What is the Solution to This Difficult Bouyancy Question?

[Adam Rabe]

Homework Statement

Homework Equations

F = ma
F = pVg
p = m/V

3. The Attempt at a Solution [/B]
First i tried finding the volume of displaced water which i did by...

(50/1000) * 10 = 1000 * 10 * V ---> V = 0.00005 m^3
Next as the metal sits on the bottom its weight force minus the buoyant force contributes to the 100 g mass increase (1 N increase) in weight force on the scales. Using this we can find Mass
Buoyant force provided by 50g water = 0.5 N
Therefore weight force of metal = 1 N - 0.5 N = 0.5 N

F = ma
0.5 = m *10
m = 0.05 kg

p = m/V = 0.05 / 0.00005 m^3
p = 1000...
Which is dead wrong.
Answer says its B.) but i don't know how.
I'm sorry to ask but i urgently need the answer to this one.
Is it ok to ask for working out, or a really big hint?

Thanks in advance
Adam

 

[Orodruin]

1 N is the weight minus the buoyant force ... so what do you need to do with the buoyant force and 1 N to get the weight?

Also, computing the buoyant force is to overcomplicate things ...

 

[Adam Rabe]

1 N is the weight minus the buoyant force ... so what do you need to do with the buoyant force and 1 N to get the weight?

Also, computing the buoyant force is to overcomplicate things ...

hello sorry for the late reply...

1 N is the weight minus the buoyant force ... so what do you need to do with the buoyant force and 1 N to get the weight?

Also, computing the buoyant force is to overcomplicate things ...

oh i see. so you need to add the buoyant force?
you then get 1 + 0.5 = 1.5N
1.5 N ---> 0.15 kg
0.15/0.00005 = 3000
thanks a lot!
but i don't get why you added, ill have to think about it

 

[Adam Rabe]

1 N is the weight minus the buoyant force ... so what do you need to do with the buoyant force and 1 N to get the weight?

Also, computing the buoyant force is to overcomplicate things ...

ok i understand now, the mass of the ball at the bottom already has buoyant force accounted for and so if it was out of the water it would have that weight force added back to it.
thanks a lot for helping me with my stupidity

if i may ask how would you go about this without calculating anything? i think that's too advanced for me

 

[Orodruin]

if i may ask how would you go about this without calculating anything? i think that's too advanced for me

You will always need to do some computation. However, the easiest way is to note that the weight of the ball is 3 times that of the water removed and the volume is the same. Therefore, the density is three times that of water.