Is there anything that would prevent me from entering international water territories on a kayak?

Kayak floating on water problem..?

• A 21 kg plastic ocean kayak has a sealed interior filled with air (like a big, hard-plastic balloon), so that the paddler sits on top of the floating kayak. The kayak has a total volume of 0.55 m^3. (Assume ρ_water = 1000. kg/m^3 throughout this problem). A) While the kayak is floating on water, what mass of water does is displace? _____ B) While the kayak is floating on water, what volume of water does it displace? _____ C) While the kayak is floating on water, what is the magnitude of the NET force acting on it? _____ Could someone please help me out with this problem? Would I go about solving it by using hydrostatic equilibrium? P = pgh + P_o ?

• Answer:

  "Would I go about solving it by using hydrostatic equilibrium? P = rho*g*h + P_o ?" You could, but that isn't worth it. You will waste your efforts modeling it with a crazy calculus model, when the Archimedes principle works as a great shortcut. Because this is a situation of fluid statics (no vertical acceleration of kayak), the Archimedes principle is applicable. Thus, the weight of the water displaced equals the upward buoyancy force. Because the kayak is in contact with no other bodies than the body of water, the upward buoyancy force must equal its weight. And because weight is proportional to mass, this means mass of displaced water equals total mass of kayak. m_net = m_boat + m_rider m_waterdisplaced = m_net m_waterdisplaced = m_boat + m_rider B) Just associate this mass water to the volume of water via the density of water. m_waterdisplaced = rho_water*V_waterdisplaced V_waterdisplaced = m_waterdisplaced/rho_water V_waterdisplaced = (m_boat + m_rider)/rho_water Summary: A) m_waterdisplaced = m_boat + m_rider B) V_waterdisplaced = (m_boat + m_rider)/rho_water Data: m_boat:=21 kg; m_rider:= wait, we weren't given the mass of the rider; rho_water:=1000 kg/m^3; Well, let's assume we are talking about a kayak unoccupied, since no other information was given. m_rider:=0 kg; Results: A) m_waterdisplaced = 21 kg B) V_displaced = 0.021 m^3 C) ZERO. This is a situation of fluid statics, and thus all forces acting on the floating kayak must add up to zero, since it isn't accelerating up or down.