Six empty 200 L drums whose mass is 20 kg each are used as floats for a boat dock in a freshwater tank. The dock platform is 1.8 x 0.9 m and is made of pine planks 40 mm thick. Find the maximum number of 75 kg people who can stand on the platform w/out getting their feet wet. The density of pine is 370 km/m^3.

Question

mrnood · Answer

Maximum Buoyancy force when the drums and pine are JUST about to be immersed

1200l of water = 1200kg *g
+ 1.8*0.9*.4 m^3 water @ 1000kg/m^3 *g

Downward force = 6*20kg*g +weight of wood (density*volume*g) + n *75*g

These 2 forces are equal (although I think it would be a challenge to stay balanced on such a dock when it is on the point of submersion)

Calculate n so that the downward force <= buoyancy

mrnood · Answer

Maximum Buoyancy force when the drums and pine are JUST about to be immersed

1200l of water = 1200kg *g
+ 1.8*0.9*.4 m^3 water @ 1000kg/m^3 *g

Downward force = 6*20kg*g +weight of wood (density*volume*g) + n *75*g

These 2 forces are equal at the point of sinking
(although I think it would be a challenge to stay balanced on such a dock when it is on the point of submersion)

Calculate the largest value of n so that the downward force <= buoyancy

blackbird02 · Answer

@MrNood thanks!