A water tumbler is in the shape of a uniform, thin, hollow cylinder that is closed at the bottom and open at the top (without its lid). The tumbler has a mass of 60.0 g, a height of 16.0 cm, and a diameter of 6.00 cm. (a) If the tumbler is empty, at what height above its base is its center of mass? (b) What is the maximum mass of water (density Pw = 1.00 g/cm³) that the tumbler can contain? (c) If the tumbler contains 350.0 mL of water, where is the center of mass of the combined system of the tumbler and the water it contains? (Note: 1 cm³ = 1 mL.) (d) During lunch time, a student clumsily bumps the tumbler with his arm, thereby applying a force at the top of the tumbler that is horizontal and directed radially inward, as shown in Figure 3. If the tumbler has the amount ot water in (c), what is the minimum magnitude of this force that will cause the tumbler to start tumbling over? (Assume the frictional between the tumbler and the horizontal tabletop it is standing on is enough to prevent the tumbler from sliding.) (e) In (d), what is the minimum coefficient of static friction between the tumbler and the table needed so that the tumbler will tumble over instead of sliding across the table? Figure 3: Force applied to the top of a tumbler.

A water tumbler is in the shape of a uniform, thin, hollow cylinder that is closed at the bottom and open at the top (without its lid). The tumbler has a mass of 60.0 g, a height of 16.0 cm, and a diameter of 6.00 cm. (a) If the tumbler is empty, at what height above its base is its center of mass? (b) What is the maximum mass of water (density Pw = 1.00 g/cm³) that the tumbler can contain? (c) If the tumbler contains 350.0 mL of water, where is the center of mass of the combined system of the tumbler and the water it contains? (Note: 1 cm³ = 1 mL.) (d) During lunch time, a student clumsily bumps the tumbler with his arm, thereby applying a force at the top of the tumbler that is horizontal and directed radially inward, as shown in Figure 3. If the tumbler has the amount ot water in (c), what is the minimum magnitude of this force that will cause the tumbler to start tumbling over? (Assume the frictional between the tumbler and the horizontal tabletop it is standing on is enough to prevent the tumbler from sliding.) (e) In (d), what is the minimum coefficient of static friction between the tumbler and the table needed so that the tumbler will tumble over instead of sliding across the table? Figure 3: Force applied to the top of a tumbler.