In the figure, a 2.8 g ice flake is released from the edge of a hemispherical bowl whose radius r is 21 cm. The flake-bowl contact is frictionless. (a) What is the speed of the flake when it reaches the bottom of the bowl? (b) If we substituted a second flake with 5 t the mass, what would its speed be? (c) If, instead, we gave the flake an initial downward speed 1.2 m/s along the bowl, what would answer be?

A leaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. Find the work done. (Use 9.8 m/s2 for g.)

Suppose that the average U.S. household uses 14100 kWh (kilowatt-hours) of energy in a year. If the average rate of energy consumed by the house was instead diverted to lift a 1690 kg car 15.8 m into the air, how long would it take? car: S Using the same rate of energy consumption, how long would it take to lift a loaded Boeing 747 airplane, with a mass of 3.90 x 10° kg, to a cruising altitude of 9.42 km? airplane: S

Suppose you have an ice cream cone full of melted ice cream. The ice cream cone is in the shape of a right circular cone and is 0.5 feet tall with a width (diameter) of 0.25 feet at the top. You decide to drink the melted ice cream using a straw positioned at the top of the cone. How much work is necessary to drink all of the ice cream through the straw? Note that the approximate weight-density of melted ice cream is 64.05 pounds per cubic foot. Round your final answer to 3 decimal places.

In the figure, a 2.9 kg block is accelerated from rest by a compressed spring of spring constant 650 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction k = 0.210. The frictional force stops the block in distance D = 7.5 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? (a) Number (b) Number (c) Number XXX Units Units Units No friction D

A 56-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.3 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.