A 50kg woman enters an elevator and stands on a bathroom scale...?

Question

A 50kg woman enters an elevator and stands on a bathroom-type scale. If the elevator accelerates downward at 2m/s^2, would the scale read more or less than her normal weight? And what is the reading?

Answer 1

KG is a a way to measure a mass of an object.
One (1) kg has been defined by weighing 1 liter of water (10 cm x 10 cm x 10 cm = 1000 cm^3) at room temperature on the surface of the earth. The result was set with the unit : 1 kg. There is no more behind it.

Now what is gravitation ? Every object has a mass and this mass has a force which pulls on other objects. For example the mass of the earth pulls on your mass. The direction is always to the center of the earth .This force can be measured and on the earth surface it is 9.81 m/s^2 (reads meter/square seconds).

What you can calculate is the force this creates (in our daily communication we call it "weight") , the formular is:

mass (in kg) x gravitational force (9.81 m/s^2),

in your case it is 50 kgs * 9.81 m/s^2 = 490.5 (kg x m)/s^2.

This is called a "Newton". Isaac Newton found this law when he was sitting under a tree and an apple fell on his head.

In the past this force (" weight") was called kilopond and to calculate it you need:

1 Newton = 0.1012 kp , so 490 Newton which figure out to around 49.5 kilopond. (This looks very close to the 50 kgs of the mass and in the past both words were used in the same meaning. For people living on the earth this makes a lot of sense).

What you weigh with a weighing machine is not the mass of an object, but the force with which this object is pulled to the surface of the earth and in your case it is around 50 kilopond or 490 Newton.

Now: when you step into an elevator and the elevator accelerates downwards there are two forces: the gravitational force of 9.81 m/s^2 plus the acceleration in the same direction of 2 m/s^2. The key is: they are directed in the same direction.

(A guy called Albert Einstein later found out that gravitation is nothing else than acceleration, but this comes when you study physics and things become a lot more complicated).

Because they pull in the same direction you can subtract them. In other words the pull of 9.81 m/s2 is reduced by the acceleration of 2 m/s^2 and the result of the subtraction is 7.81 m/s^2.

Now: same calculation as above:

50 kgs * 7.81 m/s^2 = 390.5 Newton = around 39.5 kilopond and which equals 39.5 kilogram (but now you have learned that kg is wrong).

Now: on the moon the gravitational force is smaller than on he earth. The mass of would be still the same: 50 kgs, but calculated in Newton or kilopond it would be less. You may have seen pictures from astronauts making huuuge jumps because they weigh less than on the earth.

So the answers to your questions are:

the weighing machine would read less and the reading would be around 39.5 kgs (in fact it should say kilopond).

Answer 2

I am the worst mathematician in the world, but your question intrigued me. I conclude that (a) the elevator was descending and (b) that I don't see how either speed or the rate of acceleration can be determined by reference to just one point in time.

Answer 3

This is a moot point. She would still be too heavy and refuse to let anyone look at the scale.

Answer 4

Hi It would read less by about 20%.

Answer 5

force = mass times acceleration

Answer 6

.