# Q & A: Labs demonstrating direct proportion

Q:
Hi! I was wondering......are there any labs out there that demonstrate direct proportion other than springs and Hookés law?
- Stephan Graham (age 34)
A:
Well, you could measure the weight (or mass, if using a balance) of water compared to the volume of water (be sure to subtract off the weight of the beaker). Or how about the weight (or mass) of air compared with the air pressure in a container of fixed size.
Or the pressure compared with the (absolute) temperature for a fixed amount of gas in a fixed volume.

The gravitational potential energy of an object is proportional to its height. If you convert that into kinetic energy by letting it slide down a (frictionless!) track and then let it slide to rest on a rough surface, the distance it will travel before coming to a stop will be proportional to the height from which it started. It shouldn't roll but rather should slide.

The change in length of an object is proportional to the change in temperature of the object when it is heated up.

The electrical resistance of a piece of mechanical pencil lead should be proportional to its length. But be careful about contact resistances if using voltmeter probes.

The temperature depression of the freezing point of saltwater should be proportional to the concentration of salt.

The current through a resistor is proportional to the voltage difference between its leads.

The charge on a capacitor is proportional to the voltage difference between its leads.

Can you think of any more?

Tom

p.s. Almost all these relationships are not quite exact. E.g. if you run too much current through a resistor, it will get hot and the ratio of votage to current will change a bit.
Mike

(published on 10/22/2007)