## King 4 years ago A cork of density 0.15 g/cm^3 floats in a bucket of water with 10 cm^3 of its volume above the surface of water.Find the mass of the cork.

1. anonymous

do u know how to do this?

2. anonymous

$d=\frac{m}{V}$ Therefore, $m=dV$ Hope this helps, somehow. I'm unsure.

3. anonymous

how?can u solve it?

4. anonymous

help tomas......

5. anonymous

i think you need to use Archimedus law or something

6. anonymous

|dw:1326975917374:dw|

7. anonymous

|dw:1326976017906:dw|

8. anonymous

ya so now?

9. anonymous

also $F_a>mg$ if that matters lol

10. anonymous

i know but then i am stuck at hw to find the missin volume..............

11. anonymous

hi

12. anonymous

u hv the same problem?

13. anonymous

i posted fr u

14. anonymous

nanbenda

15. anonymous

jacob help man!

16. anonymous

wait sachin

17. anonymous

I think you have to use Archimedes Principle and Density- Mass relationship. Still I am not getting the equation.

18. anonymous

i know but how????

19. anonymous

how is d=m/g

20. anonymous

Sorry, i was saying whether we can use density = mass/volume?

21. anonymous

yeah we can use anythin

22. anonymous

Then it is simple. Mass= volume X density, so Mass= 10 * 0.15= 1.5 gm (Still u check the answer)

23. anonymous

24. anonymous

25. anonymous

Saw it, but confused about the equation

26. anonymous

volume is 10+some x

27. anonymous

I will consult and say u tomorrow

28. anonymous

$\rho=0.15\,g/cm^3\quad,\quad \rho_w=1\,g/cm^3\quad,\quad V\uparrow=10\,cm^3$$\rho Vg=\rho_w V\downarrow g\quad\Rightarrow\quad \frac{V}{V\downarrow}=\frac{V\uparrow+V\downarrow}{V\downarrow}=\frac{V\uparrow}{V\downarrow}+1=\frac{\rho_w}{\rho}$$V\downarrow=\frac{\rho}{\rho_w-\rho}V\uparrow$$m=\rho(V\uparrow+V\downarrow)=\rho\left(1+\frac{\rho}{\rho_w-\rho}\right)V\uparrow=\frac{\rho\rho_w}{\rho_w-\rho}V\uparrow$$m=\frac{0.15}{0.85}\cdot 10\,g=1.765\,g$

29. JamesJ

nikvist, this a good answer. I understand your notation. But perhaps for the others could you explain in words what you've done here? Thanks.

30. anonymous

|dw:1326987424332:dw|For practical purposes water is incompressible so the submerged part would displace an amount of water equal to its own volume. so same mass that is what nikivist has done ...equate the mass of cork as a whole to mass of water displaced then manipulations gives us everything written in terms of density which we know(data in the question)

31. anonymous

nikvist could u explain ure answer in words or JamesJ could u do it fr him?

32. anonymous

hmmm..... that is wat i did.............

33. anonymous

Please explain in simple words. Are we to use that Density formula or not?

34. anonymous

I WILL TELL EVERYTHING FROM FIRST by archimedes principle, the wt of cork=wt of water displaced(buoyant force) this is because the body is floating upward forces=downward then wt of cork=volume*density*g wt of water displaced=volume(V)*density oif water*g write volume of cork as volume of upper immersed portion+vol of downward immersed portion(V) REMEMBER IT IS V that we need to calculate do it in simple terms after this |dw:1327073074048:dw|

35. anonymous

knowingV it is easy to calculate the mass of that part of cork+mass of upper part of cork...........got it adarsh?

36. anonymous

Yeah

37. anonymous

u need to know here that by archimedes principle,buoyant force=wt of water displaced in this case as the cork is floating the wt mg equals the buoyant force so to to keep the cork at rest

38. anonymous

Yeah, that's right.

39. anonymous

40. anonymous

Seeing.

41. anonymous