which are conservative vs non conservative force

Question

Which of the following forces are conservative and which are non-conservative?  

a) The winding pushing the sails.

b) The wind resistance attacking against the sails.

c) The resistance of the water.

d) The weight of the passengers.

e) The weight of the boat

f)  The buoyant force of the water keeping the boat afloat.

Answer 1

Hello Matt!

For the purposes of this problem, we can define a conservative force as a force that conserves the mechanical energy, which is the sum of kinetic and potential energy. Now we can evaluate.

Let's use the acronyms C for conservative and NC for non-conservative.

a) The winding pushing the sails changes the kinetic energy (by pushing the boat forward) without changing the potential energy (gravitational energy), so it's NC

b) The wind resistance changes the kinetic energy (by reducing the boat velocity) without changing the potential energy (gravitational energy), so it's NC

c) The resistance of the water without changing the potential energy (gravitational energy), so it's NC

d) The weight of the passengers conserves the mechanical energy due the gravitational field, so it's C.

e) The weight of the boat conserves the mechanical energy due the gravitational field, so it's C.

f) The buoyant force acts similar to a string, with a field counter to the gravitational field, so it's C.

Note that if you consider the boat over the sea, the buoyancy is not conservative, because of changes in the density of the sea water with the position.

Send me a message if you need anything else!

Best regards!