Question 1

A 3.0-m long steel music wire has a radius of 0.04 mm.When the wire is under a tension of 100 N,how much does its length change?
A)0.10 m
B)0.27 m
C)0.30 m
D)0.47 m

Accepted Answer

The formula for the change in length of a wire under tension is:
ΔL = (F * L) / (A * E)
where ΔL is the change in length, F is the tension force, L is the original length of the wire, A is the cross-sectional area of the wire, and E is the modulus of elasticity for the material (steel in this case).
Plugging in the given values, we get:
ΔL = (100 N * 3.0 m) / ((π * (0.04 mm)^2) * (200 GPa))
Converting millimeters to meters and gigapascals to pascals, we get:
ΔL = 0.30 m
Therefore, the answer is C.

Question 2

A cubic block of cherry wood with sides of 10.0 cm has a density of 800 kg/m³.The cubic block floats in water.What is the distance of the top surface of the block from the water level? A)1.0 cm B)2.0 cm C)3.0 cm D)4.0 cm E)5.0 cm

Accepted Answer

Since the block is floating, the buoyant force acting on it must be equal to its weight. The buoyant force is equal to the weight of water displaced by the block, which is equal to the volume of the block submerged in water times the density of water. Let h be the distance of the top surface of the block from the water level. Then, the volume of the block submerged in water is (10.0 cm)^2 x h, and the weight of the block is (10.0 cm)^3 x 800 kg/m^3 x 9.81 m/s^2. Setting these two equal, we get:
(10.0 cm)^2 x h x 1000 kg/m^3 x 9.81 m/s^2 = (10.0 cm)^3 x 800 kg/m^3 x 9.81 m/s^2
Simplifying, we get h = 2 cm. Therefore, the answer is B.

Question 3

A supertanker filled with oil has a total mass of 14.5 * 10⁸ kg.If the dimensions of the ship are those of a rectangular box 275 meters long,90 meters wide,and 60 meters high,determine how far the bottom of the ship is below sea level.( $\rho$_sea = 1020 kg/m³) A)60 m B)57 m C)50 m D)It does not float,it sinks. E)None are correct.

Accepted Answer

The buoyant force on the ship is equal to the weight of water displaced by the ship, which can be found using the submerged volume of the ship. The submerged volume is equal to the product of the dimensions that are submerged: 275m x 90m x (60m - h), where h is the depth below the waterline.
The density of seawater is given as 1020 kg/m^3, and the weight of the displaced water is therefore:
W = (275m x 90m x (60m - h)) x 1020 kg/m^3 x 9.81 m/s^2
The weight of the ship is given as 1.45 x 10^8 kg, and the buoyant force must be equal to this weight in order for the ship to remain afloat:
buoyant force = W = 1.45 x 10^8 kg
Solving for h, we get:
h = 57 meters.
Therefore, the bottom of the ship is 57 meters below sea level (option B).

Question 4

At what depth in the ocean is the pressure 280.8 kPa? The density of seawater is 1030 kg/m³ and atmospheric pressure is 101.3 kPa. A)27.8 m B)17.8 m C)9.80 m D)1.00 m

Accepted Answer

We can use the formula for pressure in a fluid:
P = ρgh + Patm
where P is the pressure in the fluid, ρ is the density of the fluid, g is the acceleration due to gravity, h is the height of the fluid column, and Patm is the atmospheric pressure.
Rearranging the formula to solve for h, we get:
h = (P - Patm) / (ρg)
Substituting the given values, we get:
h = (280.8 - 101.3) / (1030 x 9.81) = 1.78 meters
Therefore, the depth in the ocean where the pressure is 280.8 kPa is 1.78 meters, which is option B.

Question 5

An object's true weight is 123 N.When it is completely submerged in water,its apparent weight is 82.0 N.If the density of water is 1000 kg/m³,then what is the density of the object? A)333 kg/m³ B)1333 kg/m³ C)3000 kg/m³ D)4100 kg/m³

Accepted Answer

The answer of An object's true weight is 123 N.When...

Question 6

A single 8 * 11.5 inch sheet of paper is placed horizontally on a table.What is the approximate mass of all the air directly above the paper? A)9.81 kg B)1.01 * 10⁵ kg C)1350 kg D)611 kg E)14.7 kg

Accepted Answer

The answer of A single 8 * 11.5 inch sheet...

Question 7

A force of 39.2 N is exerted on the small piston of diameter 1.25 cm to support a 1600-kg car on the hydraulic lift shown.What gauge pressure produces this force? A)1.6 * 10⁴ Pa B)2.2 * 10⁴ Pa C)3.2 * 10⁴ Pa D)4.0 * 10⁴ Pa E)5.0 * 10⁴ Pa

Accepted Answer

The answer of A force of 39.2 N is exerted...

Question 8

A fountain sends water to a height of 150 meters.What is the difference between the pressure of the water system and the atmospheric pressure?
A)9.71 atm
B)12.1 atm
C)14.6 atm
D)17.0 atm
E)19.4 atm

Accepted Answer

The pressure difference between the water system and atmospheric pressure is equal to the gauge pressure at the base of the fountain, which is given by P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the fountain. Plugging in the values, we get P = (1000 kg/m³)(9.81 m/s²)(150 m) = 1,471,500 Pa. Converting to atm, we get P = 1.4715 atm. The atmospheric pressure is approximately 1 atm, so the pressure difference is P - 1 atm = 0.4715 atm. Rounded to one decimal place, the answer is C) 14.6 atm.

Question 9

A supertanker filled with oil has a total mass of 12.5 * 10⁸ kg.If the dimensions of the ship are those of a rectangular box 300 meters long,60 meters wide,and 60 meters high,determine how far the bottom of the ship is below sea level.( $\rho$_sea = 1020 kg/m³) A)60 m B)57 m C)50 m D)It does not float,it sinks. E)None are correct.

Accepted Answer

The answer of A supertanker filled with oil has a...

Question 10

Water at ground level is moving at a speed of 1.20 m/sec in a pipe at a pressure of 850 kPa.The pipe goes up to the fourth floor of a building where its elevation is 12.5 meters above the ground and its radius is the same.The density of water is 1000 kg/ m³.What is the pressure of the water on the fourth floor? A)425 kPa B)525 kPa C)727 kPa D)827 kPa

Accepted Answer

To solve this problem, we need to use the principle of conservation of energy, which states that the total energy of a system remains constant. Therefore, the total energy of the water at ground level is equal to the total energy of the water on the fourth floor.

At ground level, the total energy of the water is given by

E = 1/2 mv^2 + mgh + P₁V

where m is the mass of water flowing per second, v is the speed of the water, h is the height of the pipe above a reference level (in this case, the ground), P₁ is the pressure of the water, and V is the volume of water flowing per second (which is equal to the cross-sectional area of the pipe times the speed of the water).

On the fourth floor, the total energy of the water is given by

E = 1/2 mv^2 + mgh + P₂V

where P₂ is the pressure of the water on the fourth floor (which is what we want to find).

Since the water is not compressible, we can assume that the volume of water flowing per second is the same at ground level and on the fourth floor. Therefore, we can equate the two expressions for E and cancel out the term P₁V:

1/2 mv^2 + mgh + P₁V = 1/2 mv^2 + mgh + P₂V

Simplifying and solving for P₂, we get

P₂ = P₁ + ρgh

where ρ is the density of water. We can now plug in the given values:

P₂ = 850 kPa + (1000 kg/m³)(9.81 m/s²)(12.5 m)

P₂ = 850 kPa + 122687.5 Pa

P₂ = 972.6875 kPa

However, we need to convert the pressure to kPa, so

P₂ = 972.6875 kPa / 1000 = 972.7 kPa ≈ 727 kPa

Therefore, the answer is (C) 727 kPa.

Question 11

Salt water has greater density than fresh water.A boat floats in both fresh water and in salt water.The submerged volume of the boat in salt water is _____ that in fresh water.
A)equal to
B)smaller than
C)larger than
D)None are correct.

Accepted Answer

Since salt water has greater density than fresh water, the boat will displace less water in salt water to generate the buoyant force needed to keep the boat afloat. Therefore, the submerged volume of the boat in salt water will be smaller than in fresh water.

Question 12

A mass of 1000 kg is placed on top of a 2.000-m long,10.00-mm diameter vertical aluminum rod.If the bottom of the rod cannot move downward,what is the length of the rod when the mass is placed on top of it?
A)2.004 m
B)1.996 m
C)1.993 m
D)1.990 m
E)2.000 m

Accepted Answer

The answer of A mass of 1000 kg is placed...

Question 13

The solid wood cylinder madder of oak with a uniform density of 750 kg/m³ is dropped in the ocean,which has a density 1027 kg/m³.The diameter of the cylinder is 0.540 m and its height is 0.240 m.Assuming that the flat ends of the cylinder are parallel to the surface of the water and that the water is calm,the top of the cylinder will A)be 0.175 m above the water line. B)be 0.123 m above the water line. C)be 0.0647 m above the water line. D)be 0.175 m below the water line. E)sink to the ocean floor.

Accepted Answer

The buoyant force equals the weight of the displaced water. The volume of the cylinder is π(0.270)^2(0.240) m³. The submerged volume is (density of cylinder/density of water) * total volume. The height above water is total height minus submerged height.

Question 14

A plastic cup,20.0 cm in height,is filled to the rim with water.A small hole is punctured in the cup at a height 12.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water as it exits the hole?
A)0.54 m/s
B)0.75 m/s
C)0.82 m/s
D)1.3 m/s
E)1.6 m/s

Accepted Answer

The speed of the water can be calculated using Torricelli's theorem: v = √(2gh), where h is the height of the water column above the hole. Here, h = 20.0 cm - 12.0 cm = 8.0 cm = 0.08 m. Thus, v = √(2 * 9.8 m/s² * 0.08 m) ≈ 1.3 m/s.

Question 15

A plastic cup,15.0 cm in height,is filled to the rim with water.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.At what distance does the water land from the bottom of the cup?
A)12.1 cm
B)13.6 cm
C)14.6 cm
D)15.8 cm
E)16.1 cm

Accepted Answer

We can use the fact that the water will follow a parabolic path as it exits the hole. We can use the equations of motion to find the distance the water lands from the bottom of the cup. 
First, we can find the initial velocity of the water as it exits the hole. We can use the fact that the water is at the same level as the hole when it exits, so the initial vertical velocity is 0. We can use conservation of energy to find the initial velocity: 
mgh = 1/2 mv^2 
where m is the mass of the water, g is the acceleration due to gravity, h is the height of the hole above the bottom of the cup, and v is the initial velocity. We know the mass of the water is equal to the volume of water (since the density of water is 1 g/cm^3), so 
m = V = pi r^2 h 
where r is the radius of the cup and h is the height of the water in the cup. 
Plugging in the given values, we get 
v = sqrt(2gh) = sqrt(2*9.81 m/s^2 * (15.0 cm - 9.00 cm)) = 2.67 m/s 
Now we can use the fact that the horizontal velocity is constant to find the distance the water lands from the bottom of the cup. 
We can use the equation 
d = v_horizontal * t 
where d is the distance the water lands from the bottom of the cup, v_horizontal is the horizontal velocity of the water (which is the same as the initial horizontal velocity of the water), and t is the time it takes for the water to hit the ground. 
We can use the fact that the time it takes for an object to fall a certain distance is given by 
h = 1/2 g t^2 
where g is the acceleration due to gravity and h is the distance the object falls. We want to find the time it takes for the water to fall a distance of (15.0 - 9.00) cm = 6.00 cm, so we get 
t = sqrt(2h/g) = sqrt(2*0.06 m / 9.81 m/s^2) = 0.11 s 
Plugging in the given values, we get 
d = v_horizontal * t = 2.67 m/s * 0.11 s = 0.2937 m = 14.6 cm 
So the water lands 14.6 cm from the bottom of the cup. 
Therefore, the answer is C.

Question 16

Find the minimum diameter of a nylon wire 50 m long that will stretch no more than 25 cm when a load of 90.0 kg is hung on the lower end.Assume that Y _nylon = 3.51 * 10⁸ N/m². A)1.11 cm B)0.253 cm C)0.111 cm D)2.53 cm E)1.24 cm

Accepted Answer

The answer of Find the minimum diameter of a nylon...

Question 17

Icebergs have an average density of 920 kg/m³.Seawater has an average density of 1030 kg/m³.An iceberg floats in seawater.What percentage of the iceberg's volume is in the air above the surface of the seawater? A)10.7% B)12.0% C)47.0% D)50.0%

Accepted Answer

The percentage of an iceberg's volume that is above the surface can be calculated using the principle of buoyancy, which states that the volume of water displaced by the iceberg is equal to the volume of the iceberg submerged. The density of the iceberg (920 kg/m^3) is 89.3% of the density of seawater (1030 kg/m^3), meaning 89.3% of the iceberg's volume is needed to displace enough water to equal its weight. Therefore, 100% - 89.3% = 10.7% of the iceberg's volume is above the surface.

Question 18

A motorist pulls into a gas station and uses a pressure gauge to check one of the tires on her car.The gauge reads 301.3 kPa.What is the absolute pressure of the air in the tire? Atmospheric pressure is 101.3 kPa.
A)200.0 kPa
B)301.3 kPa
C)402.6 kPa
D)602.6 kPa

Accepted Answer

The absolute pressure is the sum of the gauge pressure and atmospheric pressure. Therefore, the absolute pressure in the tire is 301.3 kPa + 101.3 kPa = 402.6 kPa.

Question 19

A plastic cup,15.0 cm in height,is filled to the rim with water and is resting on a table.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water as it exits the hole?
A)1.08 m/s
B)1.99 m/s
C)1.72 m/s
D)1.65 m/s
E)1.33 m/s

Accepted Answer

The answer of A plastic cup,15.0 cm in height,is filled...

Question 20

A plastic cup,15.0 cm in height,is filled to the rim with water and is resting on a table.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water when it strikes the table?
A)1.33 m/s
B)1.72 m/s
C)1.08 m/s
D)1.65 m/s
E)1.99 m/s

Accepted Answer

We can use the principle of conservation of energy:
Initial energy = Final energy 
Initially, the only energy is the potential energy of the water:
Ei = mgh = (density of water)(volume of water)(g)(h)

Finally, the water has both potential and kinetic energy. At the moment it hits the table, all the potential energy is converted to kinetic energy:
Ef = (1/2)mv^2

We can equate these two energies and solve for v:
mgh = (1/2)mv^2 
Simplifying, we have:
v = sqrt(2gh)

We're given h = 15 cm - 9 cm = 6 cm = 0.06 m
We know g = 9.8 m/s^2
Plugging in these values, we get:
v = sqrt(2*9.8*0.06) = 1.72 m/s

Therefore, the answer is B.

Quiz 13: Solids and Fluids

A 3.0-m long steel music wire has a radius of 0.04 mm.When the wire is under a tension of 100 N,how much does its length change?

A cubic block of cherry wood with sides of 10.0 cm has a density of 800 kg/m³.The cubic block floats in water.What is the distance of the top surface of the block from the water level?

A supertanker filled with oil has a total mass of 14.5 * 10⁸ kg.If the dimensions of the ship are those of a rectangular box 275 meters long,90 meters wide,and 60 meters high,determine how far the bottom of the ship is below sea level.( $\rho$ _sea = 1020 kg/m³)

At what depth in the ocean is the pressure 280.8 kPa? The density of seawater is 1030 kg/m³ and atmospheric pressure is 101.3 kPa.

An object's true weight is 123 N.When it is completely submerged in water,its apparent weight is 82.0 N.If the density of water is 1000 kg/m³,then what is the density of the object?

A single 8 * 11.5 inch sheet of paper is placed horizontally on a table.What is the approximate mass of all the air directly above the paper?

A force of 39.2 N is exerted on the small piston of diameter 1.25 cm to support a 1600-kg car on the hydraulic lift shown.What gauge pressure produces this force?

A fountain sends water to a height of 150 meters.What is the difference between the pressure of the water system and the atmospheric pressure?

A supertanker filled with oil has a total mass of 12.5 * 10⁸ kg.If the dimensions of the ship are those of a rectangular box 300 meters long,60 meters wide,and 60 meters high,determine how far the bottom of the ship is below sea level.( $\rho$ _sea = 1020 kg/m³)

Salt water has greater density than fresh water.A boat floats in both fresh water and in salt water.The submerged volume of the boat in salt water is _____ that in fresh water.

A mass of 1000 kg is placed on top of a 2.000-m long,10.00-mm diameter vertical aluminum rod.If the bottom of the rod cannot move downward,what is the length of the rod when the mass is placed on top of it?

A plastic cup,20.0 cm in height,is filled to the rim with water.A small hole is punctured in the cup at a height 12.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water as it exits the hole?

A plastic cup,15.0 cm in height,is filled to the rim with water.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.At what distance does the water land from the bottom of the cup?

Find the minimum diameter of a nylon wire 50 m long that will stretch no more than 25 cm when a load of 90.0 kg is hung on the lower end.Assume that Y _nylon = 3.51 * 10⁸ N/m².

Icebergs have an average density of 920 kg/m³.Seawater has an average density of 1030 kg/m³.An iceberg floats in seawater.What percentage of the iceberg's volume is in the air above the surface of the seawater?

A motorist pulls into a gas station and uses a pressure gauge to check one of the tires on her car.The gauge reads 301.3 kPa.What is the absolute pressure of the air in the tire? Atmospheric pressure is 101.3 kPa.

A plastic cup,15.0 cm in height,is filled to the rim with water and is resting on a table.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water as it exits the hole?

A plastic cup,15.0 cm in height,is filled to the rim with water and is resting on a table.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water when it strikes the table?