Answer to Question #16341 in Mechanics | Relativity for WILLYN JEAN
WHEN A POLAR BEAR JUMPS ON AN ICEBERG, HE NOTICES THAT HIS 1870 NEWTON WEIGHT IS JUST SUFFICIENT TO SINK THE ICEBERG. WHAT IS THE WEIGHT OF THE ICEBERG?
Let M be the weight and V be the volume of an iceberg. Then, according to the Archimedes' principle:
M*g + 1870[N] = p(water)*g*V, (1)
where p(water) is the density of water. As
V = M/p(ice),
where p(ice) is the density of ice, we can rewrite (1) as
M*g + 1870[N] = p(water)*g*M/p(ice).
M = 1870[N]/(g*( p(water)/p(ice) - 1 )).
The density of ocean water p(water) = 1025 kg/m³ and the density of ice is p(ice) = 916.7 kg/m³, so
M = 1870[N]/(9.8[m/s²]*( 1025[kg/m³]/916.7[kg/m³] - 1 )) ≈ 1615[kg].
So, the weight of an iceberg is about 1615 kg.