g)

Felevator/m = 75%

You know g, find a.
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Old Feb 27th 2011, 06:34 AM   #3
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I get the problem to

75= a + 9.78

but whatever answer i get is wrong according to the one in the back of the book.

The correct answer is 2.45...
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Old Feb 27th 2011, 07:07 AM   #4
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Oops, I shouldn't have put the last line. I actually forgot to delete it, sorry for that. =S

Felevator = 0.75 mg
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Old Feb 27th 2011, 02:46 PM   #5
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so it should be

0.75 mg = a + 9.78 ?
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Old Feb 28th 2011, 07:30 AM   #6
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0.75 mg = m(a + g)

0.75 g = a + g
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Old Feb 28th 2011, 02:44 PM   #7
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Thank you
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Old Mar 1st 2011, 01:44 AM   #8
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0.75*9.78=9.78 + a
is what i get.

But i cant solve to match the answer in the back of the book

2.45m/s^2
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Old Mar 1st 2011, 07:40 AM   #9
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Hm... this is a calculation mistake...

Okay:

0.75 * 9.78 = 7.335

Hence:

7.335 = 9.78 + a

So, a = 7.335 - 9.78 = -2.445 = -2.45 m/s^2

This means that the acceleration has magnitude 2.45 m/s^2 and acting downwards (the answer to the second part),

since I first assumed that the force of the elevator was acting upwards, from here:

Felevator - Weight = ma

Obviously, weight is downwards and I took the up direction as positive.
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Old Mar 1st 2011, 02:39 PM   #10
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