Does weighing machine actually show your weight?

Did you know that what is displayed on the scale is actually your mass, the amount of substance in your body. Your weight on Earth is about 10 times more than your mass and a negative number!

The Weighing Scale Does Not Actually Show Your Weight but, Your Mass!

To understand this better, we need to understand vectors and scalars. 

Let’s understand the difference between scalar and vector quantities, applied in Kinematics.

Scalar quantities – are positive, they simply represent magnitude.

Vector quantities – can be both negative and positive, they represent both magnitude and direction.

Magnitude – the precise amount of something

Direction – the way in which the quantity is acting

So, with vectors, you can tell if you’re going backwards or forwards, left or right.

Scalars only indicate how much you have. Now, for some examples!

Pick up a few rubberbands in your hand and count them. Will you ever count a negative number? No, so, the number of rubberbands is a scalar quantity.

The length of a pencil, measured by a scale, is only positive, with no direction. So, it’s scalar.

Now, for more complex quantities:

Time is a scalar because it has no direction. You can’t reverse time!

Distance is… well, the distance travelled – How much of the road I have covered in total, like in the picture below. The car cannot cover negative of the road and the direction it travelled does not matter hence, distance is scalar too. 

Screen Shot 2018-04-23 at 7.13.59 PM

But, displacement is different. It shows the difference in position of the car from start to end. Think of it this way, if your favourite tennis ball rolled away in the white dashed path, would you follow the same path? Most likely, you would simply walk to its new position following the yellow path. That’s the displacement, distance from starting position with direction, it is a vector. 

Screen Shot 2018-04-24 at 8.38.39 AM.png

Similarly, speed, the rate of change of distance per unit time is scalar. But, velocity, the rate of change of displacement per unit time is a vector. That means, if

velocity = – 5m/s, it tells me you’re going backwards. Like this cute fella:

Screen Shot 2018-04-23 at 7.14.31 PMScreen Shot 2018-04-23 at 7.14.36 PM

So, that’s how we distinguish between scalars and vectors.

Now, back to Weight and Mass.

Mass is the amount of substance in your body. Do you think you can have negative substance in you body? No, and so, mass is a scalar quantity, just like how the scale on the measuring scale does not go below zero.

But, weight is a vector.

It is the measure of force acting on a body due to gravity. Since gravity can pull you down or up or left or right, weight is vector. Like this:

Screen Shot 2018-05-07 at 9.41.02 PM

The weight acting on the astronaut due to Earth’s gravity is downwards on the Astronaut hence, the negative sign indicates downward direction. This is important to us in physics to find the resultant of any two forces on any object

The negative sign conventionally indicates downward or leftward direction.

Your weight is actually different on all the Planets. Click here to check it out via our weight calculator tool!

Screen Shot 2018-05-11 at 6.02.33 AM

Here’s an interesting example from Aerodynamics as well.

Have you ever wondered how a plane can fly in the sky without falling, but humans can’t? Like we saw, your weight pulls you down to the ground and the plane experiences this downward weight force too, larger in fact. However, the engine of the plane also create an upward lift force, like below.

To maintain a constant altitude, resultant force must be 0N. 

Screen Shot 2018-04-23 at 7.15.09 PM

Hence, the resultant force = Up force + down force = 0. We get 0 when adding the two forces because, the downward weight force is a negative, like we saw earlier!

Now let’s stretch our thinking even further. As the plane flies, we know that the propeller create a forward force and air creates backward resistance force. Imagine the plane moving forward but at a constant speed. Do you think the forward force is greater than the backward force? In reality, they are equal! Explore this by reading up on Newton’s first law of motion: F = ma. 

-Contributed by

Anshiqa Agrawal (Grade 12, 2018)

References
Creative Commons. “Tennis ball PNG image”. Pngimg, n.d, http://pngimg.com/download/10416.
Dianne. “CAR PINK TRANSPORT CARTOON CLIP ART”. Clker, 12 Feb 2012, http://www.clker.com/clipart-car-pink-transport-cartoon.html.
“Earth Free Download png”. Freepnging, n.d. http://www.freepngimg.com/png/13550-earth-free-download-png
Mauistik. “Austion Pet Care”. n.d. http://petservicesaustin.com/
Nolertgolen Ltd. “Body Weight Scale Simulator APK”. Apkpure, 18 Sep 2015, http://www.freepngimg.com/world/earth
Roelsmith. “Astronaut”.  OpenClipArt, 29 Dec 2012, https://openclipart.org/detail/292892/astronaut
Taira. “Artificial Grass Field Top View Texture”. Freepik, n.d. https://br.freepik.com/fotos-premium/artificial-grass-field-top-view-texture_1422068.htm.

2 thoughts on “Does weighing machine actually show your weight?

Add yours

  1. Interesting Article. Is the gravitational force of a planet is a factor of its mass? How can we find the weight of planets?

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  2. Thank you for encouraging my student. Yes, the gravitational force of a planet depends on its mass. F = GMm/(square of r). M = mass of the planet, m = mass of the object, r = radius of planet, G = gravitational constant, F = Gravitational force. To find out the weight of planet, we can use the formula : g = GM/(square of r), M : mass of the planet , r = radius of the planet.

    Like

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