Buoyancy question?

Question

Hey, I need some help with this question, so any information would be great!

A 5.25-kg piece of wood (specific gravity= 0.5) floats on water (density= 1000 kg/m^3). A mass of lead (density=11,300 kg/m^3) is hung from the bottom of the wood block. What minimum mass of lead will cause the lead/wood combination to sink?

I found the density of wood to be 500 kg/m^3.
I know that there are two buoyancies going up and two weights going down.
I also know that I should use this equation:
Buoyancy= (density)(Volume)(gravity). But the thing is, there's no information that would be able to give me a volume, so that's where I'm stuck.

So please help if you can because it'll be much appreciated! Thanks.

Answer 1

To sink the combination of lead and wood must be equal or actually exceed the density of water.

(m1+m2)/(V1+V2) > p(water)
m1= p(wood) V1
m2= p(lead) V2
V2= m2/p(lead)

(m1+m2)/(V1+m2/p(lead)) > p(water

(m1+m2) > p(water) (V1+m2/p(lead))

m2 - p(water)m2/p(lead)) > p(water)V1 - m1

m2 [1- (p(water)/p(lead)) ] > p(water)V1 - m1

finally the mass of lead required to sink the wood is

m2 > [p(water)V1 - m1] / [1- (p(water)/p(lead)) ]

V1= m1/p(wood)
m2 > [1,000 x 5.25/ 500 - 5.25] / [1- 1,000/11,300]
m2 > 5.76 kg

Answer 2

Your water density is way too high, rho = 1000 g/m^3 or 1 kg/m^3, not 1000 kg.

When the combined weight (m + M)g > rho g V the buoyancy, the combo will sink; where m is wood mass and M is lead mass. mg = Rho v; where Rho = .5 N/v the specific gravity.

Thus mg + Mg > rho g V; Rho v + Mg > rho g V so that Mg > rho g V - mg and M > rho V - m,

Bottom line, your combo will sink if the lead mass is greater than the mass of the displaced water minus the mass of the wood. And, you are right, until we know how much volume is displaced by the shape of the wood/lead combo, we cannot get a specific M number.

Answer 3

you know the mass (5.25 kg) and the density (1000 kg/m^3) of the wood. You can find the volume.
D = m/v
v = m/D = (5.25 kg) / (1 000 (kg / (m^3))) = 0.00525 m^3

Answer 4

fat human beings have extra buoyancy whether it has no longer something to do with how nicely they might swim. whilst i became into scuba diving whilst i became into very skinny, i wanted no weights. whilst i became into 10-15 pounds fatter, i wanted 6-8 pounds of weights.