Lab 5: Ball Point Pens and Pie

Winter 2004

The Physics of Ball Point Pens

This experiment was described in Robert Ehrlich, Why Toast Lands Jelly-side Down: Zen and the Art of Physics Demonstrations, Princeton University Press, 1997.

Find a ball point pen that has a retractable head and a spring inside. Unscrew the pen and put aside the top part of the pen (the half that has the "clicky thing" in it.) By holding down the bottom plastic part, compressing the spring, and letting go, you can launch the plastic part into the air. Give it a try.

We can use conservation of energy to predict how high the plastic part should fly. First, let's establish some notation:

1. m = mass of plastic projectile
2. k = spring constant of the pen's spring
3. M = mass with which we must compress the spring
4. x = distance through which the spring is compressed
5. h = maximum height of m

1. Suppose we compress the spring by an amount x and then release the mass m. How high will the mass go? Find an expression for h in terms of k, g, and x.
2. Measure x. Do this by determining how much the string is compressed when it's pressed in as far as possible.
3. Measure m. Use one of the digital scales in the chem lab.
4. Measure k. This is the tricky part. It turns out that the magnitude of the force needed to compress a spring a distance x is equal to kx. Here's how to measure the force. When you press down on the spring, the ground pushes back up on the ink cartridge an equal and opposite amount. Instead of resting the pen on the table, put the end of the pen on the pan of a pan balance. (You'll need to use one of the larger pan balances in the chem lab.) Adjust the mass on the scale until it balances out your pushing down around when the spring is completely compressed. The force with which you're pushing down the pen equals the force of gravity MG on the mass M on the scale. Thus, kx = Mg.
5. Using your result from part 1 and your measurements, estimate h. Then measure h using a meter stick. You'll need to make sure that the pen flies straight up, and that you release the pen top quickly. How close does the measured value agree with the calculated value? Last night I got an agreement to within around 10%. The author of the above-cited book claims that he was able to obtain agreement within 1 or 2 percent.

Pieces of Pie

Web page maintained by dave@hornacek.coa.edu.