Introductory Mechanics
Problems Laboratory
1
The Waiter
Goals: Calculate the center of mass of an
individual object and a collection of objects.
Understand the role of the center of mass for
stability and equilibrium.
PROBLEM
We have all watched as a waiter carries an amazing numebr of items on a tray without
dropping any. Perhaps, you’ve even had the chance to wait or bus tables as well. The act
of balancing a number of different items on a large tray requires balance by the waiter,
but also requires placement of items based on physics.
Our waiter has two types of items: plates and glassware. The plates can be treated as
uniform thin disks with a mass of 900 g and a 28 cm diameter. The glasses have a mass
of 300 g and are cylinders with a radius of 4 cm and a height of 16 cm. The mass is not
uniform in a glass. Two thirds of the mass is in the base which is 3 cm tall.
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The Waiter
The waiter has a choice of two trays. One is a narrow rectangular tray that measures 21
cm by 88 cm and has a mass of 500 g. On the narrow tray, items are lined up in a row
without overlapping. The other is a large circular tray with a diameter of 76 cm and
mass of 1000 g. Items on this tray can be placed in any position if they don’t overhang
the edge and don’t overlap.
The waiter carries his tray supported on one hand that spans a diameter of 20 cm. What
arrangements of plates and glasses can be balanced on a tray?
PROBLEM SKILLS
We are used to problems with variables to stand for quantities that may change during a
the course of a problem. Problems that have a changing number of items with the same
types of variables use a shorthand notation to represent a set of variables. In this short
hand the same variable name is given to all variables of a certain type. A subscript is
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 Spring '08
 staff
 Center Of Mass, Mass, Weight function, A. Center of Mass

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