Pulling a submerged car wreck out of the water

[Doyouevenlift]

A submerged wreck, mass 104 kg and mean density 8 x 103 kg m-3, is lifted out of the
water by a crane with a steel cable 10 m long, cross-sectional area 5 cm2 and Young’s
modulus 5 x 1010 N m-2. Determine the change in the extension of the cable as the wreck
is lifted clear of the water. /b]


This is from the British physics olympiad, and they also have solutions up on their site. Their method of solving this problem was straightforward, just using Young´s modulus = stress/strain, where stress = force/area normal to the force, and strain = extension/original length. This all seems logical, but what confused me is that they calculated the upthrust, and that was their force. Isn't this incorrect? I would guess that you'd have to use the weight - upthrust as your force, but apparently I'm wrong. Why?

 

[voko]

The weight stays constant. What changes is that the upthrust disappears as the wreck is pulled out of water. Hooke's law is linear.

 

[Doyouevenlift]

The weight stays constant. What changes is that the upthrust disappears as the wreck is pulled out of water. Hooke's law is linear.

So if I get this right: The upthrust equals the gravitational pull. Once it is cleared from the water, the upthrust is removed so the same force needs to be created by the machine?

 

[voko]

Perhaps we are not using "upthrust" to denote the same thing. I understand it is the buoyant force. So it cannot be equal to the gravitational pull (unless the wreck is floating, which it is not).

 

[Doyouevenlift]

Perhaps we are not using "upthrust" to denote the same thing. I understand it is the buoyant force. So it cannot be equal to the gravitational pull (unless the wreck is floating, which it is not).

Sounds logical, but what is then the justification of using the upthrust as the force required to pull the wreck out of the water? Intuitively, I'd say that you just subtract the upthrust from the car's weight (using w=mg), to get the force required. I always thought that things weigh less under water because you have to subtract the upthrust by the water from the weight.

 

[voko]

All you say is correct. But the problem only wants the change in extension when the wreck is pulled out. That change is due to the vanishing of the upthrust.

 

[Doyouevenlift]

All you say is correct. But the problem only wants the change in extension when the wreck is pulled out. That change is due to the vanishing of the upthrust.

But why? It the wreck tries to pull the car out of the water, I'm assuming there still is an upthrust while it is in the process of being pulled out. Yet, there must be some sort of change in extension, because pulling it out of the water still requires a force, eventhough there might be an upthrust..

 

[voko]

I am not sure what you are talking about. What car are you referring to?

When the wreck is in the water, there are three forces: weight + upthrust + tension in the cable. When it is out, there are two: weight + tension in the cable. Assuming it is pulled at a constant speed, in both cases the net force is zero, so the change in the tension is minus the upthrust. That change in the tension corresponds to the change in the extension of the cable via Hooke's law.