A small, smooth cube made of wood that has a mass density of 850 kg/m3 is droppe

Question

A small, smooth cube made of wood that has a mass density of 850 kg/m3 is dropped from rest 4.00 m above the surface of a lake.

Part A

Determine the maximum depth the cube reaches.

Express your answer with the appropriate units.

d= ?

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.

t = ?

Explanation / Answer

A)
velocity of the cube when it touches the water, v = sqrt(2*g*h)

= sqrt(2*9.8*4)

= -8.85 m/s (downward)

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 - 8.85^2)/(2*1.73)

= 22.7 m <<<<<------------Answer

B) total time taken for travel inside water, T = 2*v/a (it

= 2*8.85/1.73

= 10.2 s <<<<<------------Answer

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