How can students derive a torque equation using scales and mobiles?

[Head_Unit]

Hi Folks:

I'm pondering teaching torque and having students build mobiles as part of that. I started wondering if I could have them derive a torque equation.

That started me wondering-if they were placing weights along different lengths of straws or skewers or something, could they weigh that on a scale to get the force? It seemed like it should work, but them I'm thinking maybe not as the scale will support the mass since the mass rests on it.

?

And if that won't work, what would? How could you derive this? (One plan would be to have students make the mobiles first and THEN analyze them, however I'm looking for alternate ideas).

 

[Simon Bridge]

Use a see-saw balance and show how the concept of torque is useful for working out the mass or distance for the balance.

In all your ideas you are comparing linear forces ... you could rig a pulley system t reverse the direction of the force so it pushes down on the scales for eg. But what does that show?

Even with the mobiles, it's all levers - how are you motivating the need for torque?

 

[Gurdian]

why not weigh afterwards?

 

[berkeman]

why not weigh afterwards?

Weigh what afterwards?

 

[Gurdian]

Weigh what afterwards?

I meant calculate the force afterwards based on the change in position.

 

[Head_Unit]

...But what does that show?...

Yeah, I'm not sure exactly what I want. Well, I know WHAT I want, just not how. Instead of just giving it to them, I want the students to discover that to balance the forces, mass1 x lever arm length1 =mass2 x lever arm length2 instead of giving it to them.

I suppose they could build the mobiles, then weigh and calculate. Somehow account for the mass of the supporting rods (bamboo barbecue skewers unless someone has an even cheaper idea). Mmmm, maybe a pre-activity just balancing masses on the rod, like a see-saw?

Thanks for the input, all ideas welcome!

 

[Simon Bridge]

I want the students to discover that to balance the forces, mass1 x lever arm length1 =mass2 x lever arm length2 instead of giving it to them.

OK - then you want them to discover the lever laws.

I use this approach myself - it can be very effective.
You'll have seen that the trick is usually to choose the situation so the relationship falls out.
If there is too much freedom, then the data will end up just confusing. An additional problem with mobiles is that there is often a couple applied near the axis by the knot in the thread used to suspend each arm... i.e. they can be a tad too sensitive.

An exercise I've used effectively is to get the students to build a balance to weight something small, like a paperclip or a pin, accurately. They have to use some known masses (1-5g say - all heavier than the object to be weighed) and popsicle sticks (or a ruler or whatever).

They'll quickly set up a see-saw, and discover they need to find out how the weight on one end is balanced by the position of the weight on the other end. Those who don't can be nudged.

Torque can be introduced then as a concept that makes that sort of relationship simple ... especially as you devise more complicated experiments.