The bottom of a steel "boat" is a 5.00 mm ×× 10.0 mm ×× 4.00 cmcm piece of steel (ρsteel=7900kg/m3)(ρsteel=7900kg/m3). The sides are made of 0.480 cmcm -thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?

A block of wood has a mass of 3.88 kg and a density of 647 kg/m³. It is to be loaded with lead (1.13 x 104 kg/m³) so that it will float in water with 0.823 of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood? (a) Number i (b) Number i Units Units

A stick of butter has dimensions 130 mm × 30 mm × 30 mm and density pt = 870 kg/m³. It is placed in a bowl of cool water and floats with its long side oriented horizontally. What volume of butter is submerged? (As always, drawing a force diagram is a great first step.) What is the smallest amount of mass m you must place on top so that the butter becomes fully submerged? Suppose that the stick is balanced very delicately so that it floats with its long side oriented vertically. How would this change your answers above?

12.17 A large air-filled rubber ball is tethered to the bottom of a swimming pool. The tension in the tether is 100 N. The mass of the rubber in the ball itself is 2 kg while ?water = 1000 kg m−3 and ?air = 1.2 kg m−3. What is the volume of the ball?

A raft is made of 11 logs lashed together. Each is 41 cm in diameter and has a length of 6.2 m . How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 67 kg ? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

A block of wood with dimensions 60.0 cm × 40.0 cm × 8.0 cm floats on water with 75% of its volume below the surface of the water. While floating on water, how much mass can be placed on top of the block before it is completely submerged? The density of water is 1000 kg·m−3

On another planet that you are exploring, a large tank is open to the atmosphere and contains ethanol. A horizontal pipe of cross-sectional area 7.0×10−4m27.0×10−4m2 has one end inserted into the tank just above the bottom of the tank. The other end of the pipe is open to the atmosphere. The viscosity of the ethanol can be neglected. You measure the volume flow rate of the ethanol from the tank as a function of the depth hh of the ethanol in the tank. If you graph the volume flow rate squared as a function of hh, your data lie close to a straight line that has slope 2.09×10−5m5/s22.09×10−5m5/s2.   What is the value of gg, the acceleration of a free-falling object at the surface of the planet? Express your answer with the appropriate units.

A block of wood has a mass of 3.94 kg and a density of 545 kg/m³. It is to be loaded with lead (1.13 x 104 kg/m³) so that it will float in water with 0.924 of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood? (a) Number i (b) Number i Units Units

(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 26.2 m. Assume the density of the water is 1.00 x 103 kg/m3 and the air above is at a pressure of 101.3 kPa. Pa (b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 31.0 cm? N

A block of wood has a mass of 3.81 kg and a density of 684 kg/m3. It is to be loaded with lead (1.13 × 104 kg/m³) so that it will float in water with 0.851 of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood? (a) Number Units (b) Number i Units