Question

PS8-1 A wooden block, made of maple and having arbitrary shape, is placed in water. The densities of the maple and of the water are 675 and 997 kg/m, respectively. Will the maple block float or sink? Defend your answer fully, using principles of hydrostatic pressure and buoyancy. 1. 2. Deeminethe perenhe waers surface Draw figure and show work, using the problem-solving format specified for this course.

Answer 1

Let m be the mass of block and v be the volume of block density of maple is rho_maple = 675 kg/m^3 density of water is rho_water = 997 kg/m^3. The maple block will float Because rho_maple < rho_water \r\n where F_b be the buoyant force on the block F_b = v_in rho_water g where v_in be the volume of block inside the water The block is floating so from Newton's second law F_b = mg v_in rho_water g = mg v_in rho_water = m we know that mass = volume times density m = v times rho_maple than v_in rho_water = v times rho_maple v_in/v = rho_maple/rho_water = 675/997 v_in/v = 0.667 than % is = v_in/v times 100% = 0.667 times 100% = 67.7%