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GRADE 7 PRACTICE

Physics Problems: Buoyant force and floating, Grade 7

Pushing, navigation conditions, ships and aeronautics.

18 problems across 3 sub-topics
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Problem statements

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18 problems
Position in this set: 1 from 18

Problem #43

Buoyant force

What concept does the description correspond to: “The upward resultant of the pressure forces exerted by a liquid or gas on an immersed object.»?

Answer options

  1. \text{Buoyant force}
  2. \text{Archimedes' principle}
  3. \text{Measuring buoyant force}
  4. \text{Physical phenomenon}
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Given
\text{Description}
\text{The upward resultant of the pressure forces exerted by a liquid or gas on an immersed object.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    The bottom of an object is usually deeper and experiences higher pressure, producing a net upward force.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Buoyant force}

Answer\text{Concept} = \text{Buoyant force}

Position in this set: 2 from 18

Problem #44

Buoyant force

What concept does the description correspond to: “Buoyant force equals the weight of the liquid or gas occupying the volume of the immersed part of an object.»?

Answer options

  1. \text{Archimedes' principle}
  2. \text{Buoyant force}
  3. \text{Measuring buoyant force}
  4. \text{Physical phenomenon}
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Given
\text{Description}
\text{Buoyant force equals the weight of the liquid or gas occupying the volume of the immersed part of an object.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    The force depends on the medium's density, gravitational acceleration and displaced volume, but not on depth in a uniform medium.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Archimedes' principle}

Answer\text{Concept} = \text{Archimedes' principle}

Position in this set: 3 from 18

Problem #45

Buoyant force

The block is completely immersed in water and displaces 0.002 m³. Find the Archimedean force for a water density of 1000 kg/m³ and g = 9.8 m/s².

Answer options

  1. 19{,}6\,\text{Н}
  2. 0{,}0196\,\text{Н}
  3. 4{,}9\,\text{Н}
  4. 19600\,\text{Н}
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Given
\rho
1000\,\text{кг/м}^{3}
V
0{,}002\,\text{м}^{3}
g
9{,}8\,\text{м/с}^{2}
Find

F_A

  1. F_A=\rho gVF_A=1000\cdot9{,}8\cdot0{,}002\,\text{Н}F_A = 19{,}6\,\text{Н}

Answer19{,}6\,\text{Н}

Position in this set: 4 from 18

Problem #46

Floating objects, ships and balloons

What concept does the description correspond to: “A floating object is in equilibrium when buoyant force equals gravitational force in magnitude.»?

Answer options

  1. \text{Condition for floating equilibrium}
  2. \text{Sinking and rising}
  3. \text{Ships and balloon flight}
  4. \text{Physical phenomenon}
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Given
\text{Description}
\text{A floating object is in equilibrium when buoyant force equals gravitational force in magnitude.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    If an object's average density is lower than the liquid's density, it rises and floats partly immersed.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Condition for floating equilibrium}

Answer\text{Concept} = \text{Condition for floating equilibrium}

Position in this set: 5 from 18

Problem #47

Floating objects, ships and balloons

What concept does the description correspond to: “If only gravity and buoyancy act on an object released from rest, it starts sinking when gravity is greater and rising when buoyancy is greater.»?

Answer options

  1. \text{Sinking and rising}
  2. \text{Condition for floating equilibrium}
  3. \text{Ships and balloon flight}
  4. \text{Physical phenomenon}
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Given
\text{Description}
\text{If only gravity and buoyancy act on an object released from rest, it starts sinking when gravity is greater and rising when buoyancy is greater.}
Find

\text{name concepts}

  1. \text{Let's compare approval with definition}

    Comparing forces tells us how velocity changes. An object already moving can travel against the resultant force for a while. Adjusting ballast or envelope volume changes average density, controlling the buoyancy of craft and balloons.

  2. \text{Let's formulate conclusion}\text{Concept} = \text{Sinking and rising}

Answer\text{Concept} = \text{Sinking and rising}

Position in this set: 6 from 18

Problem #48

Floating bodies

The average density of a dry wooden block is 800 kg/m³, the density of water is 1000 kg/m³. What happens to the block after a quiet dive?

Answer options

  1. \text{Will pop up and there will be swim partially submerged}
  2. \text{will remain on any depth}
  3. \text{Will drown on day}
  4. \text{Will dissolve because of less density}
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Given
\rho_{\text{т}}
800\,\text{кг/м}^{3}
\rho_{\text{ж}}
1000\,\text{кг/м}^{3}
Find

\text{character movement}

  1. \rho_{\text{т}}<\rho_{\text{ж}}
  2. \text{При полном погружении }F_A>F_{\text{тяж}}\text{block pops up}
  3. F_A=F_{\text{тяж}}

    Equilibrium will be established upon partial immersion.

Answer\text{floats partially submerged}

Position in this set: 7 from 18

Problem #142

Buoyant force

The body has supplanted 0{,}002 m³ liquid density 1000 kg/m³. Find the Archimedes force at g = 10 N/kg.

Answer options

  1. 20\,\text{Н}
  2. 40\,\text{Н}
  3. 10\,\text{Н}
  4. 60\,\text{Н}
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Given
V
0{,}002\,\text{м}^{3}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

F_A

  1. F_A=\rho gVF_A=1000 \cdot 10 \cdot 0{,}002F_A=20\,\text{Н}

    We take the density of the liquid and the displaced volume.

Answer20\,\text{Н}

Position in this set: 8 from 18

Problem #143

Buoyant force

The body has supplanted 0{,}003 m³ liquid density 800 kg/m³. Find the Archimedes force at g = 10 N/kg.

Answer options

  1. 48\,\text{Н}
  2. 24\,\text{Н}
  3. 12\,\text{Н}
  4. 72\,\text{Н}
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Given
V
0{,}003\,\text{м}^{3}
r
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

F_A

  1. F_A=\rho gVF_A=800 \cdot 10 \cdot 0{,}003F_A=24\,\text{Н}

    We take the density of the liquid and the displaced volume.

Answer24\,\text{Н}

Position in this set: 9 from 18

Problem #144

Buoyant force

Dynamometer shows 30 H in the air and 20 H when the body is completely immersed in water. Density of water 1000 kg/m³, g = 10 N/kg. Find the volume of the body.

Answer options

  1. 0{,}002\,\text{м}^{3}
  2. 0{,}001\,\text{м}^{3}
  3. 0{,}0005\,\text{м}^{3}
  4. 0{,}003\,\text{м}^{3}
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Given
P_1
30\,\text{Н}
P_2
20\,\text{Н}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

V

  1. F_A=P_1-P_2F_A=30 - 20F_A=10\,\text{Н}

    The decrease in reading is equal to the buoyancy force.

  2. V=\frac{F_A}{\rho g}V=\frac{10}{(1000 \cdot 10)}V=0{,}001\,\text{м}^{3}

    The immersion is complete, so the displaced volume is equal to the volume of the body.

Answer0{,}001\,\text{м}^{3}

Position in this set: 10 from 18

Problem #145

Buoyant force

Dynamometer shows 50 H in the air and 30 H when the body is completely immersed in water. Density of water 1000 kg/m³, g = 10 N/kg. Find the volume of the body.

Answer options

  1. 0{,}004\,\text{м}^{3}
  2. 0{,}001\,\text{м}^{3}
  3. 0{,}002\,\text{м}^{3}
  4. 0{,}006\,\text{м}^{3}
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Given
P_1
50\,\text{Н}
P_2
30\,\text{Н}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

V

  1. F_A=P_1-P_2F_A=50 - 30F_A=20\,\text{Н}

    The decrease in reading is equal to the buoyancy force.

  2. V=\frac{F_A}{\rho g}V=\frac{20}{(1000 \cdot 10)}V=0{,}002\,\text{м}^{3}

    The immersion is complete, so the displaced volume is equal to the volume of the body.

Answer0{,}002\,\text{м}^{3}

Position in this set: 11 from 18

Problem #146

Buoyant force

Body mass 2 kg and volume 500 cm³ completely immersed in a liquid with a density 1000 kg/m³ and hangs on the dynamometer. Find his testimony; g = 10 N/kg.

Answer options

  1. 30\,\text{Н}
  2. 7{,}5\,\text{Н}
  3. 15\,\text{Н}
  4. 45\,\text{Н}
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Given
m
2\,\text{кг}
V
500\,\text{см}^{3}
r
1000\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

P

  1. v=\frac{V}{10^6}v=\frac{500}{1000000}v=0{,}0005\,\text{м}^{3}

    Convert cubic centimeters to cubic meters.

  2. F_A=\rho gvF_A=1000 \cdot 10 \cdot 0{,}0005F_A=5\,\text{Н}

    We find the buoyant force.

  3. P=mg-F_AP=2 \cdot 10 - 5P=15\,\text{Н}

    The dynamometer maintains the difference between gravity and the Archimedes force.

Answer15\,\text{Н}

Position in this set: 12 from 18

Problem #147

Buoyant force

Body mass 3 kg and volume 800 cm³ completely immersed in a liquid with a density 800 kg/m³ and hangs on the dynamometer. Find his testimony; g = 10 N/kg.

Answer options

  1. 47{,}2\,\text{Н}
  2. 11{,}8\,\text{Н}
  3. 70{,}8\,\text{Н}
  4. 23{,}6\,\text{Н}
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Given
m
3\,\text{кг}
V
800\,\text{см}^{3}
r
800\,\text{кг/м}^{3}
g
10\,\text{Н/кг}
Find

P

  1. v=\frac{V}{10^6}v=\frac{800}{1000000}v=0{,}0008\,\text{м}^{3}

    Convert cubic centimeters to cubic meters.

  2. F_A=\rho gvF_A=800 \cdot 10 \cdot 0{,}0008F_A=6{,}4\,\text{Н}

    We find the buoyant force.

  3. P=mg-F_AP=3 \cdot 10 - 6{,}4P=23{,}6\,\text{Н}

    The dynamometer maintains the difference between gravity and the Archimedes force.

Answer23{,}6\,\text{Н}

Position in this set: 13 from 18

Problem #148

Floating objects, ships and balloons

Body mass 2 kg floats B water density 1000 kg/m³. Find volume submerged parts.

Answer options

  1. 0{,}004\,\text{м}^{3}
  2. 0{,}002\,\text{м}^{3}
  3. 0{,}001\,\text{м}^{3}
  4. 0{,}006\,\text{м}^{3}
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Given
m
2\,\text{кг}
r
1000\,\text{кг/м}^{3}
Find

V

  1. V=\frac{m}{\rho}V=\frac{2}{1000}V=0{,}002\,\text{м}^{3}

    When swimming, the mass of displaced water is equal to the mass of the body.

Answer0{,}002\,\text{м}^{3}

Position in this set: 14 from 18

Problem #149

Floating objects, ships and balloons

Body mass 5 kg floats B water density 1000 kg/m³. Find volume submerged parts.

Answer options

  1. 0{,}01\,\text{м}^{3}
  2. 0{,}0025\,\text{м}^{3}
  3. 0{,}005\,\text{м}^{3}
  4. 0{,}015\,\text{м}^{3}
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Given
m
5\,\text{кг}
r
1000\,\text{кг/м}^{3}
Find

V

  1. V=\frac{m}{\rho}V=\frac{5}{1000}V=0{,}005\,\text{м}^{3}

    When swimming, the mass of displaced water is equal to the mass of the body.

Answer0{,}005\,\text{м}^{3}

Position in this set: 15 from 18

Problem #150

Floating objects, ships and balloons

Density homogeneous bar 600 kg/m³, Liquid density 1000 kg/m³. How much percent volume floating bar loaded?

Answer options

  1. 120\,\text{\%}
  2. 30\,\text{\%}
  3. 60\,\text{\%}
  4. 180\,\text{\%}
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Given
r_1
600\,\text{кг/м}^{3}
r_2
1000\,\text{кг/м}^{3}
Find

p

  1. f=\frac{\rho_1}{\rho_2}f=\frac{600}{1000}f=0{,}6\,\text{доля}

    From equilibrium follows the ratio of the immersed volume to the total volume.

  2. p=100fp=0{,}6 \cdot 100p=60\,\text{\%}

    We express the share as a percentage.

Answer60\,\text{\%}

Position in this set: 16 from 18

Problem #151

Floating objects, ships and balloons

Density homogeneous bar 720 kg/m³, Liquid density 1200 kg/m³. How much percent volume floating bar loaded?

Answer options

  1. 120\,\text{\%}
  2. 30\,\text{\%}
  3. 180\,\text{\%}
  4. 60\,\text{\%}
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Given
r_1
720\,\text{кг/м}^{3}
r_2
1200\,\text{кг/м}^{3}
Find

p

  1. f=\frac{\rho_1}{\rho_2}f=\frac{720}{1200}f=0{,}6\,\text{доля}

    From equilibrium follows the ratio of the immersed volume to the total volume.

  2. p=100fp=0{,}6 \cdot 100p=60\,\text{\%}

    We express the share as a percentage.

Answer60\,\text{\%}

Position in this set: 17 from 18

Problem #152

Floating objects, ships and balloons

Raft volume 0{,}5 m³ done from material density 600 kg/m³ and floats B water density 1000 kg/m³. Which maximum mass cargo you can add up to full dives raft? volume cargo neglect.

Answer options

  1. 400\,\text{кг}
  2. 100\,\text{кг}
  3. 600\,\text{кг}
  4. 200\,\text{кг}
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Given
V
0{,}5\,\text{м}^{3}
r_1
600\,\text{кг/м}^{3}
r_2
1000\,\text{кг/м}^{3}
Find

R

  1. M=\rho_2 VM=1000 \cdot 0{,}5M=500\,\text{кг}

    At full immersion, this is the maximum supported mass.

  2. m=\rho_1 Vm=600 \cdot 0{,}5m=300\,\text{кг}

    Part of the carrying capacity is occupied by the raft itself.

  3. R=M-mR=500 - 300R=200\,\text{кг}

    The mass difference remains on the load.

Answer200\,\text{кг}

Position in this set: 18 from 18

Problem #153

Floating objects, ships and balloons

Raft volume 0{,}8 m³ done from material density 500 kg/m³ and floats B water density 1000 kg/m³. Which maximum mass cargo you can add up to full dives raft? volume cargo neglect.

Answer options

  1. 400\,\text{кг}
  2. 800\,\text{кг}
  3. 200\,\text{кг}
  4. 1200\,\text{кг}
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Given
V
0{,}8\,\text{м}^{3}
r_1
500\,\text{кг/м}^{3}
r_2
1000\,\text{кг/м}^{3}
Find

R

  1. M=\rho_2 VM=1000 \cdot 0{,}8M=800\,\text{кг}

    At full immersion, this is the maximum supported mass.

  2. m=\rho_1 Vm=500 \cdot 0{,}8m=400\,\text{кг}

    Part of the carrying capacity is occupied by the raft itself.

  3. R=M-mR=800 - 400R=400\,\text{кг}

    The mass difference remains on the load.

Answer400\,\text{кг}

The theory behind these problems

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Buoyant forceOrigin of buoyant force and its measurement.Floating objects, ships and balloonsSinking, rising, equilibrium and average density.

Formulas by topic

Look up symbols and units of measurement in the reference.

Densityρ · кг/м³ForceF · Н