Question

A block of wood (density 713 kg/m3) of length L = 50.0 cm, width W = 40.0 cm, and thickness H = 30.0 cm floats in water (density 1.000 × 103 kg/m3).

What is the volume percentage of the wood that is above water?

If the wood is set to oscillate, what is its frequency?

How much can the wood carry without sinking?

Answer #1

Weight of the wood = 713*0.5*0.4*0.3*9.8 = 42.8*9.8 = 419.4 N

let the volume of wood inside the water be V

So, the upthrust , U = 1000*V*g

For floating condition,

U = Weight of wood

So, 1000*V*9.8 = 419.4

So, V = 0.0428 m3

So, percentage of wood inside water = 0.0428/(0.5*0.4*0.3) = 0.713 = 71.3 percent

b)

frequency of oscillation is given by:

f = sqrt(o*g/(*h))/(2*pi)

So,

f = sqrt(1000*9.8/(713*0.3))/(2*pi)

So, f = 1.08 Hz <------answer

c)

For this part:

1000*9.8*0.5*0.4*0.3 = 713*0.5*0.4*0.3*9.8 +m*9.8

So, m = 17.22 kg <-----answer

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