Newton 2nd law of a fish in an elevator

[Agent M27]

Homework Statement

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.

Homework Equations

$$\Sigma$$F_y=T-F_g=ma_y

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

F_g=mg

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= ma_y+F_g

But the book gave me an equation of this form:

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

I don't understand where they got the a divided by g + 1 factor from. Any clues would be greatly appreciated. Thanks in advance.

Joe

 

[kuruman]

Start from

T = mg + ma

Factor out on the right side mg.

What do you get?

 

[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.