Question

A raft is made of solid wood and is 2.31 m long and 1.59 m wide. The raft is floating in a

lake. A woman who weighs 149 lb steps onto the raft. How much further
(cm) into the water does the raft sink? You do not need the thickness of the raft or the
density of the wood to solve this problem

Answer 1

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answer 2

This can be somewhat confusing since lb is a unit of force and kg is a unit of mass. That 1 kg of mass weighs 2.20 lbs. Another conversion factor is 1 lb force weighs 4.45 N.

We need to find the mass of the woman that will displace a force of 149 lbs.

149 lbs = 663 N

W = d g V = 663 N where d is the density of the water displaced

V = 663 N / (9.8 m/s^2 * 1000 kg / m^3) = .0676 m^3 water displaced

Note: 1 m^3 water weighs 1000 kg so 67.6 m^3 of water is displaced

A * L = volume of raft that must sink

L = .0676 m^3 / (2.31 m * 1.59 m) = .0184 meters the raft must sink