Wednesday, May 7, 2025

SIN Bin: 90

By Department Faculty

Problem

Polar bear walking on ice relative to sea level.

A polar bear, of mass 1250kg, sits at rest on a flat-topped chunk of ice floating as shown with its top at water level (bearly submerged??). The density of the ice is 925 kg/m3 and the density of the water is 1030 kg/m3. (After all it is salt water, silly!). Calculate the mass of the chunk of ice. Provide your answer in kg.  

  1. 41,700 
  2. 27,200 
  3. 15,400 
  4. 11,000 
  5. 9,600 

Solution SIN Bin: 90

D. 11,000

Answer Explanation: Any object floating in liquid displaces an equal weight of liquid. (This can most easily be shown by a free-body-diagram of the “void” filled with water. The vector sum of all the pressure forces acting over the entire surface of the “void” is able to just support either the chunk of water or the object.) If V is the volume of the submerged ice, then we have the following: 

Polar bear with mass, M, standing on ice with volume submerged, V.

ρ w Vg = ρ1 Vg+ MB g 

V = MB / (ρw – ρI ) 

MI = ρI MB / (ρw – ρI ) 

= 11,000 kg