Understanding Normal Force: Weight, Apparent Weight, and Scales

good morning let's continue with our investigation of the normal force so today's topic is

weight normal force also called apparent weight and scales

a bathroom scale's measurement of mass is proportional to the normal force acting on a person which in turn is

proportional to the mass of the person regardless of where the person is his or her actual mass does not change

so often students believe that a scale measures the force of gravity but this is incorrect a scale measures

the normal force however a person's registered weight changes depending on where they are

an accelerating elevator the person's registered weight depends on the acceleration of the

elevator so ultimately our goal today is to understand that scales measure normal force or the

apparent weight so here's the video i want to show you what i want you to notice is how the

needle swings when the elevator begins to move upwards and then again when it comes to a stop

while it is moving upwards the velocity is constant and the needle's position does not change

so i'm standing in an elevator on top of the scale let's see what happens so we are

currently stationing the elevator and now we are going to move upwards i have now pressed button two

the elevator began to move and now the elevator came to a stop and it's come to a complete stop now

we'll go the opposite direction we're going downwards so

so a few key points of this video at around the six second mark well let's start off with the three

second mark and now we are going to move upwards i have now pressed buttons

you'll notice that the needle jerks to a significantly greater mass at the very beginning when the elevator begins

to lift upwards and then button two the elevator began to move it's fairly

steady the mass while the elevator is moving at a constant velocity upwards

and then the mass decreases significantly as you can see so now we're going to try to understand

this in terms of a question this is a common question students often face on a physics test

a book is traveling in four different elevators find the apparent weight that a bathroom scale would register

find a normal force acting on the book in the following four different situations so we're gonna look

at this situation right now first situation is when we're at rest so for the video this was at the very

beginning of the video and the question is determine normal force

so gravity acts downwards gravity's value is 49 newtons why is it 49 newtons 5 kilograms

multiplied by the acceleration due to gravity which is 9.8 5 times 9.8 is 49. normal force

opposes the force of gravity in the situation acts upwards it's the support so here's our book five kilogram book

we have a scale underneath it measuring its registered mass positive direction is up

because the elevator is moving upwards negative direction is down so we write a net force statement and

our goal is to get the normal force normal subtract fg normal is positive because it points up

that's the direction the elevator is heading in gravity is negative because it opposes the

motion of the elevator f net is always equal to m a in this situation our acceleration is

zero and we get a normal force that is identical to the force of gravity so

this situation should not really surprise you the forces are balanced

but there's one problem with this diagram so please note if the forces are

balanced the vectors should be drawn the same length that's very important in physics diagrams

so the next situation we look at is when the elevator begins to move upwards that was at the very beginning of the

video so i've randomly chosen an acceleration of 3 meters per second squared

we're assuming that we have a textbook or some sort of book in an elevator a scale is underneath it

measuring its mass our goal is to figure out the normal force once again in this situation because there's

acceleration we say it's unbalanced the forces are unbalanced so once again we have fnet equals normal

normal acts upwards subtract gravity that acts downwards normal is in the direction of

motion that's why it's positive gravity is negative because it opposes the motion

and it's accelerating upwards f net is always m a this time the acceleration is 3

5 times 3 is 15 we have to bring the 49 over sometimes students make a simple error

and they divide by 49 but we have to add 49 to each side of the equation and we end up getting 64 newtons well

this answer makes sense yeah it does why well first of all it's accelerating upwards

it's being lifted upwards so for something to accelerate upwards the upwards force has to be bigger than the

downwards force and that's the situation 64 newtons is larger than 49 units so it makes

sense from that perspective we expected the normal force to be larger

the net force always has to point in the direction of the acceleration if the acceleration is upwards the net

force has to point upwards and so normal has to be bigger than gravity

now to calculate the mass registered by the scale all we do is we take the normal force

and divide by 9.8 and in this situation interestingly the recorded mass on the scale the scale

here would be six and a half kilograms larger than five kilograms now does this make sense

well yes if you recall in the video and this is the beautiful thing about physics

often we can show our results in real life by doing simple experiments if you recall the video at this

situation it was stationary at the two second mark of the video

and i mean you could see where the needle is at the eight second mark it begins to

accelerate upwards actually just a little bit before that actually began to accelerate

upwards and clearly you could see the needle has shifted to a greater mass so it makes sense

that when we have an acceleration upwards the weight or the mass as registered by

the scale is going to increase you see if scales measured gravity the needle

wouldn't shift but it's because scales measure normal force

and the normal force is changing that the needle shifts now during that video the elevator came

to a stop as it was moving upwards let's examine the forces this time

well assuming the acceleration while coming to a stop is negative one i want you to solve for the normal force

please pause video now okay hopefully you paused the video and tried this

not going to go into all the details because the mathematics is very similar but this time the net force is negative

5 and when we bring the 49 over by adding we end up with 44 newtons

does that make sense well remember this time the object in this case the textbook is slowing

down or the book is slowing down so if the book is slowing down then that means the force pointing down

has to be greater than the force pointing up and that makes sense 44 because 44 is

less than 49. notice in addition that because 44 is less than 49 then this vector

should be drawn a little longer than that vector to calculate mass register by a scale

once again divide by 9.8 the normal force and notice this time we get a

smaller mass the mass here is five kilograms and the mass as indicated by the scale

is only four and a half kilograms does this make sense again it does here at the 16 second mark

of the video you can see the needle clearly and notice

at the 17 second mark of the video about a second later it begins to come to a stop and the

needle shifts it's registering a lower mass again that's because these scales

do not measure gravity gravity never changes always 49 newtons

force of gravity they register the normal force and while the object is slowing down

the normal force is going to decrease and if you're interested in more details about normal force

please watch the next video bye-bye