Energy changes moving through fluids

[Jimmy87]

Homework Statement

A ball is dropped from a height 'h' above a tube containing oil. Describe what happens to the GPE when the ball has reached terminal velocity in the oil.

Homework Equations

KE = 1/2mv^2 GPE = mgh

The Attempt at a Solution

When the ball is dropped,if we ignore air resistance then GPE will be converted directly into KE. When it strikes the surface of the oil, the ball's velocity will decrease which means the KE will also decrease. There is also still GPE which is not going into KE. So I think that both the decrease in kinetic energy and GPE both go into doing work against the drag force. When the ball reaches terminal velocity the KE will no longer change so there will be no more contribution from the kinetic energy, however GPE is still being lost which will go into work against the drag force. I am confused as I checked the answer for this question in my book and it just says "at terminal velocity GPE of the ball is converted into thermal energy". Surely GPE is being converted into both thermal energy and energy from doing work against the drag force or are these two the same? i.e. is heat lost due to friction with the oil the same as work done against the drag force?

 

[Chestermiller]

Yes, the latter.

Chet

 

[Jimmy87]

Yes, the latter.

Chet

So, all the GPE goes into thermal energy as soon as it hits the oil? How is work done against drag and thermal energy mean the same thing? If work done is force x distance doesn't some of the energy go into moving the object therefore it doesn't go into heat, e.g. if you push a block over a certain distance, the energy goes into the motion of the block. Does the work done by gravity change as it falls through the oil?

 

[Chestermiller]

So, all the GPE goes into thermal energy as soon as it hits the oil?

No. As the object is slowed down by the oil, it is losing KE, and that is being converted into internal energy of the oil.

How is work done against drag and thermal energy mean the same thing?

As the object moves through the fluid, it is causing the fluid to deform, and this causes viscous forces to develop at the surface of the object to slow it down. Meanwhile, the deformation that the object causes in the fluid combines with the viscous forces to do work on the fluid locally, and, as a result, to increase its internal energy.

If work done is force x distance doesn't some of the energy go into moving the object therefore it doesn't go into heat?

The drag force of the fluid on the object acts in the direction opposite to the motion of the object, and this reduces its kinetic energy (i.e., velocity). At the same time, the fluid that the object is contacting is caused to accelerate by the object, and to deform. So the kinetic energy of the object does work on the fluid, and the deformational work on the fluid causes the mechanical energy to be dissipated within the fluid, and converted into internal energy (heat).

Does the work done by gravity change as it falls through the oil?

The potential energy change resulting from the decrease in elevation of the object within the fluid is converted to internal energy of the fluid also.

Chet