Newton 2nd law of a fish in an elevator

1. Jun 5, 2010

Agent M27

1. The problem statement, all variables and given/known data
A person weighs a fish of mass m on a spring scale atached to the ceiling of an elevator.
(a) Show that if the elevator accelerates either up or down, the spring scale gives a reading different from the weight of the fish.

2. Relevant equations

$$\Sigma$$Fy=T-Fg=may

Where T is the tension of the scale acting opposite to that of gravity, Fg

Fg=mg

3. The attempt at a solution
I figure that I needed to solve for the tension in terms of the acceleration of the elevator and accelleration due to gravity.

I found T= may+Fg

But the book gave me an equation of this form:

T=mg+ma=mg($$\frac{a}{g}$$+1)

I dont understand where they got the a divided by g + 1 factor from. Any clues would be greatly appreciated. Thanks in advance.

Joe

2. Jun 5, 2010

kuruman

Start from

T = mg + ma

Factor out on the right side mg.

What do you get?

3. Jun 5, 2010

pgardn

When the texts rewrite an equation like this, they are usually trying to make the ideas easier to understand. If a = 0 then T = mg If a = g then T = 2mg and so on... so the larger a gets in the +y direction, the greater the tension, which makes sense. If a = -9.8 (down), then T would be equal to zero and the object is in free fall.

So essentially the text is saying try out different accelerations, a, and when you do, does this make physical sense.

Last edited: Jun 5, 2010