Problem 18.66 A small, smooth cube made of wood that has a mass density of 850 k
ID: 1463046 • Letter: P
Question
Problem 18.66 A small, smooth cube made of wood that has a mass density of 850 kg/m^3 is dropped from rest 3.00 in above the surface of a lake. Express your answer with the appropriate units. Part A Determine the maximum depth the cube reaches. Part B Determine the time interval the wood is under water before it returns to the surface. Assume that viscous drag is negligible so that the only force the water exerts on the cube is the buoyant force. Express your answer to two significant digits and include the appropriate units.Explanation / Answer
A)
speed of the cube when it touches the water, v = sqrt(2*g*h)
= sqrt(2*9.8*3)
= -7.67 m/s (downward)
Let V is volume of the cube.
when it is moving towards bottom buyonat force acts upward.
Fnet = B - m*g
m*a = rho_water*V*g - rho_wood*V*g
rho_wood*V*a = rho_water*V*g - rho_wood*V*g
a = rho_water*g/rho_wood - g
= 1000*9.8/850 - 9.8
= 1.73 m/s^2 (upward)
maximum depth, d = (vf^2 - vi^2)/(2*a)
= (0^2 - 7.67^2)/(2*1.73)
= 17 m
B) total time taken for travel inside water, T = 2*v/a
= 2*7.67/1.73
= 8.87 s