randomm13
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A student investigated the relationship between the mass m a boat can carry and the depth d
below the water surface of the lowest point of the boat.
He modelled the boat using a glass beaker.
He added 10-gram slotted masses and marked the position of the water surface on the
beaker, as shown
(I can't paste the pic page 4 on this pdf
https://doc-0k-1k-apps-viewer.google...c3cpgdfpjrttti )

The student assumed the beaker was a cylinder with radius r cm and the water had a
density of 1 g cm–3.
(a) Show that the upthrust U on the beaker could be calculated using the equation
U=( Pi * r^2 *g*d)/1000
where d is in cm and U is in N.

what am I supposed to do here??
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Stonebridge
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The upthrust U is given by Archimedes Principle.
Have you heard of that?
If yes, then the volume (and hence mass/weight) of the displaced water can be calculated from the dimensions of the beaker and how far it is displaced in that water.
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phobobs
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Archimedes principle is that "the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.".

You know the volume of fluid that the beaker displaces (the volume of the beaker), and you know the density of water. If you know the volume and the density of the water, you can work out the mass and thus the weight of the water, and archimedes principle tells you that this weight is equal to the upthrust, U, in Newtons
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randomm13
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(Original post by phobobs)
Archimedes principle is that "the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.".

You know the volume of fluid that the beaker displaces (the volume of the beaker), and you know the density of water. If you know the volume and the density of the water, you can work out the mass and thus the weight of the water, and archimedes principle tells you that this weight is equal to the upthrust, U, in Newtons
oh ok I'll try it out
thank you very much
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randomm13
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(Original post by Stonebridge)
The upthrust U is given by Archimedes Principle.
Have you heard of that?
If yes, then the volume (and hence mass/weight) of the displaced water can be calculated from the dimensions of the beaker and how far it is displaced in that water.
I'll have to try that out
thnx a lot
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randomm13
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(Original post by phobobs)
Archimedes principle is that "the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.".

You know the volume of fluid that the beaker displaces (the volume of the beaker), and you know the density of water. If you know the volume and the density of the water, you can work out the mass and thus the weight of the water, and archimedes principle tells you that this weight is equal to the upthrust, U, in Newtons
but we don't know the volume of water
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randomm13
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(Original post by Stonebridge)
The upthrust U is given by Archimedes Principle.
Have you heard of that?
If yes, then the volume (and hence mass/weight) of the displaced water can be calculated from the dimensions of the beaker and how far it is displaced in that water.
how do I get volume?
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Stonebridge
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The beaker is a cylinder, so use the formula for the volume of a cylinder. You have the radius of the end of the beaker and the 'length' in this case is the depth it is inserted under the water. This gives the volume of water displaced when the cylindrically shaped beaker is inserted to a particular depth.
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randomm13
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(Original post by Stonebridge)
The beaker is a cylinder, so use the formula for the volume of a cylinder. You have the radius of the end of the beaker and the 'length' in this case is the depth it is inserted under the water. This gives the volume of water displaced when the cylindrically shaped beaker is inserted to a particular depth.
but they haven't given the radius
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username3331778
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(Original post by randomm13)
but they haven't given the radius
It's r
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Stonebridge
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They have given it as 'r', and you have to show the formula, containing 'r', to be correct.
Agreed it isn't given numerically, but you are not being asked to find a numerical value here.
Question says 'could be calculated using'...
Hope this clarifies.

(Didn't see Meowstic's reply before I replied.)
Last edited by Stonebridge; 1 year ago
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randomm13
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(Original post by Meowstic)
It's r
I realized it a bit too late
smh
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randomm13
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(Original post by Stonebridge)
They have given it as 'r', and you have to show the formula, containing 'r', to be correct.
Agreed it isn't given numerically, but you are not being asked to find a numerical value here.
Question says 'could be calculated using'...
Hope this clarifies.

(Didn't see Meowstic's reply before I replied.)
oh God
I should pay attention to the question
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randomm13
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(Original post by Meowstic)
It's r
(Original post by Stonebridge)
They have given it as 'r', and you have to show the formula, containing 'r', to be correct.
Agreed it isn't given numerically, but you are not being asked to find a numerical value here.
Question says 'could be calculated using'...
Hope this clarifies.

(Didn't see Meowstic's reply before I replied.)
thank you very much
sending love to the both of u
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phobobs
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(Original post by randomm13)
but we don't know the volume of water
the volume of the water is the same as the volume of the submerged beaker- volume is just size, so the amount of space (volume)taken up by the beaker underwater is the same as the amount of space (volume) of water displaced. The beaker is a cylinder, and we know the depth, or height (d), and we know the radius (r) so you just need the equation for volume of a cylinder to work out that volume
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DreamWeaver2772
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(Original post by randomm13)
A student investigated the relationship between the mass m a boat can carry and the depth d
below the water surface of the lowest point of the boat.
He modelled the boat using a glass beaker.
He added 10-gram slotted masses and marked the position of the water surface on the
beaker, as shown
(I can't paste the pic page 4 on this pdf
https://doc-0k-1k-apps-viewer.google...c3cpgdfpjrttti )

The student assumed the beaker was a cylinder with radius r cm and the water had a
density of 1 g cm–3.
(a) Show that the upthrust U on the beaker could be calculated using the equation
U=( Pi * r^2 *g*d)/1000
where d is in cm and U is in N.

what am I supposed to do here??
Which is this question paper?
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DreamWeaver2772
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(Original post by randomm13)
oh God
I should pay attention to the question
can you send me the mark scheme please?
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crazy_person001
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i need the markscheme for this. does anyone have it? pls help me out
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user171
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can you pls provide the year of this question and mention from which board is it?
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user171
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(Original post by randomm13)
A student investigated the relationship between the mass m a boat can carry and the depth d
below the water surface of the lowest point of the boat.
He modelled the boat using a glass beaker.
He added 10-gram slotted masses and marked the position of the water surface on the
beaker, as shown
(I can't paste the pic page 4 on this pdf
https://doc-0k-1k-apps-viewer.google...c3cpgdfpjrttti )

The student assumed the beaker was a cylinder with radius r cm and the water had a
density of 1 g cm–3.
(a) Show that the upthrust U on the beaker could be calculated using the equation
U=( Pi * r^2 *g*d)/1000
where d is in cm and U is in N.

what am I supposed to do here??
can you pls provide the year and also mention from which board is it?
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