Interpreting Scale Readings in a Moving Lift

[Aysce]

Homework Statement

A mass of 2kg is sitting on a dial scale balance on the floor of a lift. What is the reading on the balance when the lift is moving downward with acceleration of 3 m/s²

Homework Equations

F = ma

F = mg where g = 10 m/s² in this question.

The Attempt at a Solution

Consider the mass first. Mass = 2kg and under gravity, the force is F = mg = 20N.

Consider the reading on the scale, let's say x. Under gravity, F = mg = 10xN.

It is given that the lift is accelerating downwards at 3 m/s² and let's establish that moving downwards is negative. Using F = ma, we get F = ma = -6N.

Since the scale and the mass are experiencing a net downwards force, we equate them to -6N.

This is where I get stuck. The solutions give the equation:

10x - 20 = -6.

Firstly, why is there a negative sign on the left hand side? Shouldn't it be positive since both objects are experiencing a downwards motion? And why does 10x go first as opposed to 20 being first? I'm not understanding the logic behind the left hand side.

Thanks to those who answer!

 

[lendav_rott]

If you get on an elevator and ride to higher floors what do you feel initially? Feels as if you are getting heavier, pushed harder to the elevator floor. If you ride to lower floors it feels like you are getting lighter, feels like your feet are lifting off the floor.
If you get heavier it must mean your total weight is m(g+a), but now the lift is moving down, therefore the weight is m(g-a).
You could also think of it like this: As the elevator moves down, it has a downward acceleration OR it is decelerating while on the way up, both mean the same thing. If its acceleration downward is a, then its deceleration while on the way up is -a.

If you establish that moving downwards is negative, what happens? Acceleration downward is -a, but now g is -g instead. The formula would change into m(-g -(-a)) => -mg + X = [something], just as the equation given in the solution.

 

[tiny-tim]

Welcome to PF!

Hi Aysce! Welcome to PF!

Firstly, why is there a negative sign on the left hand side? Shouldn't it be positive since both objects are experiencing a downwards motion? And why does 10x go first as opposed to 20 being first? I'm not understanding the logic behind the left hand side.

It's a matter of convenience and personal taste.

x (the force from the scale) is in the opposite direction to the weight and the acceleration.

Since x is what we're looking for, there's something to be said for making it positive, and everything else negative.

But you could do it the other way round!

(personally, i would)

 

[lendav_rott]

I would, aswell, but I remember this from my school physics - they try to make the student think in inverse, out of the "regular" comprehension limits. If you are told "write 6" you would just write 6, you could also write it as -(-6) , but you don't immediately think about it. That's why these assignments are given like this.

 

[Aysce]

Thank you very much Lendav and tiny-tim! :)