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Using Archimedes' Principle to find the Buoyant Force on a Partially Submerged Object

  • 1.

    A 2.50 m{eq}^3 {/eq} cylinder floats with 80.5% of its volume submerged in water. Determine the buoyant force on the cylinder. Given the density of water is 1000 kg /m{eq}^3 {/eq}. Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}2.23\times 10^4 {/eq} N

    • {eq}1.97\times 10^4 {/eq} N

    • {eq}3.27\times 10^4 {/eq} N

    • {eq}1.07\times 10^4 {/eq} N

  • 2.

    Find the buoyant force exerted on a 1.08 m{eq}^3 {/eq} hollow cube that has 68.5% of its volume submerged in kerosene. Given the density of kerosene is 820.1 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}3.22\times 10^3 {/eq} N

    • {eq}5.95\times 10^3 {/eq} N

    • {eq}7.20\times 10^3 {/eq} N

    • {eq}6.32\times 10^3 {/eq} N

  • 3.

    0.760 m{eq}^3 {/eq} wedge has 50.0% of its volume immersed in seawater. What is the buoyant force exerted on the wedge if the density of seawater is 1060 kg/m{eq}^3 {/eq}?

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}3.95\times 10^3 {/eq} N

    • {eq}1.99\times 10^3 {/eq} N

    • {eq}9.98\times 10^2 {/eq} N

    • {eq}2.76\times 10^3 {/eq} N

  • 4.

    A swimmer has a volume of 0.0620 m{eq}^3 {/eq} and he has 87.3% of his volume under the surface of chlorinated water that has a density of 996.5 kg/m{eq}^3 {/eq}. Compute the buoyant force exerted on the swimmer.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}6.77\times 10^2 {/eq} N

    • {eq}5.29\times 10^2 {/eq} N

    • {eq}6.27\times 10^2 {/eq} N

    • {eq}5.97\times 10^2 {/eq} N

  • 5.

    A 1.46 m{eq}^3 {/eq} rectangular block floats with 75.0% of its volume submerged in saltwater. Calculate the buoyant force on the block. Given the density of salt water is 1040 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}1.83\times 10^4 {/eq} N

    • {eq}1.12\times 10^4 {/eq} N

    • {eq}1.02\times 10^4 {/eq} N

    • {eq}1.65\times 10^4 {/eq} N

  • 6.

    Calculate the buoyant force exerted on a 0.1205 m{eq}^3 {/eq} small electric car that has 65.0% of its volume submerged in glycerine. Given the density of glycerine is 1259 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}9.75\times 10^2 {/eq} N

    • {eq}9.67\times 10^2 {/eq} N

    • {eq}9.02\times 10^2 {/eq} N

    • {eq}9.27\times 10^2 {/eq} N

  • 7.

    0.0350 m{eq}^3 {/eq} crate has 82.5% of its volume immersed in petrol. What is the buoyant force exerted on the crate if the density of petrol is 737 kg/m{eq}^3 {/eq}?

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}2.09\times 10^2 {/eq} N

    • {eq}2.72\times 10^2 {/eq} N

    • {eq}9.26\times 10^2 {/eq} N

    • {eq}1.87\times 10^2 {/eq} N

  • 8.

    What is the buoyant force exerted on a 0.00150 m{eq}^3 {/eq} doll that has 90.0% of its volume submerged in coconut oil? Given the density of coconut oil is 930 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}1.67\times 10^1 {/eq} N

    • {eq}1.23\times 10^1 {/eq} N

    • {eq}1.01\times 10^1 {/eq} N

    • {eq}1.80\times 10^1 {/eq} N

  • 9.

    79.5% of a 0.00250 m{eq}^3 {/eq} wedge is dipped in ethyl alcohol of 785.1 kg/m{eq}^3 {/eq}. What will be the buoyant force on the wedge?

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}1.86\times 10^1 {/eq} N

    • {eq}1.53\times 10^1 {/eq} N

    • {eq}1.17\times 10^1 {/eq} N

    • {eq}1.34\times 10^1 {/eq} N

  • 10.

    A 0.125 m{eq}^3 {/eq} steel block floats with 55.5% of its volume immersed in mercury. Determine the buoyant force on the block. Given the density of mercury is 13590 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}9.25\times 10^3 {/eq} N

    • {eq}9.02\times 10^3 {/eq} N

    • {eq}8.82\times 10^3 {/eq} N

    • {eq}9.42\times 10^3 {/eq} N

  • 11.

    A closed bottle has a volume of 0.00100 m{eq}^3 {/eq} and has 59.9% of its volume under the surface of oil of turpentine that has a density of 870 kg/m{eq}^3 {/eq}. Find the buoyant force exerted on the bottle.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}5.71 {/eq} N

    • {eq}6.77 {/eq} N

    • {eq}5.11 {/eq} N

    • {eq}6.21 {/eq} N

  • 12.

    Determine the buoyant force exerted on a 0.0900 m{eq}^3 {/eq} cube that has 45.0% of its volume submerged in seawater. Given the density of seawater is 1026 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}4.08\times 10^2 {/eq} N

    • {eq}4.65\times 10^2 {/eq} N

    • {eq}4.43\times 10^2 {/eq} N

    • {eq}4.23\times 10^2 {/eq} N

  • 13.

    0.00590 m{eq}^3 {/eq} bucket has 70.0% of its volume immersed in a glucose solution. What is the buoyant force exerted on the bucket if the density of the glucose solution is 1350 kg/m{eq}^3 {/eq}?

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}5.01\times 10^1 {/eq} N

    • {eq}4.82\times 10^1 {/eq} N

    • {eq}5.47\times 10^1 {/eq} N

    • {eq}5.24\times 10^1 {/eq} N

  • 14.

    What is the buoyant force exerted on a 0.00120 m{eq}^3 {/eq} milk can that has 65.5% of its volume immersed in milk? Given the density of milk is 1020 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}8.32 {/eq} N

    • {eq}7.10 {/eq} N

    • {eq}7.86 {/eq} N

    • {eq}7.32 {/eq} N

  • 15.

    78.0% of a 0.00650 m{eq}^3 {/eq} rod is dipped in beer that has a density of 1010 kg/m{eq}^3 {/eq}. Find the buoyant force on the rod.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}5.47\times 10^1 {/eq} N

    • {eq}5.23\times 10^1 {/eq} N

    • {eq}5.76\times 10^1 {/eq} N

    • {eq}5.02\times 10^1 {/eq} N

  • 16.

    A 0.00980 m{eq}^3 {/eq} crate floats with 79.0% of its volume immersed in methyl alcohol. Calculate the buoyant force on the crate. Given the density of methyl alcohol is 786.5 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}5.24\times 10^1 {/eq} N

    • {eq}6.20\times 10^1 {/eq} N

    • {eq}5.97\times 10^1 {/eq} N

    • {eq}5.45\times 10^1 {/eq} N

  • 17.

    Compute the buoyant force exerted on a 0.00405 m{eq}^3 {/eq} cube that has 68.0% of its volume immersed in mercury. Given the density of mercury is 13590 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}3.67\times 10^2 {/eq} N

    • {eq}3.04\times 10^2 {/eq} N

    • {eq}3.98\times 10^1 {/eq} N

    • {eq}3.87\times 10^1 {/eq} N

  • 18.

    A wedge has a volume of 0.00120 m{eq}^3 {/eq} and he has 35.0% of his volume under the surface of coconut oil that has a density of 930 kg/m{eq}^3 {/eq}. What will be the buoyant force exerted on the wedge?

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}3.56 {/eq} N

    • {eq}3.18 {/eq} N

    • {eq}3.83 {/eq} N

    • {eq}3.23 {/eq} N

  • 19.

    38.0% of a 0.00250 m{eq}^3 {/eq} cylinder is dipped in kerosene that has a density of 820.1 kg/m{eq}^3 {/eq}. Determine the buoyant force on the cylinder.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}7.02 {/eq} N

    • {eq}7.64 {/eq} N

    • {eq}7.98 {/eq} N

    • {eq}7.32 {/eq} N

  • 20.

    A boy has a volume of 0.0525 m{eq}^3 {/eq} and he has 89.3% of his volume under the surface of water that has a density of 1000 kg/m{eq}^3 {/eq}. Calculate the buoyant force exerted on the boy.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}4.30\times 10^2 {/eq} N

    • {eq}4.60\times 10^2 {/eq} N

    • {eq}4.05\times 10^2 {/eq} N

    • {eq}4.82\times 10^2 {/eq} N

  • 21.

    0.00360 m{eq}^3 {/eq} glass rod has 30.0% of its volume immersed in methyl alcohol. Find the buoyant force exerted on the rod if the density of methyl alcohol is 786.5 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}8.45 {/eq} N

    • {eq}8.54 {/eq} N

    • {eq}8.02 {/eq} N

    • {eq}8.33 {/eq} N

  • 22.

    What is the buoyant force exerted on a 0.00115 m{eq}^3 {/eq} cylindrical object that has 75.0% of its volume immersed in olive oil? Given the density of olive oil is 911 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}8.33 {/eq} N

    • {eq}7.71 {/eq} N

    • {eq}6.76 {/eq} N

    • {eq}9.12 {/eq} N

  • 23.

    A log has a volume of 0.0895 m{eq}^3 {/eq} and it has 67.8% of its volume under the surface of water that has a density of 992 kg/m{eq}^3 {/eq}. Compute the buoyant force exerted on the log.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}5.34\times 10^2 {/eq} N

    • {eq}5.45\times 10^2 {/eq} N

    • {eq}5.63\times 10^2 {/eq} N

    • {eq}5.91\times 10^2 {/eq} N

  • 24.

    85.0% of a 0.00670 m{eq}^3 {/eq} cylindrical object is dipped in petrol that has a density of 737 kg/m{eq}^3 {/eq}. Determine the buoyant force on the object.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}4.12\times 10^1 {/eq} N

    • {eq}4.87\times 10^1 {/eq} N

    • {eq}4.05\times 10^1 {/eq} N

    • {eq}4.32\times 10^1 {/eq} N

  • 25.

    Compute the buoyant force exerted on a 0.00500 m{eq}^3 {/eq} conical body that has 33.3% of its volume immersed in coconut oil. Given the density of coconut oil is 930 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}1.52\times 10^1 {/eq} N

    • {eq}1.52\times 10^1 {/eq} N

    • {eq}1.77\times 10^1 {/eq} N

    • {eq}1.08\times 10^1 {/eq} N

  • 26.

    A 0.00540 m{eq}^3 {/eq} brass cylinder with 20.5% of its volume immersed in oil of turpentine. What will be the buoyant force on the cylinder? Given the density of oil of turpentine is 870 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}9.45 {/eq} N

    • {eq}9.14 {/eq} N

    • {eq}9.28 {/eq} N

    • {eq}9.36 {/eq} N

  • 27.

    A globe has a volume of 0.1200 m{eq}^3 {/eq} and it has 40.0% of its volume under the surface of water that has a density of 1000 kg/m{eq}^3 {/eq}. Find the buoyant force exerted on the globe.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}4.21\times 10^2 {/eq} N

    • {eq}4.71\times 10^2 {/eq} N

    • {eq}5.10\times 10^2 {/eq} N

    • {eq}4.54\times 10^2 {/eq} N

  • 28.

    What is the buoyant force exerted on a 0.0850 m{eq}^3 {/eq} sphere that has 65.8% of its volume immersed in methyl alcohol? Given the density of methyl alcohol is 785.1 kg/m{eq}^3 {/eq}.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}4.23\times 10^2 {/eq} N

    • {eq}4.31\times 10^2 {/eq} N

    • {eq}4.43\times 10^2 {/eq} N

    • {eq}4.54\times 10^2 {/eq} N

  • 29.

    20.5% of a 0.0620 m{eq}^3 {/eq} gate is dipped in petrol that has a density of 737 kg/m{eq}^3 {/eq}. Determine the buoyant force on the gate.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}9.43\times 10^1 {/eq} N

    • {eq}9.32\times 10^1 {/eq} N

    • {eq}9.19\times 10^1 {/eq} N

    • {eq}9.56\times 10^1 {/eq} N

  • 30.

    An object has a volume of 0.0298 m{eq}^3 {/eq} and 45.0% of its mass has been submerged in a liquid of density 890 kg/m{eq}^3 {/eq}. Determine the buoyant force that the liquid exerts on the object.

    Take g = 9.81 m/s{eq}^2 {/eq}

    Answers:

    • {eq}1.85\times 10^2 {/eq} N

    • {eq}1.02\times 10^2 {/eq} N

    • {eq}1.72\times 10^2 {/eq} N

    • {eq}1.17\times 10^2 {/eq} N

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