# Newton's Second Law and a bathroom scale

• nguyentech
In summary, the physics teacher decides to use bathroom scales (calibrated in Newtons) in an elevator. The scales provide a measure of the force with which they push up on the teacher. When the lift is stationary the reading on the bathroom scales is 823 N. When the elevator is moving upwards or downwards, the apparent answer at the back of the textbook reads: 700 N or 5.6 x 10^2 N, respectively. My answers are: 823 N or 991 N, respectively.

#### nguyentech

This question has been troubling me... :

A physics teacher decides to use bathroom scales (calibrated in Newtons) in an elevator. The scales provide a measure of the force with which they push up on the teacher. When the lift is stationary the reading on the bathroom scales is 823 N. What will be the reading on the scales when the elevator is:

a) moving upwards at a constant speed of 2.0 m/s/s
b) accelerating downwards at 2.0 m/s/s
c) accelerating upwards at 2.0 m/s/s

The apparent answers at the back of the textbook read:
a) 700 N
b) 5.6 x 10^2 N
c) 8.4 x 10^2 N

I think they are wrong?

My answers are:
a) 823 N
b) 655 N
c) 991 N

Are my answers correct?

How did you arrive at your answers? That way we can see if you are faulted in your method or not.

Yes, place where your work here so we could determine where any potential problem went.

For lift accelerating upwards : T = mg + ma, therefore answer = 84*9.8 + 84*2 = 991
For lift accelerating downwards : T = mg - ma, therefore answer =
84*9.8 - 84*2 = 655

Ok, well for 1, i assume it said moving at a constant 2 m/s not m/s/s...in that case, you are right, the Normal force(what the scale reads) is the same

Ok, your equation is Fn-Fg=m*a

For 2 m/s^2 upward, you have Fn-823=(823/9.8)*2

Which means Fn=991...which is what u got...

And for downward Fn-823=(823/9.8)*-2 which gives Fn= 655

Either were both making the same mistake (I haven't done these in a while lol) or the book is just wrong..

Lemme try to use g=10 for the calculations..
Fn=987 and Fn=658..yea still close to our answers and far from the books..

I think the fact that they say that with constant speed, the normal force changes, says that the book is broken

Yeah, the book is wrong.

the book is wrong

This is why i never trust books.

## What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

## How does Newton's Second Law relate to a bathroom scale?

When you stand on a bathroom scale, your weight is the force applied to the scale. According to Newton's Second Law, the scale will show a greater reading if you apply a greater force (i.e. increase your weight) and a smaller reading if you apply a smaller force (i.e. decrease your weight).

## Why does the reading on a bathroom scale change when I move it to different locations?

The reading on a bathroom scale may change when you move it to different locations because the scale is affected by the force of gravity, which varies slightly depending on where you are on Earth. This is due to differences in the Earth's shape and density.

## How does the mass of an object affect the reading on a bathroom scale?

The mass of an object does not directly affect the reading on a bathroom scale. However, according to Newton's Second Law, a greater mass requires a greater force to accelerate, so a heavier person will apply more force to the scale and therefore show a higher reading.

## Is the reading on a bathroom scale affected by air resistance?

The reading on a bathroom scale is not directly affected by air resistance. However, if a person is falling onto a bathroom scale, air resistance may slow them down and decrease the force they apply to the scale, resulting in a lower reading.