### Density – Pressure & Speed – Physics

This Physics chapter covers density – pressure and speed.

The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?**a. 21.5 g/cm3 – correct**

b. 19.3 g/cm3

c. 13.6 g/cm3

d. 10.7 g/cm

The quantity “pressure” expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:

a. MLT−1**b. ML−1 T−2 – correct**

c. M2 L−1 T−3

d. a dimensionless quantity.

The pressure inside a commercial airliner is maintained at 1.00 atm (105 Pa). What is the net outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure is 0.30 atm?

a. 140 N

b. 1 400 N

c. 14 000 N**d. 140 000 N – correct**

A stonecutter’s chisel has an edge area of 0.50 cm2. If the chisel is struck with a force of 45N, what is the pressure exerted on the stone?

a. 9 000 Pa

b. 90 000 Pa

c. 450 000 Pa**d. 900 000 Pa – correct**

An ideal fluid, of density 0.90 × 103 kg/m3, flows at 6.0 m/s through a level pipe with radius of 0.50 cm. The pressure in the fluid is 1.3 × 105 N/m2. This pipe connects to a second level pipe, with radius of 1.5 cm. Find the speed of flow in the second pipe.

a. 54 m/s

b. 18 m/s**c. 0.67 m/s – correct**

d. 0.33 m/s

The flow rate of blood through the average human aorta, of radius 1.0 cm, is about 90 cm3/s. What is the speed of the blood flow through the aorta?

a. 14 cm/s

b. 32 cm/s

c. 37 cm/s**d. 29 cm/s – correct**

The Earth’s gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion of the satellite at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee). At these two points:

a. the tangential velocities are the same.

b. the angular velocities are the same.**c. the angular momenta are the same. – correct**

d. the kinetic energies are the same.

The Earth’s gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee). At the point closest to the Earth:

a. the angular speed will be greatest although the linear speed will be the same.

b. the speed will be greatest although the angular speed will be the same.

c. the kinetic energy and angular momentum will both be greater.**d. None of the above. – correct**

A tetherball is attached to a pole with a 2.0-m rope. It is circling at 0.20 rev/s. As the rope wraps around the pole it shortens. How long is the rope when the ball is moving at 5.0 m/s?

a. 1.8 m

b. 1.5 m

c. 1.2 m**d. 1.0 m – correct**

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 5g = 49 m/s2 ?

a. 10.1 m

b. 50.0 m**c. 72.7 m – correct**

d. 89.9 m

An object with mass m and moment of inertia I is spinning with an angular momentum L. Its kinetic energy is:

a. 0.5 I2/L.**b. 0.5 L2/I. – correct**

c. 0.5 L2/m.

d. 0.5 I2/m.

An object of mass m and moment of inertia I has rotational kinetic energy KR. Its angular momentum is:

a. 0.5 I/m.**b. (2 IKR)1/2. – correct**

c. (2 mKR)1/2.

d. not given above

The bulk modulus of a material, as a meaningful physical property, is applicable to which of the following?

a. only solids

b. only liquids

c. only gases**d. solids, liquids and gases – correct**

A uniform pressure of 7.0 × 105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 × 1010 N/m2)

a. 2.4 × 10−2 %

b. 0.4 × 10−2 %

c. 8.4 × 10−2 %**d. 0.5 × 10−3 % – correct**

Bar One has a Young’s modulus that is bigger than that of Bar Two. This indicates Bar One:

a. is longer than Bar Two.

b. has a greater cross-sectional area than Bar Two.

c. has a greater elastic limit than Bar Two.**d. is made of material that is different from Bar Two.- correct**

Consider two steel rods, A and B. B has three times the area and twice the length of A, so Young’s modulus for B will be what factor times Young’s modulus for A?

a. 3.0

b. 0.5

c. 1.5**d. 1.0 – correct**

A tire stops a car by use of friction. What modulus should we use to calculate the stress and strain on the tire?

a. Young’s modulus

b. compression modulus**c. shear modulus**

d. bulk modulus

How large a force is necessary to stretch a 2.0-mm-diameter steel wire (Y = 2.0 × 1011 N/m2) by 1.0%?

a. 3.1 × 103 N**b. 6.3 × 103 N – correct**

c. 9.4 × 103 N

d. 1.3 × 104 N

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 × 109 Pa, and 1 atm = 1.0 × 105 Pa.)

a. 18 atm

b. 270 atm

c. 1 080 atm**d. 1 800 atm – correct**

The Greenland ice sheet can be one km thick. Estimate the pressure underneath the ice. (The density of ice is 918 kg/m3.)

a. 9.0 × 105 Pa (9 atm)

b. 2.5 × 106 Pa (25 atm)

c. 4.5 × 106 Pa (45 atm)**d. 9.0 × 106 Pa (90 atm) – correct**

What is the total mass of the Earth’s atmosphere? (The radius of the Earth is 6.4 × 106 m, and atmospheric pressure at the surface is 105 N/m2.)

a. 5 × 1016 kg

b. 1 × 1018 kg**c. 5 × 1018 kg – correct**

d. 1 × 1020 kg

A solid object is made of two materials, one material having density of 2000 kg/m3 and the other having density of 6 000 kg/m3. If the object contains equal volumes of the materials, what is its average density?

a. 3 000 kg/m3**b. 4 000 kg/m3 – correct**

c. 5 300 kg/m3

d. more information is needed

A solid object is made of two materials, one material having density of 2000 kg/m3 and the other having density of 6 000 kg/m3. If the object contains equal masses of the materials, what is its average density?**a. 3 000 kg/m3 – correct**

b. 4 000 kg/m3

c. 5 300 kg/m3

d. more information is needed

What is the total force on the bottom of a 2.0-m-diameter by 1.0-m-deep round wading pool due to the weight of the air and the weight of the water? (Note the pressure contribution from the atmosphere is 1.0 × 105 N/m2, the density of water is 1 000 kg/m3, and g = 9.8 m/s2.)**a. 3.4 × 105 N – correct**

b. 2.4 × 106 N

c. 3.2 × 106 N

d. 6.0 × 106 N

Which state of matter is associated with the very highest of temperatures?

a. liquid**b. plasma – correct**

c. gas

d. solid

A copper wire of length 2.0 m, cross sectional area 7.1 × 10−6 m2 and Young’s modulus 11 × 1010 N/m2 has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)

a. 0.50 mm

b. 1.0 mm

c. 2.5 mm**d. 5.0 mm – correct**

In an elastic solid there is a direct proportionality between strain and:

a. elastic modulus.

b. temperature.

c. cross-sectional area.**d. stress. – correct**

The quantity “stress” expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:

a. MLT−1**b. ML−1 T−2 – correct**

c. M2 L−1 T−3

d. a dimensionless quantity.

The quantity “strain” expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:

a. MLT−1

b. ML−1 T−2

c. M2 L−1 T−3**d. a dimensionless quantity. – correct**

In a large tank of liquid, the hydrostatic pressure at a given depth is a function of:

a. depth.

b. surface area.

c. liquid density.**d. Choices a and c are both valid. – correct**

A 15 000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.040-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?**a. 600 N – correct**

b. 1 500 N

c. 3 000 N

d. 15 000 N

By what factor is the total pressure greater at a depth of 850 m in water than at the surface where pressure is one atmosphere? (water density = 1.0 × 103

kg/m3, 1 atmosphere pressure = 1.01 × 105 N/m2, and g = 9.8 m/s2)

a. 100**b. 83 – correct**

c. 74

d. 19

If the column of mercury in a barometer stands at 72.6 cm, what is the atmospheric pressure? (The density of mercury is 13.6 × 103 kg/m3 and g = 9.80 m/s2)**a. 0.968 × 105 N/m2 – correct**

b. 1.03 × 105 N/m2

c. 0.925 × 105 N/m2

d. 1.07 × 105 N/m2

Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at the top of both dams. The Dam #2 is twice as high and twice as wide as Dam#1. How much greater is the force of the water on Dam #2 than the force on Dam#1? (Ignore atmospheric pressure; it is pushing on both sides of the dams.)

a. 2

b. 4**c. 8 – correct**

d. 16

Atmospheric pressure is 1.0 × 105 N/m2, and the density of air is 1.29 kg/m3. If the density of air is constant as you get higher and higher, calculate the height of the atmosphere needed to produce this pressure.**a. 7 900 m – correct**

b. 77 000 m

c. 1 260 m

d. 10 300 m

The water behind Grand Coulee Dam is 1 200 m wide and 150 m deep. Find the hydrostatic force on the back of the dam. (Hint: the total force = average pressure × area)

a. 5.2 × 109 N

b. 8.8 × 1010 N**c. 13.2 × 1010 N – correct**

d. 18.0 × 1010 N

How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 105 Pa)

a. 1.00 m

b. 9.80 m**c. 10.3 m – correct**

d. 32.2 m

A piece of aluminum has density 2.70 g/cm3 and mass 775 g. The aluminum is submerged in a container of oil (oil’s density = 0.650 g/cm3). How much oil does the metal displace?**a. 287 cm3 – correct**

b. 309 cm3

c. 232 cm3

d. 1 125 cm

A piece of aluminum has density 2.70 g/cm3 and mass 775 g. The aluminum is submerged in a container of oil of density 0.650 g/cm3. A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal?

a. 960 g

b. 775 g**c. 588 g – correct**

d. 190 g

A block of wood has density 0.50 g/cm3 and mass 1 500 g. It floats in a container of oil (the oil’s density is 0.75 g/cm3). What volume of oil does the wood displace?

a. 3 000 cm3**b. 2 000 cm3 – correct**

c. 1 500 cm3

d. 1 000 cm

What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 103 kg/m3 and water density = 1.0 × 103 kg/m3)**a. 7.4 × l0−4 m3 – correct**

b. 1.4 × 103 m3

c. 9.9 × 103 m3

d. 6.0 × 102 m

A ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water?

a. 1.000 N

b. 0.788 N

c. 0.516 N**d. 0.258 N – correct**

A cube of wood of density 0.78 g/cm3 is 10 cm on a side. When placed in water, what height of the block will float above the surface? (water density = 1.00 g/cm3)

a. 7.8 cm

b. 5.0 cm**c. 2.2 cm – correct**

d. 6.4 cm

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m2 and the boat’s mass is 60 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.0 × 103 kg/m3)

a. 0.060 m**b. 0.015 m – correct**

c. 0.030 m

d. 0.075 m

The bottom of a flat-bottomed aluminum boat has area = 4.0 m2 and mass = 60 kg. If two fishermen and their fishing gear with total mass of 300 kg are placed in the boat, how much lower will the boat ride in the water? (H2O density = 1.0 × 103 kg/m3)

a. 0.15 m

b. 0.090 m**c. 0.075 m – correct**

Legend says that Archimedes, in determining whether or not the king’s crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 g/cm3, and the crown’s mass is 600 g, what volume would be necessary to prove that it is pure gold?**a. 31.1 cm3 – correct**

b. 114 × 103 cm3

c. 22.8 × 103 cm3

d. 1.81 × 10−2 cm3

A solid rock, suspended in air by a spring scale, has a measured mass of 9.00 kg. When the rock is submerged in water, the scale reads 3.30 kg. What is the density of the rock? (water density = 1 000 kg/m3)

a. 4.55 × 103 kg/m3

b. 3.50 × 103 kg/m3

c. 1.20 × 103 kg/m3**d. 1.58 × 103 kg/m3 – correct**

As ice floats in water, about 10% of the ice floats above the surface of the water. If we float some ice in a glass of water, what will happen to the water level as the ice melts?

a. The water level will rise 10% of the volume of the ice that melts.

b. The water level will rise, but not as much as the 10% indicated in answer a.**c. The water level will remain unchanged. – correct**

d. The water level will become lower.

A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the:

a. weight of the stone.

b. weight of the water displaced.

c. sum of the weight of the stone and the weight of the displaced water.**d. difference between the weight of the stone and the weight of the displaced water. – correct**

A blimp is filled with 400 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3; the density of helium is 0.18 kg/m3.)

a. 111 kg

b. 129 kg

c. 215 kg**d. 444 kg – correct**

A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond?

a. It stays the same.

b. It goes up.**c. It goes down. – correct**

d. More information is needed to reach a conclusion.

A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water. What happens to the surface level of the pond?**a. It stays the same**.**– correct**

b. It goes up.

c. It goes down.

d. More information is needed to reach a conclusion.

A block of wood has specific gravity 0.80. When placed in water, what percent of the volume of the wood is above the surface?

a. 0, the block sinks.**b. 20% – correct**

c. 25%

d. 80%

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 3.0 inches, respectively. The speed of the fluid flow through the 3.0-inch section will be what factor times that through the 1.0-inch section?

a. 6.0

b. 9.0

c. 1/3**d. 1/9 – correct**

The flow rate of a liquid through a 2.0-cm-radius pipe is 0.008 0 m3/s. The average fluid speed in the pipe is:

a. 0.64 m/s.

b. 2.0 m/s.

c. 0.040 m/s.**d. 6.4 m/s. – correct**

Think of Bernoulli’s equation as it pertains to an ideal fluid flowing through a horizontal pipe. Imagine that you take measurements along the pipe in the direction of fluid flow. What happens to the sum of the pressure and energy per unit volume?

a. It increases as the pipe diameter increases.

b. It decreases as the pipe diameter increases.**c. It remains constant as the pipe diameter increases. – correct**

d. No choices above are valid.

An ideal fluid, of density 0.85 × 103 kg/m3, flows at 0.25 kg/s through a pipe of radius 0.010 m. What is the fluid speed?

a. 0.85 m/s

b. 1.3 m/s

c. 3.0 m/s**d. 0.94 m/s – correct**

Water (density = 1 × 103 kg/m3) flows at 15 m/s through a pipe with radius 0.040 m. The pipe goes up to the second floor of the building, 3.0 m higher, and the pressure remains unchanged. What is the speed of the water flow in the pipe on the second floor?**a. 13 m/s – correct**

b. 14 m/s

c. 15 m/s

d. 16 m/s

Water (density = 1 × 103 kg/m3) flows at 10 m/s through a pipe with radius 0.030 m. The pipe goes up to the second floor of the building, 2.0 m higher, and the pressure remains unchanged. What is the radius of the pipe on the second floor?

a. 0.046 m**b. 0.034 m – correct**

c. 0.015 m

d. 0.012 m

Air pressure is 1.0 × 105 N/m2, air density is 1.3 kg/m3, and the density of soft drinks is 1.0 × 103 kg/m3. If one blows carefully across the top of a straw sticking up 0.100 m from the liquid in a soft drink can, it is possible to make the soft drink rise half way up the straw and stay there. How fast must the air be blown across the top of the straw?

a. 76 m/s**b. 27 m/s – correct**

c. 19 m/s

d. 0.99 m/s

A hole is poked through the metal side of a drum holding water. The hole is 18 cm below the water surface. What is the initial speed of outflow?**a. 1.9 m/s – correct**

b. 2.96 m/s

c. 3.2 m/s

d. 3.5 m/s

Water comes down the spillway of a dam from an initial vertical height of 170 m. What is the highest possible speed of the water at the end of the spillway?

a. 15 m/s

b. 25 m/s**c. 58 m/s – correct**

d. 1 370 m/s

Water pressurized to 3 × 105 Pa is flowing at 5.0 m/s in a pipe which contracts to 1/3 of its former area. What are the pressure and speed of the water after the contraction? (Density of water = 1 × 103 kg/m3.)**a. 2 × 105 Pa, 15 m/s – correct**

b. 3 × 105 Pa, 10 m/s

c. 3 × 105 Pa, 15 m/s

d. 4 × 105 Pa, 1.5 m/s

A fountain sends water to a height of 100 m. What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 105 N/m2)

a. 1 atm

b. 4.2 atm

c. 7.2 atm**d. 9.8 atm – correct**

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,

which is 1.2 m in diameter. If the speed of flow is 3.0 m/s in the large-diameter pipe, determine the speed of flow in the test section.

a. 9.0 m/s

b. 18 m/s**c. 27 m/s – correct**

d. 1.0 m/s

A Boeing-737 airliner has a mass of 20 000 kg. The total area of the wings is 100 m2. What must be the pressure difference between the top and bottom of the wings to keep the airplane up?**a. 1 960 Pa – correct**

b. 3 920 Pa

c. 7 840 Pa

d. 15 700 Pa

How much air must be pushed downward at 40.0 m/s to keep an 800-kg helicopter aloft?

a. 98.0 kg/s**b. 196 kg/s – correct**

c. 294 kg/s

d. 392 kg/s

A jet of water flowing from a hose at 15 m/s is directed against a wall. If the mass flow in the fluid stream is 2.0 kg/s, what force is the water applying to the wall if backsplash is negligible?**a. 30 N – correct**

b. 40 N

c. 65 N

d. 127 N

A Venturi tube may be used as the inlet to an automobile carburetor. If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter, what is the pressure drop in the constricted section for airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m3.)

a. 70 Pa**b. 84 Pa – correct**

c. 100 Pa

d. 115 Pa

Water is sent from a fire hose at 30 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the water?

a. 7.5 m**b. 11 m – correct**

c. 15 m

d. 19 m

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls

a vertical distance of 100 m?**a. 980 kW – correct**

b. 98 kW

c. 4 900 W

d. 980 W

A fluid is drawn up through a tube as shown below. The atmospheric pressure is the same at both ends. Use Bernoulli’s equation to determine the speed of fluid flow out of the tank. If the height difference from the top of the tank to the bottom of the siphon is 1.0 m, then the speed of outflow is:

a. 1.1 m/s.

b. 2.2 m/s.**c. 4.4 m/s**.**– correct**

d. 8.8 m/s.

It takes 2.0 minutes to fill a gas tank with 40 liters of gasoline. If the pump nozzle is 1.0 cm in radius, what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

a. 0.27 m/s**b. 1.1 m/s – correct**

c. 11 m/s

d. 64 m/s

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm. If the nozzle has an opening of diameter 0.50 cm, and if the water leaves the nozzle at a speed of 10 m/s, what is the speed of the water inside the hose?**a. 0.63 m/s – correct**

b. 0.80 m/s

c. 2.5 m/s

d. also 10 m/s

A unit for viscosity, the centipoise, is equal to which of the following?**a. 10-3 N·s/m2 – correct**

b. 10-2 N·s/m2

c. 10-1 N·s/m2

d. 102

N·s/m2

The condition for onset of turbulent flow is that the Reynolds Number reaches what value?

a. 1 000

b. 2 000**c. 3 000 – correct**

d. 4 000

A fluid has a density of 1 040 kg/m3. If it rises to a height of 1.8 cm in a 1.0-mm diameter capillary tube, what is the surface tension of the liquid? Assume a contact angle of zero.**a. 0.046 N/m – correct**

b. 0.056 N/m

c. 0.092 N/m

A pipe carrying water has a radius of 1.0 cm. If the flow velocity is 9.0 cm/s, which of the following characterizes the flow? Take the viscosity of water to be 1.0 × 10-3 N·s/m.**a. streamlined – correct**

b. unstable

c. turbulent

d. stagnant

In order to overcome a surface tension of a fluid, a force of 1.32 × 10-2 N is required to lift a wire ring of circumference 12.0 cm. What is the surface tension of the fluid?**a. 0.055 N/m – correct**

b. 0.11 N/m

c. 0.035 N/m

d. 0.018 N/m

A pipe of diameter three cm is replaced by one of the same length but of diameter six cm. If the pressure difference between the ends of the pipe remains the same, by what factor is the rate of flow of a viscous liquid through it changed?

a. 2

b. 4

c. 8**d. 16 – correct**

Spherical particles of density 2.0 g/cm3 are shaken in a container of water (viscosity = 1.0 × 10-3 N·s/m3). The water is 8.0 cm deep and is allowed to stand for 30 minutes. What is the greatest terminal velocity of the particles still in suspension at that time?

a. 0.55 × 10-5 m/s

b 1.1 × 10-5 m/s

c. 2.2 × 10-5 m/s**d. 4.4 × 10-5 m/s – correct**

Spherical particles of density 2.0 g/cm3 are shaken in a container of water (viscosity = 1.0 × 10-3 N·s/m3). The water is 8.0 cm deep and is allowed to stand for 30 minutes. What is the radius of the largest particles still in suspension at that time?**a. 4.5 × 10-6 m – correct**

b. 9.0 × 10-6 m

c. 2.3 × 10-6 m

d. 5.6 × 10-6 m

A centrifuge rotates at 100 rev/s (i.e., 628 rad/s). If the test tube places the suspension at 8.0 cm from the axis of rotation, by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?**a. 3.2 × 102 – correct**

b. 64

c. 800

d. 3.9 × 105

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

a. It is at a maximum.

b. It is upwards.

c. It is downwards.**d. It is zero. – correct**

A vault is opened by applying a force of 300 N perpendicular to the plane of the door, 0.80 m from the hinges. Find the torque due to this force about an axis through the hinges.

a. 120 N⋅m**b. 240 N****⋅m – correct**

c. 300 N⋅m

d. 360 N⋅m

A 3.0-m rod is pivoted about its left end. A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque, and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot. The 5.2 N is at an angle of 30o to the rod and causes a cw torque. What is the net torque about the pivot?

a. 15 N·m

b. 0 N·m

c. -6.3 N·m**d. -0.6 N·m – correct**

A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F is now removed and another force F’ is applied at the midpoint of the rod. If F’ is at an angle of 30° with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

a. F

b. 2F

c. 3F**d. 4F – correct**

Two children seat themselves on a seesaw. The one on the left has a weight of 400 N while the one on the right weighs 300 N. The fulcrum is at the midpoint of the seesaw. If the child on the left is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the right?

a. 600 N·m

b. 450 N·m**c. -600 N·m – correct**

d. -450 N·m

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s2)

a. 34 N⋅m

b. 17 N⋅m**c. 11 N****⋅m – correct**

d. 23 N⋅m

A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope’s mass is negligible, that cylinder turns on friction less bearings, and that g = 9.8 m/s2.)**a. 45 N – correct**

b. 68 N

c. 90 N

d. 135 N

A uniform bridge span weighs 50.0 × 103 N and is 40.0 m long. An automobile weighing 15.0 × 103 N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the left pier provide?**a. 29.5 × 103 N – correct**

b. 35.5 × 103 N

c. 65.0 × 103 N

d. 32.5 × 103 N

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0, 0.0) m, 4.0 kg at (2.0, 0.0) m, and 5.0 kg at (2.0, 3.0) m. What is the x-coordinate of the center of gravity of this system of masses?

a. 18 m

b. 2.0 m**c. 1.2 m – correct**

d. 1.0 m

Masses are distributed in the xy-plane as follows: 10 kg at (2.0, 6.0) m, 4.0 kg at (2.0, 0.0) m, and 6.0 kg at (0.0, 3.0) m. Where would a 20-kg mass need to be positioned so that the center of gravity of the resulting four mass system would be at the origin?

a. (1.4, 3.9) m

b. (3.9, 1.4) m**c. (-1.4, -3.9) m – correct**

d. (-3.9, -1.4) m

A hoop of radius 1.0 m is placed in the first quadrant of an xy-coordinate system with its rim touching both the x-axis and the y-axis. What are the coordinates of its center of gravity?**a. (1.0, 1.0) m – correct**

b. (0.7, 0.7) m

c. (0.5, 0.5) m

d. Since there is nothing at the center of the hoop, it has no center of gravity.

Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system’s center of gravity when she sits on one end of the board. How far is she from the support point?

a. 2.0 m

b. 1.0 m**c. 0.67 m – correct**

d. 0.33 m

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, friction less wall. If the ladder has a mass of 20 kg and it makes an angle of 60° with the ground, find the force of friction of the ground on the foot of the ladder.

a. 7.8 x 102 N

b. 2.0 x 102 N

c. 50 N**d. 1.7 x 102 N – correct**

A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.40. What minimum angle can the ladder make with the floor before it slips?

a. 22°**b. 51° – correct**

c. 18°

d. 42°

4. A meter stick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 20-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

a. 20 cm

b. 70 cm**c. 30 cm – correct**

d. 25 cm

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?

a. 450 N

b. 500 N

c. 800 N**d. 850 N – correct**

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 550 N in that rope?

a. 1.4 m

b. 2.0 m**c. 2.5 m – correct**

d. 2.7 m

A woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing?

a. 4.0 m

b. 2.0 m

c. 2.7 m**d. 1.6 m – correct**

A uniform, horizontal beam of length 6.0 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60° with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium?

a. 35 N**b. 69 N – correct**

c. 60 N

d. 120 N

A uniform 1.0-N meter stick is suspended horizontally by vertical strings attached at each end. A 2.0-N weight is suspended from the 10-cm position on the stick, another 2.0-N weight is suspended from the 50 cm position, and a 3.0-N weight is suspended from the 60 cm position. What is the tension in the string attached at the 100-cm end of the stick?

a. 1.9 N

b. 3.0 N

**c. 3.5 N**

**– correct**d. 4.0 N

The quantity “moment of inertia” (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

a. ML2 T−2

b. ML.**c. ML2 – correct**

d. ML−1 T−2

.

A 4.2-kg mass is placed at (3.0, 4.0) m. Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

a. (-3.0, -4.0) m

b. (-6.0, -8.0) m

c. (-1.5, -2.0) m**d. There is no position giving this result. – correct**

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the x-axis?**a. 160 kg·m2 – correct**

b. 90 kg·m2

c. 250 kg·m2

d. 32 kg·m2

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the y-axis?

a. 160 kg·m2**b. 90 kg·m2 – correct**

c. 250 kg·m2

d. 180 kg·m2

A 4.0-kg mass is placed at (3.0, 4.0)m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the z-axis?

a. 160 kg·m2

b. 90 kg·m2**c. 250kg·m2 – correct**

d. 180 kg·m2

If a net torque is applied to an object, that object will experience:

a. a constant angular speed.**b. an angular acceleration. – correct**

c. a constant moment of inertia.

d. an increasing moment of inertia.

According to Newton’s second law, the angular acceleration experienced by an object is directly proportional to:

a. its moment of inertia.**b. the net applied torque**.**– correct**

c. the object’s size.

d. choices a and b above are both valid.

A ventilation fan with a moment of inertia of 0.034 kg⋅m2 has a net torque of 0.11 N⋅m applied to it. What angular acceleration does it experience?

a. 5.3 rad/s2

b. 4.0 rad/s2**c. 3.2 rad/s2 – correct**

d. 0.31 rad/s2

A disk has a moment of inertia of 3.0 × 10−4 kg⋅m2 and rotates with an angular speed of 3.5 rad/sec. What net torque must be applied to bring it to rest within 3 s?

a. 4.5 × 10−3 N⋅m

b. 7.5 × 10−4 N⋅m**c. 3.5 × 10−4 N****⋅m – correct**

d. 5.0 × 10−4 N⋅m

The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, which of the following best describes the Earth-Sun system’s moment of inertia?**a. decreases – correct**

b. increases

c. remains constant

d. none of the above choices are valid

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 × 10−2 kg⋅m2 and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its angular speed?

a. 0.80 rad/s

b. 10 rad/s

c. 0.050 rad/s**d. 40 rad/s – correct**

A baseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

a. 0.067 rad/s2**b. 94 rad/s2 – correct**

c. 15 rad/s2

d. 37 rad/s2

A baseball pitcher loosens up his pitching arm. He tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.32 m?**a. 1.5 × 10−2 kg****⋅m2 – correct**

b. 16 × 10−2 kg⋅m2

c. 4.0 × 10−2 kg⋅m2

d. 7.6 × 10−2 kg⋅m2

A baseball pitcher loosens up his pitching arm. He tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what torque is applied to the ball while being held by the pitcher’s hand to produce the angular acceleration?

a. 1.1 N⋅m

b. 11 N⋅m

c. 7.2 N⋅m**d. 1.4 N****⋅m – correct**

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg⋅m2. If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope’s mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)**a. 3.2 m/s2 – correct**

b. 6.3 m/s2

c. 7.4 m/s2

d. 9.8 m/s2

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?

a. 39 rad/s

b. 79 rad/s

c. 120 rad/s**d. 160 rad/s – correct**

A majorette takes two batons and fastens them together in the middle at right angles to make an “x” shape. Each baton was 0.80 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

a. 0.048 kg⋅m2**b. 0.064 kg****⋅m2 – correct**

c. 0.19 kg⋅m2

d. 0.32 kg⋅m2

A majorette takes two batons and fastens them together in the middle at right angles to make an “x” shape. Each baton was 0.80 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

a. 0.064 kg⋅m2

b. 0.096 kg⋅m2**c. 0.13 kg****⋅m2 – correct**

d. 0.32 kg⋅m

A solid cylinder (I = MR2/2) has a string wrapped around it many times. When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds. What is the downward acceleration of the cylinder as it falls?

a. 0

b. 4.9 m/s2**c. 6.5 m/s2 – correct**

d. 9.8 m/s2

A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:

a. the platform doesn’t rotate.

b. the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground.**c. the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground. – correct**

d. both go around with equal angular velocities but in opposite directions.

A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?

a. 3.70 rad/s2

**b. 7.35 rad/s2 – correct**

c. 2.45 rad/s2

d. 4.90 rad/s2

Two hoops or rings (I = MR2) are centered, lying on a turntable. The smaller ring has radius = 0.050 m; the larger has radius = 0.10 m. Both have a mass of 3.0 kg. What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

a. 0.030 kg⋅m2

b. 0.007 5 kg⋅m2**c. 0.038 kg****⋅m2 – correct**

d. 0.075 kg⋅m2

An automobile accelerates from zero to 30 m/s in 6.0 s. The wheels have a diameter of 0.40m. What is the average angular acceleration of each wheel?

a. 5.0 rad/s2

b. 15 rad/s2**c. 25 rad/s2 – correct**

d. 35 rad/s2

An object consists of a rod (of length 3.0 m and negligible moment of inertia) to which four small 2.0-kg masses are attached, one at each end and one at each point on the rod 1.0 m from each end. (The masses are one meter apart.) The moment of inertia of this object about an axis perpendicular to the rod and through one of the inner masses:

a. is 72 kg⋅m2**b. is 12 kg****⋅m2 – correct**

c. is 4 kg⋅m2

d. cannot be uniquely determined until it is stated which inner mass the axis goes through.

A ventilation fan with a moment of inertia of 0.034 kg⋅m2 has a net torque of 0.11 N⋅m applied to it. If it starts from rest, what kinetic energy will it have 8.0s later?

a. 31 J

b. 17 J**c. 11 J – correct**

d. 6.6 J

45. The total kinetic energy of a baseball thrown with a spinning motion is a function of:

a. its linear speed but not rotational speed.

b. its rotational speed but not linear speed.**c. both linear and rotational speeds. – correct**

d. neither linear nor rotational speed.

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 × 10−2 kg⋅m2 and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its total kinetic energy?

a. 45 J

b. 32 J

c. 11 J**d. 78 J – correct**

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.12 kg⋅m2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?

a. 2.1 × 103 J**b. 1.5 × 103 J – correct**

c. 0.70 × 103 J

d. 0.40 × 103 J

A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15°. It rolls to the bottom without slipping. The upper end of the ramp is 1.2 m higher than the lower end. Find the sphere’s total kinetic energy when it reaches the bottom.

a. 70 J**b. 47 J – correct**

c. 18 J

d. 8.8 J

A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15°, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR2 for a solid sphere and g = 9.8 m/s2)

a. 4.7 m/s**b. 4.1 m/s – correct**

c. 3.4 m/s

d. 2.4 m/s

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15°, and rolls to the bottom without slipping. (For a cylinder I = 0.5MR2) The upper end of the ramp is 1.2 m higher than the lower end. Find the linear speed of the cylinder when it reaches the bottom of the ramp. (g = 9.8 m/s2)

a. 4.7 m/s

b. 4.3 m/s**c. 4.0 m/s – correct**

d. 2.4 m/s

A gyroscope has a moment of inertia of 0.14 kg⋅m2 and an initial angular speed of 15 rad/s. Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque?

a. 3.3 × 10−2 N⋅m

b. 8.1 × 10−2 N⋅m

c. 14 × 10−2 N⋅m**d. 7.0 × 10−2 N****⋅m – correct**

A gyroscope has a moment of inertia of 0.140 kg⋅m2 and has an initial angular speed of 15.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 × 10−2N⋅m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

a. 150 s

**b. 105 s**

**– correct**c. 90.0 s

d. 180 s

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR2. If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy?**a. 1/l0 – correct**

b. 1/5

c. 1/2

d. 1/1

A solid sphere with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy? (For a solid sphere, I = 0.4 MR2).

a. 1/4

b. 1/2

c. 1/1**d. 2/5 – correct**

A rotating flywheel can be used as a method to store energy. If it is required that such a device be able to store up to a maximum of 1.00 × 106 J when rotating at 400 rad/s, what moment of inertia is required?

a. 50 kg⋅m2

b. 25 kg⋅m2**c. 12.5 kg****⋅m2 – correct**

d. 6.3 kg⋅m2

A rotating flywheel can be used as a method to store energy. If it has 1.0 × 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N⋅m acts on the system, in what interval of time would the flywheel come to rest?

a. 3.5 min

b. 7.0 min

c. 14 min**d. 21 min – correct**

An initially installed flywheel can store 106 J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a lighter and stronger material. If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?

a. 40 × 105 J**b. 20 × 105 J – correct**

c. 10 × 105 J

d. 5.0 × 105 J

A meter stick is hinged at its lower end and allowed to fall from a vertical position. If its moment of inertia is ML2/3, with what angular speed does it hit the table?**a. 5.42 rad/s – correct**

b. 2.71 rad/s

c. 1.22 rad/s

d. 7.67 rad/s

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (Icylinder = MR2/2). If the bus requires an average power of 10.0 kW, how long will the flywheel rotate?

a. 154 s**b. 308 s – correct**

c. 463 s

d. 617 s

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest. Its total kinetic energy at the bottom of the incline:

a. is gR/I.

b. is I/gH.

c. is 0.5 Ig/H.**d. cannot be found from the given information alone. – correct**

A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

a. the mass of the sphere.

b. the radius of the sphere.

c. the mass and the radius of the sphere.**d. no more than is given in the problem. – correct**

Consider the use of the terms “rotation” and “revolution”. In physics:

a. the words are used interchangeably.

b. the words are used interchangeably but “rotation” is the preferred word.**c. the words have different meaning. – correct**

d. “rotation” is the correct word and “revolution” should not be used.

A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

a. T.**b. more than T**. **– correct**

c. less than T.

d. requires more information than given in the problem to figure out.

The quantity “angular momentum” (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

a. MLT−2**b. ML2 T−1 – correct**

c. ML2 T−3

d. ML3 T.

A ventilation fan with a moment of inertia of 0.034 kg⋅m2 has a net torque of 0.11 N⋅m applied to it. If it starts from rest, what angular momentum will it have 8.0 s later?**a. 0.88 kg****⋅m2/s – correct**

b. 0.97 kg⋅m2/s

c. 2.0 kg⋅m2/s

d. 3.25 kg⋅m2/s

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. She then pulls her arms in close to her body. Which of the following results?

a. a smaller rotational rate**b. a greater rotational rate – correct**

c. a greater angular momentum

d. a smaller angular momentum

An ice skater spins at 2.5 rev/s when his arms are extended. He draws his arms in and spins at 6.0 rev/s. By what factor does his moment of inertia change in the process?

a. 2.4

b. 1.0**c. 0.42 – correct**

d. 0.12

A figure skater on ice with arms extended, spins at a rate of 2.5 rev/s. After he draws his arms in, he spins at 6.0 rev/s. By what factor does the skater’s kinetic energy change when he draws his arms in?**a. 2.4 – correct**

b. 1.0

c. 0.42

d. 0.12

A turntable has a moment of inertia of 3.00 × 10−2 kg⋅m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

a. 40.8 rev/min**b. 22.7 rev/min – correct**

c. 33.3 rev/min

d. 27.2 rev/min

A turntable has a moment of inertia of 3.00 × 10−2 kg⋅m2 and spins freely on a friction less bearing at 25.0 rev/min. A 0.300-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center. By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?

a. 1.22**b. 1.00 (no change) – correct**

c. 0.820

d. 1.50

A turntable has a moment of inertia of 3.0 × 10−2 kg⋅m2 and spins freely on a friction less bearing at 25 rev/min. A 0.30-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center. By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?**a. 0.91 – correct**

b. 1.0

c. 0.82

d. 1.5

A cylinder (I = MR2/2) is rolling along the ground at 7.0 m/s. It comes to a hill and starts going up. Assuming no losses to friction, how high does it get before it stops?

a. 1.2 m**b. 3.7 m – correct**

c. 4.2 m

d. 5.9 m