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curator:Tim Erickson
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 The Mettler Scale

Susan English, of vegetable measurement fame, and the curator were doing a workshop at Cal State Sacramento as part of the AAPT annual meeting. We were preparing for an activity in which you put a glob of clay on an electronic scale, weigh it, and then tilt the scale. When you tilt the scale, you should see the apparent weight of the glob decrease, becasue the normal component of the weight is less.

We had tried this with our own scales, but we only had three and needed six.

So we borrowed three more scales—really slick ones, by Mettler—from the physics stockroom there.

Fortunately, we tested those scales before the workshop began, and boy did we get a surprise. As you will see, the readings increase as you tilt the scale.

The setup is, we put the scale on a board that was 30 cm wide. then we blocked up one end of the board to tilt it, and measured the height of that high end. This enabled us to calculate the angle of tilt (arcsine of that height/30 cm).

ht is the height of the top end of the board in centimeters.
theta is the angle of the board in radians (=asin(ht/30)).

What's the mass of the glob of clay?

Some say it looks quadratic. Some say it looks like a cosine. Can you tell the difference?

Can you think of any physical reason how this is possible? We can't and would like to know! Clearly this scale does not work as ours do; with our scales, the reading decreases just as you would expect.

(data by Susan English and Tim Erickson, July 2004)

0
44.79
0
4.2
56.98
0.140461
5
61.53
0.167448
5.9
68.53
0.197957
7
79.22
0.235504
8.1
90.82
0.273393
5.6
66.06
0.187768
9
101.78
0.304693
10.8
125.41
0.368268
12.1
149.12
0.415157
12.1
149.74
0.415157

<text form of the data>

 ©2005 eeps media 866.341.3377 or Last updated February 14, 2007 supported by NSF award DMI-0216656