Question

Work this out clearly and with units. Thanks.

Determine the minimum area of a flat ice floe (sheet) 100 cm thick if it must support a 1600-kg truck above seawater. Assume the top of the ice is level with the ocean. (Hint: what is the volume of the ice?) pice = 920 kg/m', psea- 1020 kg/ml. Sketch a diagram and label all forces. Calculate a rough approximation of the area of a truck, and compare it to your answer.

Answer 1

$\rho$_ice = 920 kg/cu.m;

$\rho$_sea = 1020 kg/ cu.m

mass of truck = 1600 kg

area of the ice sheet = A sq.m

volume of the ice block = A*1 = A cu.m

When the block is fully immersed ( level with ocean)

it will displace A cu.m of water equal to its volume.

upward thrust (buoyant force) = A*$\rho$_seag N

down ward force = weight of ice block + truck weight

= (A$\rho$_ice + 1600)g.

For the truck to keep floating

upward thrust = down force

A*$\rho$_seag = (A$\rho$_ice + 1600)g.

A = 1600/($\rho$_sea - $\rho$ _ice) = 1600/(100) = 16 sq.m - area of the ice sheet

Wice. Wruck ice sheet Fbuoyant