Buoyancy and Hagan-Poseuille (pipe flow)1.A racquetball with a diameter of 5.6cm and a mass of 42 g is cut in half to make a boat forAmerican pennies made after 1982.The mass and volume of an American penny made after1982 are 2.5g and 0.36 cm3. How many pennies can be placed in the racquetball boat withoutsinking it?2.A supertanker filled with oil has a total mass of 10.2 x 108kg. If the dimensions of the ship arethose of a rectangular box 250 m long, 80 m wide and 80 m high, determine how far the bottomof the ship is below sea level. (density of sea water is 1020 kg/m3)3.A box with a volume V=0.05 m3lies at the bottom of a lake whose water has a density of103kg/m3. How much force is required to lift the box, if the mass of the box is (a) 1000 kg (b) 100kg and (c) 55 kg?4.A block of cherry wood that is 20 cm long, 10 cm wide, and 2 cm thick has a density of 800kg/m3. What is the volume of a piece of iron that, if glued to the bottom of the block makes theblock float in water with its top just at the surface of the water? The density of iron is 7860kg/m3, and the density of water is 1000 kg/m3.5.A very large balloon with mass M=10kg is inflated to a volume of 20 m3using a gas of densityρgas=0.2 kg/m3. What is the maximum massmthat can be tied to the balloon using a 2 kg pieceof rope without the balloon falling to the ground? (Assume that the density of air is 1.3 kg/m3and that the volume of the balloon gas is equal to the volume of the inflated balloon.)6.A cylindrical container has a radius of 1 m and contains motor oil with a viscosity of 0.3 Pa s anda density of 670 kg m-3. Oil flows out of the 20 cm long, 0.2 cm tube at the bottom of thecontainer. How much oil flows out of the tube in a period of 10 s if the container is originallyfilled to a height of 0.5 m?Conservation of Energy (spring and near earth)1.A ball is thrown up in the air reaching a height of 5m. Using energy conservation considerations,determine its initial speed. You may neglect air friction, drag.2.A cannonball of mass 5.99 kg is shot from a cannon at an angle of 50.21orelative to the horizontaland with an initial speed of 52.61 m/s. As the cannonball reaches the highest point of its trajectorywhat is the gain in it is potential energy relative to the point from which it was shot? How high abovethe cannon does the cannonball go?3.A basketball of mass 0.624 kg is shot from a vertical height of 1.2 m and at a speed of 20.0 m/s. Afterreaching its maximum height, the ball moves into the hoop on its downward path, at 3.05 m abovethe ground.Using the principle of energy conservation, determine how fast the ball is moving justbefore it enters the hoop.

PROBLEMS TO CHALLENGE YOURSELFPHYS 2211CDensity & Pressure

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