Does Throwing an Anchor Overboard Change the Pond's Water Level?

[Ethan Godden]

Homework Statement

A person in a boat floating in a small pond throws an anchor overboard. What happens to the level of the pond?

Homework Equations

F_g=B →ρ_objectgV_object=ρ_fluidgV_displaced

The Attempt at a Solution

The answer is the water level remains the same. My attempted solution is attached. I want to know how to prove the volume displace before and after are the same.

Thank you,

Ethan

 

[TSny]

For a boat in a pond, the anchor might rest on the "seafloor". But, I guess in this problem you are to assume that the anchor is dangling in the water.

Does the total force of gravity acting on the system change when going from anchor in boat to anchor in water? What can you conclude about the total buoyant force acting on the system before and after?

In your solution, you said that T is greater than F_{g, anchor}? Is that so?

 

[Ethan Godden]

Opps, I meant T is less that F_{g anchor} as T is equal to the force of gravity on the anchor minus the buyoant force on the anchor.

The force of gravity does not change (well by a very negligible amount ).Are you implying that since the system the force of gravity before equals the force of gravity after and the system is in equalibrium, this implies the total buyoant force doesn't change which implies the total volume displaced doesn't change which means the water level stays constant?

Thank you for your help,

Ethan

 

[TSny]

The force of gravity does not change (well by a very negligible amount ).

Are you implying that since the system the force of gravity before equals the force of gravity after and the system is in equalibrium, this implies the total buyoant force doesn't change which implies the total volume displaced doesn't change which means the water level stays constant?
Ethan

Yes, I believe that's correct.