Question 1

When a container of water is placed on a laboratory scale,the scale reads 120 g.Now a 20-g piece of copper (of density 8.9 g/cm³)is suspended from a thread and lowered into the water,not touching the bottom of the container.What will the scale now read? The density of water is 1.0 g/cm³.

Accepted Answer

When the copper piece is submerged in water, it displaces a volume of water equal to its own weight divided by the density of water. Since the copper does not touch the bottom, the apparent weight increase on the scale is due to the water displaced by the copper. The weight of the displaced water is equal to the weight of the copper (20 g), so the scale now reads 120 g + 20 g = 140 g. However, the question seems to have a discrepancy in the provided choices, as the explanation points towards an answer not listed (140 g). Given the choices, the closest correct interpretation based on the principle of buoyancy and the provided options would be to consider the scale reading as 140 g, but since this option is not available, and considering the possible misunderstanding in the explanation, the correct choice based on the displacement principle and the options given should be reconsidered.

Question 2

A 4.7-kg solid sphere,made of metal whose density is 4,000 kg/ m³. hangs by a light cord.When the sphere is immersed in water,what is the tension in the cord? The density of water is 1000 kg/m³.

Accepted Answer

The tension in the cord is reduced by the buoyant force acting on the sphere when it is immersed in water. The buoyant force equals the weight of the water displaced by the sphere. First, find the volume of the sphere using its mass (m = 4.7 kg) and the density of the metal ($\rho_{metal} = 4000 \, \text{kg/m}^3$):$$V = \frac{m}{\rho_{metal}} = \frac{4.7}{4000} \, \text{m}^3.$$Then, calculate the weight of the water displaced, which has the same volume, using the density of water ($\rho_{water} = 1000 \, \text{kg/m}^3$) and gravity (g = 9.8 m/s$^2$):$$F_{buoyant} = \rho_{water} \cdot V \cdot g = 1000 \cdot \frac{4.7}{4000} \cdot 9.8 \, \text{N}.$$Finally, subtract the buoyant force from the original weight of the sphere to find the tension in the cord:$$T = mg - F_{buoyant} = 4.7 \cdot 9.8 - 1000 \cdot \frac{4.7}{4000} \cdot 9.8 = 46.06 \, \text{N} - 11.555 \, \text{N} = 34.505 \, \text{N}.$$Rounded to the nearest whole number, the tension is approximately 35 N.

Question 3

A solid object floats in water with three-fourths of its volume beneath the surface.What is the object's density? The density of water is 1000 kg/m³.

Accepted Answer

The object's density is equal to the fraction of its volume that is submerged multiplied by the fluid's density. Since three-fourths of its volume is submerged in water, its density is 0.75 * 1000 kg/m^3 = 750 kg/m^3.

Question 4

A hot air balloon along with its cargo has a mass of 4.0 × 10⁵ kg,and it holds 7.0 × 10⁵ m³ of hot air.It is floating at a constant height in air with a density of 1.29 kg/m³.What is the density of the hot air in the balloon?

Accepted Answer

The hot air balloon floats at a constant height, which means the buoyant force is equal to the weight of the balloon and its cargo (m*g). 
Buoyant force = (density of air)*(volume of displaced air)*g 
Let the density of hot air inside the balloon be rho. 
Buoyant force = (density of air)*(volume of displaced air)*g = (m+rho*V)*g 
Solving for rho gives 
rho = (density of air)*(volume of displaced air - (m/g)) 
rho = (1.29 kg/m^3)*(7.0*10^13 m^3 - 4.0*10^15 kg/9.8 m/s^2) 
rho = 0.72 kg/m^3 
Therefore, the density of the hot air in the balloon is 0.72 kg/m^3. 
The correct answer is (B).

Question 5

A barge is 10 m wide and 60 m long and has vertical sides.The bottom of the boat is 1.2 m below the water surface.What is the weight of the barge and its cargo,if it is floating in fresh water of density 1000 kg/m³?

Accepted Answer

The answer of A barge is 10 m wide and...

Question 6

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m³ while suspended from a harness.Her apparent weight is now 21.2 N.What is her density?

Accepted Answer

The answer of A person who weighs 550 N empties...

Question 7

An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m³.What is the density of the object?

Accepted Answer

The buoyant force on the object when it is immersed in water is given by:

Fb = rhoVg

where rho is the density of water, V is the volume of the object submerged in water, and g is the acceleration due to gravity.

We can find the volume of the object submerged in water by using the fact that the weight of the object reduced by the weight of the water displaced by the object gives the buoyant force:

6.86 N = 7.84 N - rhoVg

Solving for V, we get:

V = (7.84 N - 6.86 N)/(1000 kg/m^3 x 9.81 m/s^2) = 0.0100 m^3

The weight of the object is given by:

W = rho_objectVg

so we can solve for rho_object:

rho_object = W/(Vg) = 7.84 N/(0.0100 m^3 x 9.81 m/s^2) = 8000 kg/m^3

Therefore, the density of the object is 8000 kg/m^3, which corresponds to choice C.

Question 8

A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m³.What is its mass?

Accepted Answer

The buoyant force on the rod is equal to the weight of the water displaced by the rod. The volume of the water displaced is equal to the volume of the rod, which is:$$V = \pi r^2 h = \pi (1.0 	ext{ cm})^2 (12 	ext{ cm}) = 37.7 	ext{ cm}^3$$The mass of the water displaced is:$$m = ho V = (1000 	ext{ kg/m}^3)(37.7 	imes 10^{-6} 	ext{ m}^3) = 0.0377 	ext{ kg} = 37.7 	ext{ g}$$Therefore, the mass of the rod is 37.7 g.

Question 9

A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm.When the block is placed in water,it floats horizontally,with its bottom face 1.65 cm below the surface.What is the density of the wood? The density of water is 1.00 g/cm³.

Accepted Answer

The buoyant force on the wooden block is equal to the weight of water displaced by the block. 
Volume of water displaced = (10.0 cm x 4.00 cm x 1.65 cm) = 66.0 cm^3 
Weight of water displaced = (66.0 cm^3) x (1.00 g/cm^3) x (9.81 m/s^2) = 647.5 g 
Buoyant force = weight of water displaced = 647.5 g 
The weight of the wooden block is calculated by finding the product of its volume and density: 
Weight of wooden block = (10.0 cm x 4.00 cm x 2.00 cm) x (density of wood) x (9.81 m/s^2) = 392.4 x (density of wood) g 
The block is in equilibrium, hence, the buoyant force must balance the weight of the block: 
Buoyant force = weight of block 
647.5 g = 392.4 x (density of wood) g 
Density of wood = 647.5 g / 392.4 cm^3 = 1.65 g/cm^3

Therefore, the answer is (A) 0.825 g/cm^3.

Question 10

A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m³?

Accepted Answer

The mass that can be loaded onto the box before it sinks is equal to the volume of the box multiplied by the density of water, since the box will displace a volume of water equal to its own volume when it is fully submerged. The volume of the box is 5.0 m * 1.0 m * 0.50 m = 2.5 m³. Therefore, the mass is 2.5 m³ * 1000 kg/m³ = 2500 kg, or 2.5 × 10^3 kg.

Question 11

A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m³.How much deeper into the water does the barge sink when 3.0 × 10⁵ kg of coal are loaded on the barge?

Accepted Answer

The barge will sink until the weight of the water displaced by the barge and the coal equals the total weight of the barge and the coal.

Initially, the barge and water displaced by it have a weight of:
(1000 kg/m3)(60 m)(10 m)(1 m) = 6.00 × 105 kg

When 3.0 × 1015 kg of coal is added, the total weight of the barge and coal is:
6.00 × 105 kg + 3.0 × 1015 kg = 3.00 × 1018 kg

The volume of water displaced by the barge remains the same, so the depth the barge sinks is proportional to the weight of the barge and coal.

Let h be the depth the barge sinks into the water after the coal is added. Then we have:

(1000 kg/m3)(60 m)(10 m)(h) = 3.00 × 1018 kg - 6.00 × 105 kg

Solving for h gives:
h = 0.5 m = 50 cm.

Therefore, the barge sinks 50 cm deeper into the water when 3.0 × 1015 kg of coal is added.

Question 12

A solid sphere of mass 8.6 kg,made of metal whose density is 3,400 kg/ 
,hangs by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 38 N.The density of the liquid is closest to which one of the following values?

Accepted Answer

The answer of A solid sphere of mass 8.6 kg,made...

Question 13

A 200-N object floats with three-fourths of its volume beneath the surface of the water.What is the buoyant force on the object? The density of water is 1000 kg/m³.

Accepted Answer

The buoyant force equals the weight of the displaced water. Since the object floats, the buoyant force must equal the object's weight, which is 200 N.

Question 14

The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull,15.2 m long and 3.66 m in diameter,filled with gasoline with a density of 880 kg/m³ to make it buoyant.If it is totally submerged in seawater with a density of 1025 kg/m³ and neither rising nor sinking,what is the weight of the Trieste craft?

Accepted Answer

The weight of the Trieste can be found by calculating the buoyant force acting on it, which equals the weight of the displaced seawater. The volume of the Trieste is given by the volume of a cylinder, $V = \pi r^2 h$, where $r = 3.66/2$ meters and $h = 15.2$ meters. The buoyant force (and thus the weight of the Trieste) is $F_b = \rho_{water} V g$, where $\rho_{water} = 1025 \, \text{kg/m}^3$ and $g = 9.8 \, \text{m/s}^2$. Calculating this gives a weight close to 227 kN.

Question 15

A crane lifts a steel submarine of density 7800 kg/m³ and mass 20,000 kg.What is the tension in the lifting cable (a)when the submarine is submerged in water of density 1000 kg/m³,and (b)when it is entirely out of the water?

Accepted Answer

When the submarine is submerged, the buoyant force reduces the tension in the cable. The buoyant force equals the weight of the displaced water. When out of the water, the tension equals the weight of the submarine. The correct tension when submerged is less than when out of the water, making choice B correct.

Question 16

A 1.00-m³ object floats in water with 20.0% of its volume above the waterline.What does the object weigh out of the water? The density of water is 1000 kg/m³.

Accepted Answer

The answer of A 1.00-m³ object floats in water with...

Question 17

An object floats with half its volume beneath the surface of the water.The weight of the displaced water is 2000 N.What is the weight of the object? The density of water is 1000 kg/m³.

Accepted Answer

The weight of the object is equal to the weight of the water displaced, which is 2000 N, according to Archimedes' principle.

Question 18

A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick.What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m³? The density of ice is 980 kg/m³.

Accepted Answer

The answer of A polar bear of mass 200 kg...

Question 19

A 200-kg flat-bottomed boat floats in fresh water,which has a density of 1000 kg/m³.If the base of the boat is 1.42 m wide and 4.53 m long,to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257kg?

Accepted Answer

The correct answer is A.The buoyant force on the boat is equal to the weight of the water displaced by the boat. The weight of the water displaced is equal to the density of the water times the volume of the water displaced. The volume of the water displaced is equal to the area of the base of the boat times the depth of the water displaced. The depth of the water displaced is equal to the weight of the boat and the passengers divided by the area of the base of the boat times the density of the water.The weight of the boat and the passengers is:$$W = (200 	ext{ kg}) + (257 	ext{ kg}) = 457 	ext{ kg}$$The area of the base of the boat is:$$A = (1.42 	ext{ m})(4.53 	ext{ m}) = 6.44 	ext{ m}^2$$The depth of the water displaced is:$$d = \frac{W}{Aho} = \frac{457 	ext{ kg}}{(6.44 	ext{ m}^2)(1000 	ext{ kg/m}^3)} = 0.0710 	ext{ m} = 7.10 	ext{ cm}$$

Question 20

A hollow steel ball of diameter 3.0 m just barely floats in water.What is the wall thickness of the ball? (ρ_Fe = 7.87 g/cm³,ρ_water= 1.00 g/cm³)

Accepted Answer

For the steel ball to just barely float, the weight of the water displaced by the ball must equal the weight of the ball itself. The volume of the ball (V_ball) can be calculated using the formula for the volume of a sphere: V = 4/3 * π * r^3, where r is the radius of the ball. Since the diameter is 3.0 m, the radius is 1.5 m. The volume of the ball is thus 4/3 * π * (1.5)^3 m^3.The volume of the steel (V_steel) that makes up the ball is the total volume of the ball minus the volume of the hollow part inside. Since the ball just barely floats, the mass of the steel must equal the mass of the water displaced by the ball. The mass of the water displaced can be found by multiplying the volume of the ball by the density of water (ρ_water = 1.00 g/cm^3 = 1000 kg/m^3).Let's denote the thickness of the steel wall as t. The outer radius of the ball is 1.5 m, so the inner radius is (1.5 - t) m. The volume of the steel can be calculated as the volume of the outer sphere minus the volume of the inner sphere (which is hollow).The density of steel (ρ_steel) is given as 7.87 g/cm^3 = 7870 kg/m^3. Using the principle that the mass of the displaced water equals the mass of the steel, we set up the equation:ρ_steel * V_steel = ρ_water * V_ballSolving this equation for t (the thickness of the steel wall) involves algebraic manipulation and substitution of the known values. After solving, we find that the thickness of the steel wall that satisfies this condition is approximately 6.6 cm.

Quiz 15: Fluids

When a container of water is placed on a laboratory scale,the scale reads 120 g.Now a 20-g piece of copper (of density 8.9 g/cm³) is suspended from a thread and lowered into the water,not touching the bottom of the container.What will the scale now read? The density of water is 1.0 g/cm³.

A 4.7-kg solid sphere,made of metal whose density is 4,000 kg/ m³. hangs by a light cord.When the sphere is immersed in water,what is the tension in the cord? The density of water is 1000 kg/m³.

A solid object floats in water with three-fourths of its volume beneath the surface.What is the object's density? The density of water is 1000 kg/m³.

A hot air balloon along with its cargo has a mass of 4.0 × 10⁵ kg,and it holds 7.0 × 10⁵ m³ of hot air.It is floating at a constant height in air with a density of 1.29 kg/m³.What is the density of the hot air in the balloon?

A barge is 10 m wide and 60 m long and has vertical sides.The bottom of the boat is 1.2 m below the water surface.What is the weight of the barge and its cargo,if it is floating in fresh water of density 1000 kg/m³?

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m³ while suspended from a harness.Her apparent weight is now 21.2 N.What is her density?

An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m³.What is the density of the object?

A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m³.What is its mass?

A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm.When the block is placed in water,it floats horizontally,with its bottom face 1.65 cm below the surface.What is the density of the wood? The density of water is 1.00 g/cm³.

A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m³?

A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m³.How much deeper into the water does the barge sink when 3.0 × 10⁵ kg of coal are loaded on the barge?

A solid sphere of mass 8.6 kg,made of metal whose density is 3,400 kg/ ,hangs by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 38 N.The density of the liquid is closest to which one of the following values?

A 200-N object floats with three-fourths of its volume beneath the surface of the water.What is the buoyant force on the object? The density of water is 1000 kg/m³.

A crane lifts a steel submarine of density 7800 kg/m³ and mass 20,000 kg.What is the tension in the lifting cable (a) when the submarine is submerged in water of density 1000 kg/m³,and (b) when it is entirely out of the water?

A 1.00-m³ object floats in water with 20.0% of its volume above the waterline.What does the object weigh out of the water? The density of water is 1000 kg/m³.

An object floats with half its volume beneath the surface of the water.The weight of the displaced water is 2000 N.What is the weight of the object? The density of water is 1000 kg/m³.

A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick.What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m³? The density of ice is 980 kg/m³.

A 200-kg flat-bottomed boat floats in fresh water,which has a density of 1000 kg/m³.If the base of the boat is 1.42 m wide and 4.53 m long,to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257kg?

A hollow steel ball of diameter 3.0 m just barely floats in water.What is the wall thickness of the ball? (ρ_Fe = 7.87 g/cm³,ρ_water= 1.00 g/cm³)

Quiz 15: Fluids

When a container of water is placed on a laboratory scale,the scale reads 120 g.Now a 20-g piece of copper (of density 8.9 g/cm3) is suspended from a thread and lowered into the water,not touching the bottom of the container.What will the scale now read? The density of water is 1.0 g/cm3.

A 4.7-kg solid sphere,made of metal whose density is 4,000 kg/ m3. hangs by a light cord.When the sphere is immersed in water,what is the tension in the cord? The density of water is 1000 kg/m3.

A solid object floats in water with three-fourths of its volume beneath the surface.What is the object's density? The density of water is 1000 kg/m3.

A hot air balloon along with its cargo has a mass of 4.0 × 105 kg,and it holds 7.0 × 105 m3 of hot air.It is floating at a constant height in air with a density of 1.29 kg/m3.What is the density of the hot air in the balloon?

A barge is 10 m wide and 60 m long and has vertical sides.The bottom of the boat is 1.2 m below the water surface.What is the weight of the barge and its cargo,if it is floating in fresh water of density 1000 kg/m3?

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m3 while suspended from a harness.Her apparent weight is now 21.2 N.What is her density?

An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m3.What is the density of the object?

A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m3.What is its mass?

A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm.When the block is placed in water,it floats horizontally,with its bottom face 1.65 cm below the surface.What is the density of the wood? The density of water is 1.00 g/cm3.

A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m3?

A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m3.How much deeper into the water does the barge sink when 3.0 × 105 kg of coal are loaded on the barge?

A solid sphere of mass 8.6 kg,made of metal whose density is 3,400 kg/ ,hangs by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 38 N.The density of the liquid is closest to which one of the following values?

A 200-N object floats with three-fourths of its volume beneath the surface of the water.What is the buoyant force on the object? The density of water is 1000 kg/m3.

A crane lifts a steel submarine of density 7800 kg/m3 and mass 20,000 kg.What is the tension in the lifting cable (a) when the submarine is submerged in water of density 1000 kg/m3,and (b) when it is entirely out of the water?

A 1.00-m3 object floats in water with 20.0% of its volume above the waterline.What does the object weigh out of the water? The density of water is 1000 kg/m3.

An object floats with half its volume beneath the surface of the water.The weight of the displaced water is 2000 N.What is the weight of the object? The density of water is 1000 kg/m3.

A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick.What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m3? The density of ice is 980 kg/m3.

A 200-kg flat-bottomed boat floats in fresh water,which has a density of 1000 kg/m3.If the base of the boat is 1.42 m wide and 4.53 m long,to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257kg?

A hollow steel ball of diameter 3.0 m just barely floats in water.What is the wall thickness of the ball? (ρFe = 7.87 g/cm3,ρwater = 1.00 g/cm3)

When a container of water is placed on a laboratory scale,the scale reads 120 g.Now a 20-g piece of copper (of density 8.9 g/cm³) is suspended from a thread and lowered into the water,not touching the bottom of the container.What will the scale now read? The density of water is 1.0 g/cm³.

A 4.7-kg solid sphere,made of metal whose density is 4,000 kg/ m³. hangs by a light cord.When the sphere is immersed in water,what is the tension in the cord? The density of water is 1000 kg/m³.

A solid object floats in water with three-fourths of its volume beneath the surface.What is the object's density? The density of water is 1000 kg/m³.

A hot air balloon along with its cargo has a mass of 4.0 × 10⁵ kg,and it holds 7.0 × 10⁵ m³ of hot air.It is floating at a constant height in air with a density of 1.29 kg/m³.What is the density of the hot air in the balloon?

A barge is 10 m wide and 60 m long and has vertical sides.The bottom of the boat is 1.2 m below the water surface.What is the weight of the barge and its cargo,if it is floating in fresh water of density 1000 kg/m³?

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m³ while suspended from a harness.Her apparent weight is now 21.2 N.What is her density?

An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m³.What is the density of the object?

A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m³.What is its mass?

A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm.When the block is placed in water,it floats horizontally,with its bottom face 1.65 cm below the surface.What is the density of the wood? The density of water is 1.00 g/cm³.

A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m³?

A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m³.How much deeper into the water does the barge sink when 3.0 × 10⁵ kg of coal are loaded on the barge?

A 200-N object floats with three-fourths of its volume beneath the surface of the water.What is the buoyant force on the object? The density of water is 1000 kg/m³.

A crane lifts a steel submarine of density 7800 kg/m³ and mass 20,000 kg.What is the tension in the lifting cable (a) when the submarine is submerged in water of density 1000 kg/m³,and (b) when it is entirely out of the water?

A 1.00-m³ object floats in water with 20.0% of its volume above the waterline.What does the object weigh out of the water? The density of water is 1000 kg/m³.

An object floats with half its volume beneath the surface of the water.The weight of the displaced water is 2000 N.What is the weight of the object? The density of water is 1000 kg/m³.

A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick.What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m³? The density of ice is 980 kg/m³.

A 200-kg flat-bottomed boat floats in fresh water,which has a density of 1000 kg/m³.If the base of the boat is 1.42 m wide and 4.53 m long,to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257kg?

A hollow steel ball of diameter 3.0 m just barely floats in water.What is the wall thickness of the ball? (ρ_Fe = 7.87 g/cm³,ρ_water= 1.00 g/cm³)