The Angled Balance

---

The Premise

Sometime in the middle/end of our forces unit, my students walk into the room with electronic balances set out on every table.

I start class by asking the simple question "What does an electronic balance (or bathroom scale) measure?" and have the students discuss in pairs or groups before bringing the discussion to the full class.

Typically this results in a split between students that think the answer is "mass" and students that think the answer is "weight" so I ask them to use their balances to measure an object on their table (typically an eraser or ball of clay/playdough). Once they have recorded that result, I have them place the balance on a board and, while measuring the object as before, slowly tilt the surface in which the balance is sitting on. They will very quickly notice that the value displayed by the balance is going down! Obviously, the mass (and weight) of the object isn't changing when they simply angle the surface, so the electronic balance must actually be measuring something else.

​Enter the Normal Reaction Force :)

---

What's Going On?

If an object is sitting on a surface and it is not accelerating in the vertical direction than we know that vertical forces are canceling out.

If the surface that an object is sitting on is perfectly horizontal, than the downward force of gravity is supported by an upward normal reaction force that is equal in magnitude. The electronic balance assumes that it is horizontal and uses the normal force and the acceleration of gravity to calculate and display the mass.

Note: In this diagram, the notation used for the Normal Reaction Force is the letter "R". This is the standard for IB Physics and it's a little odd if you aren't used to it ;)​

If you start to tilt this balance so that it is now sitting at an angle, you will start to see the mass "getting smaller". This is because the normal reaction force is always perpendicular to the surface and will always have a magnitude equal to the component of the force of gravity that is perpendicular to the surface. As the angle increases, this component gets smaller and since the "mass" that is displayed is based on the normal reaction force, it too seems to decrease.

---

Taking Measurements

It is possible to take measurements and show that the value changes as a cosine of the angle but it is important to use a few tricks for your procedure:

• Use a phone or tablet with phyphox or level app to measure the angle by resting it flat on the angled surface with the balance.
• Use an object that is a little bit tacky so that it doesn't slide off the balance as the angle increases. It might also be good to tape or strap down your balance as well.
• Zero the balance at each new angle before placing the object back on. This is extremely important because you need to remove the changing values of the balance hardware to make sure that only the object is being measured.​

---

This post is part of a larger collection of my favorite science demonstrations

CLICK HERE FOR MORE DEMOS

---

​Click for more Forces resources ​⬇