3. A box-shaped piece of concrete measures 3ft by 2ft by 0.5ft. a) What is its w

Question

3. A box-shaped piece of concrete measures 3ft by 2ft by 0.5ft.

a) What is its weight? 3 pts

b) Find the buoyancy force that acts on it when it is submerged in water. 3pts

c) What is the net force on the concrete piece when it is under water? 4pts



4. A Styrofoam slab has thickness h and density ?s . When a swimmer of mass m is resting on it, the slab floats in fresh water with its top at the same level as the water surface. Find the area of the slab. 10 pts





5. A thin spherical shell of mass 4.00 kg and diameter 0.200 m is filled with helium (density ? = 0.180 kg/m3). It is then released from rest on the bottom of a pool of water that is 4.00 m deep. (a) Neglecting frictional effects, show that the shell rises with constant acceleration and determine the value of that acceleration. 5pts (b) How long will it take for the top of the shell to reach the water surface? 5 pts

Explanation / Answer

density of concrete is 2400kg/m^3 = 150 lb/ft^3 density of water is 1000kg/m^3 = 62.4lb/ft^3 wtg = (3*2*0.5*150)32.2 = 14490lbf buoyancy force = (3*2*0.5*62.4)*32.2 = 6027.84 lbf net force is =14490-6027.84 = 8462.16lbf wtg of water displaced = wtg of slab and man A*h*62.4 = m + A*h*p A = m/(h*(62.4+p)) V = 4*pie*r^3/3 = 4*3.14*0.2^3/3 = 0.0335m^3 net force on shell = (V*0.18 + 4 - V*1000)*g = (V*0.18 + 4)a a = 72.15 m/s^2 upwards s = ut + 0.5at^2 4 = 0 + 0.5*72.15*t^2 t = 0.33 sec

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