KCL Section 1: Upthrust (Materials)

Question 1

Water density is 1000 kgm^-3

1m^3 block

Force of water

Answer 1

1000 * 1 * 9.81 = 9810N

Question 2

Water density is 1000 kgm^-3

2m^3 block

Force of water at 1m down

Answer 2

1000 * 2 * 9.81 = 19620N

Question 3

What is upthrust?

Answer 3

the upward force that a liquid or gas exerts on a body floating in it.

Question 4

What is Archimedes principle?

Answer 4

Upthrust is equal to the weight of the displacement.

Question 5

A stone of mass 125g is attached to a spring balance and lowered into a bowl of water until it is completely immersed. The reading on the balance is seen to be 1.00N

A)What is the upthrust acting on the stone?
B)What is the volume of water displaced?
C)What is the density of the stone?

Answer 5

A) 0.23N
B) 2.5 x 10^-5
C) 5000kgm^-3

Question 6

A long cylindrical tube is weighted at the bottom so that it floats upright in water at 20 degrees celsius. Describe and explain what differences will be observed if the tube is then floated in

A) ethanol at 4 degrees celsius
B) water at 4 degrees celsius

Answer 6

The density of ethanol is less than water so the tube will float higher in the water.

Question 7

Calculate the upthrust acting on a block underwater with dimensions 15.0 cm x 4.50 cm x 6.00 cm

Answer 7

3.97 N

Question 8

Calculate the upthrust acting on a block underwater with dimensions 12.0 cm x 2.80 cm x 4.75 cm

Answer 8

1.57 x 10^-3 N

Question 9

Calculate the upthrust acting on a block underwater with dimensions 9.0 mm x 8.2 mm x 1.4 mm

Answer 9

0.00101 N

Question 10

Calculate the upthrust acting on a block underwater with dimensions 4.3 mm x 4.4 mm x 3.7 mm

Answer 10

6.9 x 10-4 N

Question 11

Calculate the upthrust acting on a ball bearing underwater with a radius of 5.06 x 10-3 m

Answer 11

5.32 x 10-3 N

Question 12

Calculate the upthrust acting on a ball bearing underwater with a radius of 2.9 x 10-2 m

Answer 12

1.0 N

Question 13

Calculate the upthrust acting on a ball bearing underwater with a radius of 6.5 mm

Answer 13

0.011 N

Question 14

Calculate the upthrust acting on a ball bearing underwater with a diameter of 9.75 x 10-3 m

Answer 14

0.0381 N

Question 15

Explain why upthrust calculations do not require the density of the object.

Answer 15

Density of the fluid is needed

Question 16

A raft is made of solid pine wood with a mass of 9600 kg. What depth of the sides will be underwater if it is floating as shown?
0.30m of the sides are above water.
Length = 4 width = 4

Answer 16

It is floating so we know weight = upthrust

W = 9600 x 9.81 = 94176
u = 94176

u = ρVg
u = 1000 x (length x width x h) x 9.81
94176 = 1000 x (4^2 x h x 9.81
94.176 / (16 x 9.81) = h
h = 0.6m

Question 17

Calculate the density of the hot air in a balloon floating at a fixed height close to the ground. The density of the cold air is 1.4kgm^3. The total mass of the balloon’s fabric, gondola, fuel, burners and occupants etc is 700kg. It’s volume is 2500m^3

Answer 17

1.1kgm^-3

Question 18

A giant garbage barge (garbarge) on New York’s Hudson river is 60m long and 10m wide. What depth of the hull will be underwater if it and it’s cargo have a combined mass of 1500 tonnes? density of water is 1000kgm^-3

Answer 18

The garbarge’s hull will be 2.5 underwater.

Question 19

Calculate the upthrust acting on an aluminium block of dimensions 10 cm x 3.0 cm x 3.0 cm, assuming it is fully submerged in water

Answer 19

0.883 N

Question 20

Calculate the upthrust acting on a wooden block of dimensions 10 cm x 3.0 cm x 3.0 cm, assuming it is fully submerged in water

Answer 20

0.883 N

Question 21

Explain, using a calculation, why the aluminium sinks but the wood floats

Answer 21

Aluminium has a density of 2700 kgm^-3 while wood has a density of 740 kgm^-3 also water has a density of 1000 kgm^-3. Water’s density minus wood’s > 0 so it will float. Whereas water’s density minus aluminium’s is <0 and so will not float.