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college physics reasoning
Questions and Answers of
College Physics Reasoning
A child of mass 35 kg stands at the edge of a merry-go-round of mass 140 kg and radius 2.5 m, and both are initially at rest. The child then walks along the edge of the merry-goround until she
Consider the rotating diver shown in Figure P9.61. Suppose she has an angular speed of 60 rpm = 6.3 rad/s when she has her arms and legs pulled close to her body as shown (called the tuck position).
A boy of mass mboy stands at the edge of a merry-go-round of radius R = 3.5 m and mass mmgr, and both are initially at rest. The boy then walks along the edge of the merry-go-round. After walking a
The flywheel of an automobile engine is a solid disk with a mass of 8.7 kg and a radius of 22 cm and is rotating at 4000 rpm. If the entire rotational kinetic energy of the flywheel were converted to
Good approximation! Often when we apply equations to calculate moment of inertia, we are making a useful approximation, such as when we approximate a wagon wheel as a disk without a hole in the
Better approximation! There exists an item in nature that is extraordinarily spherical, where the approximation of a uniform sphere is astonishingly close. A pulsar is a rotating neutron star, the
A model of solar system formation is that the Sun condensed from a disk of gas and dust through mutual gravitational attraction (Fig. P9.65). Consider a uniform disk of gas and dust that starts with
The mechanical governor shown in Figure P9.66 was invented by James Watt (Chapter 6) to regulate and limit, through feedback, a steam engine?s maximum speed. The device consists of two spherical
A large iron cylinder of mass 270 kg rests so that its circular face rolls along the edge of a table as shown in Figure P9.67. A smaller disk (radius 11 cm) is fastened to the circular face with its
Extinction. Sixty-seven million years ago, a large asteroid impacted the Earth. It is widely accepted in the field of paleontology that this impact played a large role in a mass extinction that
Some passenger jets have one engine attached to each wing. The core of a jet engine is a rotating turbine that spins at a rate of 9,000 rpm.? (a) Estimate the angular momentum of the airplane due to
The hard drive in a laptop computer or some MP3 players contains one or more platters (spinning disks), each having an angular speed of typically 10,000 rpm, a radius of 4.0 cm, and a mass of about
The spinning platter of a computer hard disk can act as a sort of gyroscope. Some early portable MP3 players contained a single hard disk, and the angular momentum of the disk could be ?felt? when
Estimate the moment of inertia of a basketball? Table 8.2 (page 264) may be helpful. ? TABLE 8.2 Moment of Inertla for Some Common Objects Object Shape Object Shape Rod pivoted at center Hoop T = mR?
A mass m1 is connected to a pulley of radius R and mass m2 as shown in Figure P9.74. The mass m1 starts from rest and then falls through a distance h.? (a) Use conservation of energy to calculate the
A bullet of mass mb = 25 g is fired with a speed of 250 m/s at a target that is a sheet of metal (mass mt = 500 g). The target is square with sides of length L = 20 cm. The target is hinged along its
A ball rolls without slipping down the track shown in Figure P9.24, starting from rest at a height h1= 20 m as shown. The ball is traveling horizontally when it leaves the bottom of the track, which
Consider the rod in Figure P9.22, but now assume it starts from rest in the ???up??? position (i.e., pointing vertically upward from the hinge). If the rod is then given a very small push, what is
A metal rod of length L = 3.0 m is free to rotate about a friction less hinge at one end (Fig. P9.22). The rod is initially at rest and oriented horizontally and then released so that it swings to
A sphere rolls down the loop-the-loop track shown in Figure P9.21, starting from rest at a height h above the bottom. The ball travels around the inside of the circular portion of the track (radius r
When a spinning figure skater pulls her arms close to her body (Fig. 9.11), she spins faster. If she then pushes her arms away from her body, her angular velocity decreases. Her rotational kinetic
A yo-yo falls through a distance of 0.50 m as its string unwinds. If it starts from rest, what is its speed?
Some early spacecrafts used tape recorders to store data. These recorders have spools of magnetic tape that are rotated in spindles to move the tape past “heads” that record or read data. Explain
A marble rolls on the track shown in Figure P9.19, with hB= 25 cm and hC= 15 cm. If the marble has a speed of 2.0 m/s at point A, what is its speed at points B and C? Figure P9.19 ? C hB hc A
Consider a hoop of mass 3.0 kg and radius 0.50 m that rolls without slipping down an incline. The hoop starts at rest from a height h = 2.5 m above the bottom of the incline and then rolls to the
Why is it possible for a gymnast to perform more rotations during an airborne somersault when she is in a tuck position than when her body is straight (called the layout position)?
Consider a child who is jumping on a trampoline as shown in Figure Q9.14. Explain how the child can have zero angular momentum, but still rotate to either the right or the left while she is in the
Consider again the system in Figure P9.14. Use the result from Problem 9.14 to find the acceleration of one of the crates. Is the acceleration constant?Figure P9.14 moulley m1 m2
A wheel of mass 0.50 kg and radius 45 cm is spinning with an angular velocity of 20 rad/s. You then push your hand against the edge of the wheel, exerting a force F on the wheel as shown in Figure
(a) Why do most small helicopters have a rotor on their tail (Fig. Q9.17)? (b) Many large helicopters have two large rotors. Why do these helicopters not need a tail rotor? Do you think the two large
The barrel of a rifle contains spiral grooves that impart some spin to a bullet as it leaves the barrel. Explain why this spin improves the rifle’s accuracy.
For the system of two crates and a pulley in Figure P9.14, what fraction of the total kinetic energy resides in the pulley? Figure P9.14 mpulley N m2
The cat in Figure 9.21 undergoes free fall due to the force of gravity. Explain why we did not consider gravity when we discussed how the cat in Figure 9.21 managed to land on its feet.Figure 9.21
A marble (radius 1.0 cm and mass 8.0 g) rolls without slipping down a ramp of vertical height 20 cm. What is the speed of the marble when it reaches the bottom of the ramp?
Two crates of mass m1= 15 kg and m2= 9.0 kg are connected by a rope that passes over a frictionless pulley of mass mp= 8.0 kg and radius 0.20 m as shown inFigure P9.14. (a) What force(s) can do
Many kilograms of asteroids land on the Earth each year. Discuss how they affect the length of a day.
What is the ratio of the rotational kinetic energy of the Earth to the rotational kinetic energy of the Moon as they spin about their axes?
Discuss how and if the moment of inertia of the Earth associated with its orbital motion around the Sun changes as the Earth moves through its orbit. How are these changes connected to changes in the
What is the rotational kinetic energy of the Earth as it spins about its axis?
The fly wheel within a car engine is a form of gyroscope, and when rotating at high rpm, it carries significant angular momentum.(A car fly wheel is just a disk attached to the engine’s main
Estimate the fraction of a bicycle’s total kinetic energy associated with the rotational motion of the wheels. Consider the kinetic energy of the bicycle and not that of the rider.
Explain why the rim brakes on a bicycle wheel are located at the outer edge of the wheel instead of near the hub. Consider the work–energy theorem (Eq. 9.9) and how the magnitude of the torque
Two balls (solid spheres) have the same radius and the same rotational kinetic energy. If the ratio of their masses is 3:1, what is the ratio of their angular velocities?
You are given the job of designing a new high-tech skateboard. For it to travel as fast as possible, you want to minimize the kinetic energy in its wheels. All else being equal (i.e., the mass and
Estimate the rotational kinetic energy of an airplane propeller.
Is it possible for the total force on a system to be nonzero but the torque to be zero? Give an example.
An automobile wheel has a mass of 18 kg and a diameter of 0.40 m. What is the total kinetic energy of one wheel when the car is traveling at 20 m/s?
Tightrope walkers often carry a long pole (Fig. Q9.7). Explain why. Figure Q9.7
Consider a wheel on a racing bicycle for an adult. If the wheel has a mass of 0.40 kg and an angular speed of 15 rad/s, what is the rotational kinetic energy of the wheel?
You are given two objects and a ramp. Explain how you could measure the ratio of the moments of inertia of the two objects. Assume the two objects are both round (so that both roll), have the same
It has been proposed that large flywheels could be used to store energy. Consider a flywheel made of concrete (density 2300 kg/m3) in the shape of a solid disk, with a radius of 10 m and a thickness
Consider the transnational and rotational kinetic energies of a disc that rolls without slipping. Show that the ratio of these energies is independent of the size (the radius) of the wheel.
Estimate the maximum rotational kinetic energy of a yo-yo. Use a rotation axis that passes through the yo-yo’s center.
Two objects having different shapes start from rest from the top of a long ramp. Both then roll without slipping down the ramp, and one reaches the bottom before the other. Which object has the
Two identical spheres start from rest at the top of a long ramp. One ball rolls down the ramp without slipping, while the other slides down without rolling. Which one reaches the bottom first?
Consider a quarter rolling down an incline. What fraction of its kinetic energy is associated with its rotational motion? Assume it rolls without slipping.
A pitcher throws a baseball (mass m = 0.14 kg, r = 7.4 cm) with linear speed v and angular velocity v. Which of the following statements is correct? Explain your answer. (a) The total kinetic
If the baseball in Problem 1 has a linear speed of 45 m/s, what is the ratio of its rotational and transnational kinetic energies?Data From Problem 1A baseball (mass 0.14 kg, radius 3.7 cm) is
A baseball (mass 0.14 kg, radius 3.7 cm) is spinning with an angular velocity of 60 rad/s. What is its rotational kinetic energy?
A steel ball bearing will float in mercury as shown in Figure P10.78. What fraction of the ball bearing’s volume is above the surface of the mercury?Figure P10.78
When an airplane is flying at a typical cruising altitude of 30,000 ft, the cabin pressure is typically about 75% of atmospheric pressure at ground level. What is the approximate force on one of the
Artesian well. In some places, the water underground is at a pressure high enough that it will flow up and out of the ground without the need of a pump. Figure P10.99A shows an example, which is
The water in the author’s house is provided by a well. Water is pumped from the well to a holding tank in the basement that is pressurized so that water can flow from the tank to the upper floors
Measuring air speed. An airplane pilot must always know her speed relative to the surrounding air. Air speed that is too low can cause the plane to stall, whereas air speed that is too high can cause
Collapsing submarines. The collapse depth of a typical military submarine—that is, the depth at which the submarine would be crushed by the force due to water pressure—is 700 m. If the pressure
(a) Water flows out of a shower in a typical house at a rate of 20 liters/min. If this shower is fed through a pipe that is 2.0 cm in diameter and 15 m from the high-pressure water tank, what is the
A backyard waterfall used in landscaping (Fig. P10.94) has water cascading down at a rate of 18 liters/min. (a) If the waterfall is fed using a hose of diameter 2.5 cm, what is the speed of
A window in a house is rectangular, with height 40 cm and width 30 cm. The pressure inside the house is normal atmospheric pressure when a hurricane arrives and the wind speed outside is 75 m/s
You can make a rough estimate of the thickness of the Earth’s atmosphere by assuming its density is constant with the value 1.3 kg/m3. How tall must the atmosphere be to give the observed pressure
In Example 10.11, we considered how the pressure ΔP across the ends of a narrowed blood vessel must increase to keep the average flow speed constant. If we instead want the smaller blood vessel to
Blood pressure is measured at the brachial artery in the upper arm (Fig. P10.89). An inflatable strap is pumped with air until the artery is collapsed, stopping all flow. The pressure in the cuff is
Pulmonary surfactant. Oxygen enters the blood in the hollow and roughly spherical alveoli of the lungs. The alveoli are small, approximately 170 mm in radius (Fig. P10.88), yet some 300 million of
Snorkeling elephants. An elephant can use its long trunk as a snorkel while swimming or walking across the bottom of rivers (Fig. P10.86). The lining of an elephant???s lung is reinforced with
A scuba diver swims in a freshwater lake (Fig. P10.85).? (a) If the maximum pressure in her tanks is 10 atm, to what depth h could she swim and still breathe?? (b) Could she go deeper in the ocean?
Long snorkel. Inhalation of a breath occurs when the muscles surrounding the human lungs move to increase the volume of the lungs, thereby reducing the air pressure there. The difference between the
Consider a faucet with water running out in a smooth stream. How could one find the flow rate in cubic centimeters per second by simply taking measurements with a ruler? Following the diagram in
Before fuel injection. Some automobile engines (mainly older ones) use a carburetor to make the liquid fuel into vapor and mix it with air for combustion. The basic principle of carburetion is shown
Drawing (up) the longest straw. Consider a contest where the challenge is to find the greatest height from which the contestant in Figure P10.81 is able to drink water through a straw. Find the
A small, square plank of oak floats in a beaker half full of water. The piece of oak is 6.0 cm on a side and 3.0 cm thick and floats on its side as shown in Figure P10.80. (a) Find the location
What will happen if water is poured on top of the mercury and ball bearing of Problem 78 such that the ball bearing is completely submerged in the water? Will the ball bearing (a) sink farther into
Blood flows through an artery of diameter d and length L, and the pressure difference between the ends of the artery is ΔP. If the diameter is reduced by a factor of two and the pressure difference
Estimate the terminal speed of a DNA molecule in water. Assume the only forces on the molecule are gravity and the Stokes drag force (Eq. 10.33).
The viscosity of normal (healthy) blood is about three times greater than the viscosity of water. Certain diseases such as polycythemia can cause the viscosity of blood to be as much as three times
A glass capillary tube with a radius of 0.050 mm is inserted into an open container filled with an unknown liquid, and the meniscus has an appearance similar to Figure 10.35A. It is found that the
Repeat Problem 72, but now for a tube of radius 10 nm. Express your answer in pascals and as a ratio relative to atmospheric pressure.Data from Problem 72What is the capillary pressure for water in a
What is the capillary pressure for water in a vertical tube of diameter 0.10 mm?
Estimate the terminal speed for a dust particle in air. Assume it has a radius of 1.0 mm and a density similar to that of balsa wood. Your answer will tell you why dust particles remain
A glass sphere of radius 1.0 mm is dropped into a lake. What is the terminal speed of the sphere?
An air duct in a building has a radius of 10 cm and a length of 10 m. What pressure is required to push air through the duct at a flow rate of 1.0 m3/s?
A blood vessel is 20 cm long and has a radius of 2.0 mm. If blood is flowing through it with a volume flow rate of 2.0 × 10–7 m3/s, what is the difference in the pressures at the two ends of
A fire extinguisher contains a high-pressure liquid so that it can spray the liquid out very quickly when needed. If the fluid leaves a fire extinguisher at a speed of 20 m/s, what is the pressure
The flow rate through a blood vessel is found to be 1.5 × 10–7 m3/s. Express this flow rate in units of cubic centimeters per second.Assume an ideal fluid (i.e., a fluid with no viscosity).
A Frisbee is observed to fly nearly horizontally, which implies that the lift force must be approximately equal to the weight of the Frisbee. If the air speed over the top of the Frisbee is 9.0 m/s,
Consider an airplane wing of area 20 m2. If the airflow speed over the top of the wing is 200 m/s, while the speed across the bottom is 150 m/s, what is the lift force on the wing at sea level at
Consider a large blood vessel that carries blood to the heart. If this blood vessel has a cross-sectional area of 1.5 cm2 and the blood speed is 30 cm/s, what volume of blood is delivered in 1.0
A house sits in a valley and is 30 m lower than the water tower that serves it. What is the speed of water when it sprays out of a shower in the house?Assume an ideal fluid (i.e., a fluid with no
A tank of water sits at the edge of a table of height 1.2 m (Fig. P10.61). The tank springs a very small leak at its base, and water sprays out a distance of 1.5 m from the edge of the table. What is
It takes the author about 60 s to fill his truck with gasoline (48 liters, about 12 gal). (a) What is the flow rate in cubic meters per second? (b) Estimate the speed of the gasoline as it
The blood flow rate through the aorta is typically 100 cm3/s, and a typical adult has about 5.0 liters of blood. (a) How long does it take for all your blood to pass through the aorta? (b)
Water is flowing through a pipe (area 4.0 cm2) that connects to a faucet adjusted to have an opening of 0.50 cm2. If the water is flowing at a speed of 5.0 m/s in the pipe, what is its speed as it
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