Work done by liquid's frictional viscosity

[imatreyu]

Homework Statement

A 0.75 sphere is dropped through a tall column of liquid. When the sphere has fallen a distance of 2.0 m, it is observed t have a velocity of 2.5 m/s. How much work was done by the frictional viscosity of the liquid?

PLEASE EXPLAIN-- I really would like to understand this concept! My review book says that intial energy is entirely potential, and it sounds like final energy is kinetic-- but isn't there PE finally as well? I'm not sure. . . Could someone just explain this situation to me? As in, what happens in terms of energy/ work/ etc?

Thank you, in advance!

Homework Equations

The Attempt at a Solution

 

[praharmitra]

Potential energy is always calculated w.r.t. a reference. What your review book is doing is taking the final position of the sphere as the reference. Relative to that, the initial P.E. of the sphere is simply m g (2.0). The final P.E. is zero because it is at its reference position.

Therefore, initially energy is entirely potential, and finally it is entirely kinetic.

 

[imatreyu]

Oh thank you! I totally forgot about that.

Still though, I really don't understand what's going on in terms of the liquid's friction and work and energy in the system. What does the liquid friction work against?

 

[praharmitra]

The liquid friction works to slow down the sphere. The final velocity of the sphere is therefore lesser than it would have been had it been thrown downwards in the air. In terms of equations, this simply means

Initial P.E = Final K.E. + Work done by friction

 

[imatreyu]

Oh, thank you so much! You really cleared it up for me.