How much does a barge rise when 7 tonnes of grain is removed?

[cd19]

Homework Statement

A barge has a waterline area 25m² and sides that can be assumed to be vertical. If 7 tonnes of grain is removed from the barge by how much will the barge rise in the water. Assume that the grain was evenly distributed and the barge rises without tilting.

Homework Equations

not fully sure, see my attempt

The Attempt at a Solution

Firstly I figure if I find the hydrostatic force acting on the area of the barge, by F=Area*(density*gravity*Height_centroid i can then find the force when 7 tonnes has been removed, and then create an integral expression to calculate the height the barge has rised..I reckon I'm thinking about this the complete wrong way, can anyone help?

 

[Doc Al]

Consider Archimedes' principle. How much less water does the boat displace once the grain is removed?

 

[cd19]

The original weight of water displaced (weight of barge which is unknown) - 7 tonnes.. I see what your saying but how will i incorporate this?

 

[Doc Al]

The original weight of water displaced (weight of barge which is unknown) - 7 tonnes.. I see what your saying but how will i incorporate this?

So what volume of water does that correspond to?

 

[cd19]

the volume of the removed grain (25m²*height_barge-volume of removed grain (7 tonnes=7000kg). would I be right to let this = force acting down on the barge to find the height of the barge or is this step unnecessary.. its the abstract that is confusing me

 

[cd19]

sorry would it correspond to the volume of water the removed grain has displaced, do i have to use integration to find the height now?

 

[Doc Al]

Maybe doing the problem backwards might help. Imagine the barge is empty. Now you dump 7000 kg of grain onto it. What additional volume of water do you have to displace? You know the cross-sectional area of the barge, so how far does the barge sink further into the water to displace that additional volume of water?

 

[Doc Al]

sorry would it correspond to the volume of water the removed grain has displaced,

Yes.

do i have to use integration to find the height now?

All you need is volume = area*height.

 

[cd19]

density = mass/volume therefore the volume = 7000/1000 = 7

volume = area * height, height=7/25 = 0.28m

does this look correct?

thanks a lot for your help.

 

[Doc Al]

density = mass/volume therefore the volume = 7000/1000 = 7

volume = area * height, height=7/25 = 0.28m

does this look correct?

Perfectly correct.