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Help physics question please

A cylinder of wood is placed in water.
The density of the wood is 6.0*10^2 km/m3. The density of water is 1.0*10^3 kg/m3.

What fraction of the volume of the cylinder is BELOW the water line?

I have no idea how to attempt this - could someone please explain?
Cylinder is in equilibrium so weight = upthrust. Let entire volume of cylinder be Vc this means mass of cylinder = density of wood * volume of cylinder = 600Vc.
Upthrust = density of water * volume of water displaced( equal to volume of cylinder under water, let this equal Vw) * g = 1000 * Vw * g.

As it is in equilibrium : 600Vc * g = 1000 Vw* g
600Vc = 1000Vw
Vw/Vc=600/1000 = 0.6
Reply 2
Original post by haarithiop
Cylinder is in equilibrium so weight = upthrust. Let entire volume of cylinder be Vc this means mass of cylinder = density of wood * volume of cylinder = 600Vc.
Upthrust = density of water * volume of water displaced( equal to volume of cylinder under water, let this equal Vw) * g = 1000 * Vw * g.

As it is in equilibrium : 600Vc * g = 1000 Vw* g
600Vc = 1000Vw
Vw/Vc=600/1000 = 0.6



Hey, thank you for the reply. I understood up to the last line - "Vw/Vc".... How do you know that gives the volume of cylinder below the water line? Why not Vc/Vw??
Vw is the volume of water displaced which is equal to the volume of cylinder under water, so the fraction of the volume of cylinder under water is Vw/Vc.
Reply 4
Original post by haarithiop
Vw is the volume of water displaced which is equal to the volume of cylinder under water, so the fraction of the volume of cylinder under water is Vw/Vc.


Makes sense, thank you.

Could you help me with this other question?

"The earth takes 1 day to rotate about its axis.
What is the angular velocity of a point on the surface of the Earth?"

I got 7.3*10^-5 but the answer says 2.0*10^-7.

I used w=2pi/(24*3600).
Original post by MrToodles4
Makes sense, thank you.

Could you help me with this other question?

"The earth takes 1 day to rotate about its axis.
What is the angular velocity of a point on the surface of the Earth?"

I got 7.3*10^-5 but the answer says 2.0*10^-7.

I used w=2pi/(24*3600).


Well I agree with your answer, maybe someone else can confirm though.
Original post by MrToodles4
Makes sense, thank you.

Could you help me with this other question?

"The earth takes 1 day to rotate about its axis.
What is the angular velocity of a point on the surface of the Earth?"

I got 7.3*10^-5 but the answer says 2.0*10^-7.

I used w=2pi/(24*3600).


ms answer is *suspiciously* similar to the angular velocity of the earths orbit... 2π/(365*24*60*60)
I hope this is alvel
Reply 8
Original post by haarithiop
Well I agree with your answer, maybe someone else can confirm though.


Thank you.

I have this last multiple choice question;

An object of mass m is attached to a string and then whirled in a horizontal circle. The speed of the object is slowly increased from zero. The string breaks when the object has a maximum speed of 1m/s.

The experiment is repeated with an identical string but with an object of mass 1.5m. The radius of circle is kept constant.

What is the maximum speed of this object when the string breaks?

So F=mv^2 / r and will F be constant?? (if so, why?) so i assumed F is constant and there m increasing must result in v decreasing?? So you get
from f/m = v^2 /r that v^2 is inversely proportional to m... so if m increases by sf of 1.5 shouldn't v decrease by 2.25?? so I do 1/2.25 but it gives the wrong answer :/
Original post by MrToodles4
Thank you.

I have this last multiple choice question;

An object of mass m is attached to a string and then whirled in a horizontal circle. The speed of the object is slowly increased from zero. The string breaks when the object has a maximum speed of 1m/s.

The experiment is repeated with an identical string but with an object of mass 1.5m. The radius of circle is kept constant.

What is the maximum speed of this object when the string breaks?

So F=mv^2 / r and will F be constant?? (if so, why?) so i assumed F is constant and there m increasing must result in v decreasing?? So you get
from f/m = v^2 /r that v^2 is inversely proportional to m... so if m increases by sf of 1.5 shouldn't v decrease by 2.25?? so I do 1/2.25 but it gives the wrong answer :/


is the answer 0.816
Original post by haarithiop
is the answer 0.816


Yes, I've managed to get that as well - but I just don't see why the method above is wrong?
Original post by MrToodles4
Yes, I've managed to get that as well - but I just don't see why the method above is wrong?


v decreases by a factor of square root(1/1.5)
Original post by haarithiop
v decreases by a factor of square root(1/1.5)


But the mass doesn't increase by a factor of square root 1.5 :/

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