past paper unit 3 forces

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.googleusercontent.com/viewer/secure/pdf/s5sju9sl6j2f82kd3iecj6u6ks8tib50/pgb8b6al88nt474l28pdtu427dng1eon/1585680825000/drive/15177618705625733428/ACFrOgA-_3-4BpBmWMN8ImogDVMOwMFWik4NjFCN3toHPj4yzkqfKdcyZAX0EfKoWwB1cQWaL9LpgVuEN_u3XOGGhscVDcx1c4s3u1tcqiNDV0_L7SMTz0PxmiGBwDIpmkOns2Q_Ijm-1B95Hl-c?print=true&nonce=o3og4pa7fsvp4&user=15177618705625733428&hash=dekmaoiv36to8m6pejc3cpgdfpjrttti )

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??

Reply 1

Stonebridge

13

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.

Reply 2

phobobs

3

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

Reply 3

randomm13

OP

9

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

Reply 4

randomm13

OP

9

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

Reply 5

randomm13

OP

9

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

Reply 6

randomm13

OP

9

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?

Reply 7

Stonebridge

13

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.

Reply 8

randomm13

OP

9

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

Reply 9

username3331778

16

Original post by randomm13

but they haven't given the radius

It's r

Reply 10

Stonebridge

13

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. :smile:

(Didn't see Meowstic's reply before I replied.)

(edited 4 years ago)

Reply 11

randomm13

OP

9

Original post by Meowstic

It's r

I realized it a bit too late
smh

Reply 12

randomm13

OP

9

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. :smile:

(Didn't see Meowstic's reply before I replied.)

oh God
I should pay attention to the question

Reply 13

randomm13

OP

9

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. :smile:

(Didn't see Meowstic's reply before I replied.)

thank you very much
sending love to the both of u

Reply 14

phobobs

3

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