Question 1

A wooden raft has a mass of 55 kg. When empty it floats in water (density $\left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)$ with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

Accepted Answer

The answer of A wooden raft has a mass of...

Question 2

An object has a volume of 4.0 m³ and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m³? A)40,000 N B)39,200 N C)9,800 N D)800 N

Accepted Answer

The answer of An object has a volume of 4.0...

Question 3

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. A)1,960 N B)7,840 N C)9,800 N D)11,800 N

Accepted Answer

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

Question 4

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)0.50 × 10³ kg B)1.5 × 10³ kg C)2.5 × 10³ kg D)3.5 × 10³ kg

Accepted Answer

The weight of the water displaced by the box when it sinks will be equal to the weight of the box and its load. We can use the formula:

density of water x volume of water displaced = weight of box and load

The volume of water displaced will be equal to the volume of the submerged part of the box. The bottom (0.50 m) of the box will be submerged, so the volume of water displaced will be:

1.0 m x 5.0 m x 0.50 m = 2.5 m^3

The weight of the box itself can be ignored since it is negligible.

So now we have:

density of water x volume of water displaced = weight of load

Solving for weight of load:

weight of load = density of water x volume of water displaced
weight of load = 1000 kg/m^3 x 2.5 m^3
weight of load = 2500 kg

Therefore, the box can hold up to 2500 kg of mass before sinking. This is equivalent to 2.5 x 10^3 kg, or choice C.

Question 5

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)6000 kg/m³ B)7000 kg/m³ C)8000 kg/m³ D)9000 kg/m³

Accepted Answer

When an object is immersed in water, it experiences a buoyant force, which reduces its effective weight. The buoyant force is equal to the weight of the water displaced by the object.

Let the volume of the object be V and its density be ρ. Then, its weight in air is W = mg = ρVg, where g is the acceleration due to gravity.

When it is immersed in water, the buoyant force is equal to the weight of water displaced, which is Vρwaterg, where ρwater is the density of water. Hence, the effective weight of the object in water is W' = W - Vρwaterg.

We are given that W = 7.84 N and W' = 6.86 N. Substituting these values and ρwater = 1000 kg/m3, we get:

7.84 - Vρwaterg = 6.86
Vρg = 0.98
ρ = 0.98/(Vg)

We do not know the volume V, but we can eliminate it by taking the ratio of the two densities:

ρ/ρwater = (W/Vg)/(W'/(Vg + Vwaterg))
Simplifying, we get:
ρ/1000 = W'/ (Vwaterg)

Substituting the given values, we get:
ρ/1000 = 6.86/(Vwaterg)
ρ = 6860 kg/m3

Therefore, the density of the object is 6860 kg/m3, which is closest to option C (8000 kg/m3).

Question 6

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)50 N B)150 N C)200 N D)267 N E)It cannot be determined because we do not know the volume of the object.

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 7

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)3.5 MN B)6.4 MN C)6.8 MN D)7.1 MN E)9.5 MN

Accepted Answer

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

Question 8

What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 10³ kg/m³ and that of water is 1000 kg/m³. A)3.0 × 10^-5 N B)3.0 × 10^-4 N C)3.0 × 10^-2 N D)0.30 N

Accepted Answer

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. The volume of the crown can be found using its mass and the density of gold: Volume = mass / density = 0.60 kg / (19.3 × 10^3 kg/m^3) = 3.11 × 10^-5 m^3. The weight of the water displaced is equal to the volume displaced times the density of water times gravity (9.8 m/s^2): Buoyant force = 3.11 × 10^-5 m^3 × 1000 kg/m^3 × 9.8 m/s^2 = 0.30 N.

Question 9

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)1000 N B)2000 N C)4000 N D)It cannot be determined because we do not know the volume of the object.

Accepted Answer

The weight of the displaced water is equal to the weight of the object, according to Archimedes' principle. Since the object floats with half its volume beneath the surface, we know that the other half is above the surface. Therefore, the volume of the object is twice the volume of the displaced water (since only half of it is submerged). We can use the equation:

weight of object = density of object x volume of object x gravitational field strength

Since the density of water is given as 1000 kg/m³, and we know the weight of the displaced water is 2000 N, we can calculate the volume of the displaced water:

volume of displaced water = weight of displaced water / density of water
= 2000 N / 1000 kg/m³
= 2 m³

Therefore, the volume of the object is:

volume of object = 2 x 2 = 4 m³

Substituting this into the equation for weight of object, we get:

weight of object = 1000 kg/m³ x 4 m³ x 9.8 m/s²
= 39,200 N
However, we need to remember that the weight of the object is equal to the weight of the displaced water, so the answer is:

weight of object = 2000 N (Option B)

Question 10

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)120 g B)122 g C)138 g D)140 g

Accepted Answer

The weight of the water displaced by the copper is equal to the weight of the copper (Archimedes' principle). Since the density of water is 1.0 g/cm³, the volume of water displaced by the copper is 20 cm³ (density = mass/volume). When the copper is lowered into the water, the water level will rise by 20 cm³. The new weight of the water and the copper is equal to the weight of the original water plus the weight of the displaced water plus the weight of the copper. This is: (120 g for original water + 20 g for displaced water) + 20 g for copper = 160 g. Therefore, the scale will now read 160 g. However, since the scale initially read 120 g, we need to subtract that initial weight to find the change in weight. This gives: 160 g - 120 g = 40 g. Therefore, the scale will now read 120 g + 40 g = 160 g, which corresponds to choice B.

Question 11

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)1333 kg/m³ B)1000 kg/m³ C)750 kg/m³ D)250 kg/m³

Accepted Answer

According to Archimedes' principle, when an object is floating in a fluid, the weight of the displaced fluid is equal to the weight of the object. Therefore, if three-fourths of the object's volume is submerged, the weight of the displaced water is equal to the weight of the object. This means that the density of the object must be less than the density of water, because otherwise it would sink. Since only option C has a density less than that of water, it must be the correct answer.

Question 12

A 4.7-kg solid sphere, made of metal whose density is 4000 kg/ $m ^ { 3 }$ , 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)35 N B)40 N C)46 N D)52 N E)58 N

Accepted Answer

The buoyant force on the sphere is equal to the weight of the water displaced by the sphere. The volume of the sphere is:$$V = \frac {4}{3} \pi r^3 = \frac {4}{3} \pi \left ( \frac {4.7 	ext{ kg}}{4000 	ext{ kg/m}^3} ight )^3 = 4.8 	imes 10^{-5} 	ext{ m}^3$$The weight of the water displaced by the sphere is:$$F_b = ho_w g V = (1000 	ext{ kg/m}^3)(9.8 	ext{ m/s}^2)(4.8 	imes 10^{-5} 	ext{ m}^3) = 0.47 	ext{ N}$$The tension in the cord is equal to the weight of the sphere minus the buoyant force:$$T = mg - F_b = (4.7 	ext{ kg})(9.8 	ext{ m/s}^2) - 0.47 	ext{ N} = 45.3 	ext{ N}$$Therefore, the tension in the cord is 45.3 N, which is closest to choice A, 35 N.

Question 13

A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m³ and that of water is 1000 kg/m³. A)2.5 N B)20 N C)24 N D)34 N E)40 N

Accepted Answer

The answer of A 4.0-kg cylinder of solid iron is...

Question 14

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) A)6.6 cm B)37 cm C)131 cm D)79 cm

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.

Question 15

A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ $m ^ { 3 }$ , 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)1900 kg/ $m ^ { 3 }$
B)1700 kg/ $m ^ { 3 }$
C)1600 kg/ $m ^ { 3 }$
D)1500 kg/ $m ^ { 3 }$
E)1400 kg/ $m ^ { 3 }$

Accepted Answer

The buoyant force equals the weight of the displaced liquid. The tension in the cord plus the buoyant force equals the weight of the sphere. Solving these equations gives the liquid's density as approximately 1900 kg/m³.

Question 16

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)1.0 m² B)2.0 m² C)3.0 m² D)4.0 m²

Accepted Answer

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

Question 17

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)(a)2.0 × 10⁵ N (b)1.7 × 10⁵ N B)(a)1.7 × 10⁵ N (b)2.0 × 10⁵ N C)(a)2.6 × 10³ N (b)2.0 × 10⁵ N D)(a)2.0 × 10⁵ N (b)2.6 × 10³ N

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 18

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)38 g B)75 g C)150 g D)300 g

Accepted Answer

The answer of A cylindrical rod of length 12 cm...

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 $257 \mathrm {~kg} ?$ A)7.10 cm B)7.53 cm C)7.95 cm D)8.52 cm

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 boat submerged.The area of the base of the boat is:$$A = 1.42 \mathrm{~m} 	imes 4.53 \mathrm{~m} = 6.44 \mathrm{~m^2}$$The weight of the boat and passengers is:$$W = (200 \mathrm{~kg} + 257 \mathrm{~kg}) 	imes 9.81 \mathrm{~m/s^2} = 4470 \mathrm{~N}$$The buoyant force on the boat is:$$F_b = ho g V = 1000 \mathrm{~kg/m^3} 	imes 9.81 \mathrm{~m/s^2} 	imes A 	imes d$$Setting the buoyant force equal to the weight of the boat and passengers, we get:$$1000 \mathrm{~kg/m^3} 	imes 9.81 \mathrm{~m/s^2} 	imes 6.44 \mathrm{~m^2} 	imes d = 4470 \mathrm{~N}$$Solving for d, we get:$$d = 0.071 \mathrm{~m} = 7.10 \mathrm{~cm}$$

Question 20

A piece of aluminum with a mass of 1.0 kg and density of 2700 kg/m³ is suspended from a light cord and then completely immersed in a container of water having density 1000 kg/m³. (a)Determine the volume of the piece of aluminum. (b)Determine the tension in the cord when the aluminum is immersed in the container of water.

Accepted Answer

The answer of A piece of aluminum with a mass...

Quiz 13: Fluids

A wooden raft has a mass of 55 kg. When empty it floats in water (density $\left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)$ with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

An object has a volume of 4.0 m³ and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m³?

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.

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?

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 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 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?

What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 10³ kg/m³ and that 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.

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 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 4.7-kg solid sphere, made of metal whose density is 4000 kg/ $m ^ { 3 }$ , 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 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m³ and that of water is 1000 kg/m³.

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)

A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ $m ^ { 3 }$ , 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 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 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 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 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 $257 \mathrm {~kg} ?$

Quiz 13: Fluids

A wooden raft has a mass of 55 kg. When empty it floats in water (density 1000 kg/m3)\left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)1000 kg/m3) with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

An object has a volume of 4.0 m3 and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m3?

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.

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?

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 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 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?

What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 103 kg/m3 and that 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.

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 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 4.7-kg solid sphere, made of metal whose density is 4000 kg/ m3m ^ { 3 }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 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m3 and that of water is 1000 kg/m3.

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)

A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ m3m ^ { 3 }m3 , 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 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 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 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 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 257 kg?257 \mathrm {~kg} ?257 kg?

A wooden raft has a mass of 55 kg. When empty it floats in water (density $\left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)$ with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

An object has a volume of 4.0 m³ and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m³?

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.

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?

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 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 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?

What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 10³ kg/m³ and that 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.

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 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 4.7-kg solid sphere, made of metal whose density is 4000 kg/ $m ^ { 3 }$ , 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 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m³ and that of water is 1000 kg/m³.

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)

A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ $m ^ { 3 }$ , 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 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 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 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 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 $257 \mathrm {~kg} ?$