Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 9, Problem 28P

(a)

To determine

Whether 1.0kg of lead or 1.0kg of aluminum has larger buoyant force acting on it when immersed in water.

(a)

Expert Solution
Check Mark

Answer to Problem 28P

Aluminum has larger buoyant force when it is immersed in water, since for the same mass aluminum is less dense and has larger volume than lead.

Explanation of Solution

Buoyant force is the force acting on object that is partially or completely immersed in water. Buoyant force is equal to weight of the water displaced by the object. Water displaced by the object depends on the volume of the object. Therefore, buoyant force is large for an object having larger volume than small volume.

Conclusion:

Lead is denser than aluminum. Therefore, for same mass lead has small volume than aluminum. Aluminum displaces more water than lead. Therefore, buoyant force will be larger for aluminum than lead.

Therefore, Aluminum has larger buoyant force when it is immersed in water, since for the same mass aluminum is less dense and has larger volume than lead.

(b)

To determine

Whether 1.0kg of steel that is sinking to the bottom of the lake or 1.0kg of wood with a density of 500kg/m3 that is floating on the lake has greater buoyant force acting on it.

(b)

Expert Solution
Check Mark

Answer to Problem 28P

Steel is denser than wood. Since their masses are same volume is larger for wood than steel. Since floating wood displaces more water than sinking steel. Buoyant force is larger force wood that is floating than steel that is sinking.

Explanation of Solution

Buoyant force is the force acting on object that is partially or completely immersed in water. Buoyant force is equal to weight of the water displaced by the object. Water displaced by the object depends on the volume of the object. Therefore, buoyant force is large for an object having larger volume than small volume.

Conclusion:

Steel is denser than wood. Since both have same mass, volume of wood is larger compared to steel. Even though the wood is floating, it displaces more water than does steel. Buoyant force is equal to weight of the water displaced. Therefore, wood has larger buoyant force than steel, since water displaced by wood that is floating is larger compared to steel that is sinking.

Therefore, steel is denser than wood. Since their masses are same volume is larger for wood than steel. Since floating wood displaces more water than sinking steel. Buoyant force is larger force wood that is floating than steel that is sinking.

(c)

To determine

Find quantitative answers for part (a) and part (b).

(c)

Expert Solution
Check Mark

Explanation of Solution

Buoyant force is equal to weight of the water displaced by object.

Write the expression for buoyant force.

Fb=ρwgVPb

Here, Fb is the buoyant force, ρw is the density of water, g is the acceleration due to gravity and Vpb is the volume of lead.

Substitute mPbρPb for VPb in above equation to get Fb.

Fb, Pb=ρwg(mPbρPb) (I)

Here, Fb, Pb is the buoyant force acting on lead ,mPb is the mass of lead and ρPb is the density of lead.

Similarly, write the expression for buoyant force acting on Aluminum.

Fb, Al=ρwgmAlρAl (II)

Here, Fb, Al is the buoyant force acting on Aluminum,ρw is the density of water, g is the acceleration due to gravity,mAl is the mass of Aluminum and ρAl is the density of Aluminum.

Similarly, write the expression for buoyant force acting on steel.

Fb, steel=ρwgmsteelρsteel (III)

Here, Fb, steel is the buoyant force acting on steel,ρw is the density of water, g is the acceleration due to gravity,msteel is the mass of steel and ρsteel is the density of steel.

Since wood is floating, its buoyant force is equal to its weight.

Calculate weight of wood.

Fb,wood=mwoodg (IV)

Here, Fb,wood is the buoyant force of wood and mwood is the mass of wood.

Conclusion:

Substitute 1.00×103kg/m3 for ρw, 9.80m/s2 for g, 1.0kg for mPb and 11300kg/m3 for ρPb in equation (I) to get buoyant force acting on lead.

Fb,Pb=(1.00×103kg/m3)(9.80m/s2)(1.0kg11300kg/m3)=0.87N

Substitute 1.00×103kg/m3 for ρw, 9.80m/s2 for g, 1.0kg for mAl and 2702kg/m3 for ρAl in equation (II) to get buoyant force acting on Aluminum.

Fb,Al=(1.00×103kg/m3)(9.80m/s2)(1.0kg2702kg/m3)=3.6N

Substitute 1.00×103kg/m3 for ρw, 9.80m/s2 for g, 1.0kg for msteel and 7860kg/m3 for ρAl in equation (III) to get buoyant force acting on Aluminum.

Fb,steel=(1.00×103kg/m3)(9.80m/s2)(1.0kg7860kg/m3)=1.2N

Substitute 1.0kg for mwood and 9.80m/s2 for g in equation (IV) to get Fb,steel.

Fb,wood=(1.0kg)(9.80m/s2)=9.8N

From above equations, Fwood>FAl>FSteel>FPb.

Therefore, buoyant force is larger force wood that is floating than steel that is sinking and Aluminum has larger buoyant force than lead.

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