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college physics reasoning

Questions and Answers of College Physics Reasoning

A Ferris wheel is moving at an initial angular velocity of 1.0 rev/30 s. If the operator then brings it to a stop in 3.0 min, what is the angular acceleration of the Ferris wheel? Express your answer
You like to swim at a nearby lake. On one side of the lake is a cliff, and the top of the cliff is 6.5 m above the surface of the lake. You dive off the cliff doing somersaults with an angular speed
Consider again the DVD in Problem 60. As was explained in Example 8.2, the data on the DVD are encoded in a long spiral “track,” where the spacing between each turn of the track is 0.74 mm and
Consider the DVD in Example 8.2. This DVD player is turned on at t - 0 and very quickly starts to play a video so that the DVD has an angular velocity of 1500 rpm just a few seconds after t - 0. The
For the system in Figure P8.58, if the coefficient of friction between crate 1 and the table is µK= 0.15, what is the acceleration? Figure P.58 ? mpulley m1 m2
Two crates of mass m1= 15 kg and m2= 25 kg are connected by a cable that is strung over a pulley of mass mpulley= 20 kg as shown in Figure P8.58. There is no friction between crate 1 and the
Two crates of mass 5.0 kg and 9.0 kg are connected by a rope that runs over a pulley of mass 4.0 kg as shown in Figure P8.57.? (a) Make a sketch showing all the forces on both crates and the
Construct a graph of the angular velocity of a car wheel as a function of time. (a) Assume the wheel starts from rest and moves with a constant (center of mass) velocity. (b) Assume the car
A potter’s wheel of radius 0.20 m is turned on at t = 0 and accelerates uniformly. After 60 s, the wheel has an angular velocity of 2.0 rad/s. Find the angular acceleration and the total angular
Construct a plot of the angular displacement of a CD as a function of time. Use information from this chapter to attach quantitative labels (numbers and units) to your graph. Take t = 0 to be the
A ceiling fan of radius 45 cm runs at 90 rev/min. How far does the tip of the fan blade travel in 1 hour?
Figure P8.52 shows the angular displacement of an object as a function of time. (a) What is the approximate angular velocity of the object at t = 0? (b) What is the approximate angular velocity at t
Figure P8.51 shows the angular displacement of an object as a function of time. What is the approximate angular velocity of the object? Figure P8.51 ? 0 (rad) 1- 0!2 t (s) 0.31 10- 0.1 3. 2.
Estimate the moment of inertia of a baseball bat for the following cases. (a) Assume the bat is a wooden rod of uniform diameter and take the pivot point to be (i) in the middle of the bat, (ii)
The moment of inertia for a square plate of mass M and length L that rotates about an axis perpendicular to the plane of the plate and passing through its center is ML2/6 (Fig. P8.49A). What is the
In our examples with CDs (such as Example 8.7), we usually ignored the hole in the center. Calculate the moment of inertia of a CD, including the effect of the hole. For a CD of radius 6.0 cm,
Consider two cylinders with the same density and the same length. If the ratio of their diameters is 1.5/1, what is the ratio of their moments of inertia?
If the mass of a wheel is increased by a factor of 2 and the radius is increased by a factor of 1.5, by what factor is the moment of inertia increased? Model the wheel as a solid disc.
Estimate the moment of inertia of a bicycle wheel.
Which has a larger moment of inertia, a disc of mass 20 kg or a hoop of mass 15 kg with the same radius?
Consider a merry-go-round that has the form of a disc with radius 5.0 m and mass 100 kg. If three children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment
Four particles with masses m1= 15 kg, m2= 25 kg, m3= 10 kg, and m4= 20 kg sit on a very light (mass less) metal sheet and are arranged as shown in Figure P8.42. Find the moment of inertia of this
Two particles of mass m1 = 15 kg and m2 = 25 kg are connected by a massless rod of length 1.2 m. Find the moment of inertia of this system for rotations about the following pivot points: (a) the
A flagpole of length 12 m and mass 30 kg is hinged at one end, where it is connected to a wall as sketched in Figure P8.40. The pole is held up by a cable attached to the other end. Find the tension
Consider again the ladder in Figure P8.38. We saw in Problem 8.38 that the force supplied by the person increases with increasing angle ?? as the ladder is initially lifted off the ground. When the
One way to put a ladder in place on a wall is to ???walk??? the ladder to the wall. One end of the ladder is held fixed (perhaps at the base of the wall), and a person slides his hands along the
Wheelbarrows are designed so that a person can move a massive object more easily than if he simply picked it up. If the person using the wheelbarrow in Figure P8.37 is able to apply a total vertical
Repeat Problem 34, but assume the force F is applied at the corner of the cube and at an angle of 30° above the horizontal direction. At what value of F will the crate begin to tip? Data from
Consider again the cube in Problem 34 (Fig. P8.34), but now assume the force is applied along a horizontal line that is 0.20 m above the floor. At what value of F will the crate begin to tip? Figure
A solid cube of mass 40 kg and edge length 0.30 m rests on a horizontal floor as shown in Figure P8.34. A person then pushes on the upper edge of the cube with a horizontal force of magnitude F. At
Consider the ladder in Example 8.5 and assume there is friction between the vertical wall and the ladder, with µS = 0.30. Find the angle ϕ at which the ladder just begins to slip.
Consider again the ladder in Figure P8.30 and imagine two scenarios. In both scenarios the ladder is in rotational equilibrium.? (1) There is no friction between the ladder and the floor, and there
Consider again the ladder in Problem 30. What is the sign of the torque on the ladder due to the force from the wall? Data from Problem 30 A painter is standing on the ladder (mass 40 kg and length
A painter is standing on the ladder (mass 40 kg and length 2.5 m) in Figure P8.30. There is friction between the bottom of the ladder and the floor with µS= 0.30, but there is no friction between
Consider the flagpole in Figure P8.29. If the flagpole has a mass of 20 kg and length 10 m and the angle the cable makes with the pole is ?? = 25°, what are the magnitude and direction of the force
The seesaw in Figure P8.28 is 4.5 m long. Its mass of 20 kg is uniformly distributed. The child on the left end has a mass of 14 kg and is a distance of 1.4 m from the pivot point while a second
Suppose a crate of mass 7.5 kg is placed on the plank in Figure P8.27 at a distance 3.9 m from the left end. If the plank has a mass of 12 kg, find the forces exerted by the two supports on the
A uniform wooden plank of mass 12 kg rests on two supports as shown in Figure P8.26. The plank is at rest, so it is in transnational equilibrium and rotational equilibrium.? (a) Make a sketch showing
A uniform pole of length 2.0 m and mass 4.5 kg hangs horizontally from two cables as shown in Figure P8.25. What are the approximate tensions in the two cables? Figure P8.25 ?
A baseball player holds a bat at the end of the handle. If the bat is held horizontally, what is the approximate torque due to the force of gravity on the bat, with a pivot point at the batter’s
A tree grows at an angle of 50° to the ground as shown in Figure Q8.5. If the tree is 25 m from its base to its top and has a mass of 500 kg, what is the approximate magnitude of the torque on the
A difficult maneuver for a gymnast is the ???iron cross,??? in which he holds himself as shown in Figure P8.22. Estimate the torque on the gymnast due to gravity. Choose a rotation axis that passes
If the length of the pole in Problem 20 is increased by a factor of three and its mass is increased by a factor of two, by what factor does the torque change? Data from Problem 20 A person carries a
A person carries a long pole of mass 12 kg and length 4.5 m as shown in Figure P8.20. Find the magnitude of the torque on the pole due to gravity. Figure P8.20 ? 60°
A rod of length 3.8 m is hinged at one end, and a force of magnitude F = 10 N is applied at the other (Fig. P8.19).? (a) If the magnitude of the torque associated with this force is 18 N · m, what
Consider the clock in Figure 8.17. Calculate the magnitude and sign of the torque due to gravity on the hour hand of the clock at 4 o???clock. Assume the hand has a mass of 15 kg, a length of 1.5 m,
Consider again the diver in Figure P8.16. Assume the diving board now has a mass of 30 kg. Find the total torque due to gravity on the diving board. Assume the mass of the board is uniformly
A diver stands at rest at the end of a massless diving board as shown in Figure P8.16.? (a) If the mass of the diver is 120 kg and the board is 4.0 m long, what is the torque due to gravity on the
Consider a race car that moves with a speed of 200 mi/h. If it travels on a circular race track of circumference 2.5 mi, what is the car’s angular speed?
Construct a graph of the angular displacement of the minute hand of a clock as a function of time. The axes of your graph should include quantitative scales (i.e., numbers and units). What is the
What are the angular velocity and the period of the second hand of a clock? If the linear speed of the end of the hand is 5.0 mm/s, what is the clock’s radius?
An adult is riding on a carousel and finds that he is feeling a bit nauseated. He then decides to move from the outer edge of the carousel to a point a distance r2 from the center so that his linear
Mercury orbits the Sun with a period of approximately 88 days. What is the angular speed of Mercury’s orbital motion?
Mercury spins about its axis with a period of approximately 58 days. What is the rotational angular speed of Mercury?
What is the angular speed with respect to the Earth’s rotation axis of a person standing (a) At the equator? (b) At a latitude of 45°?
What is the angular speed of the Earth’s center of mass as it orbits the Sun?
A car engine is initially rotating at 200 rad/s. It is then turned off and takes 3.0 s to come to a complete stop. What is the angular acceleration of the engine? Assume α is constant.
The tachometer in the author’s car has a maximum reading of 8000 rpm. (A tachometer is a gauge that shows the angular speed of a car’s engine.) Express this angular speed in rad/s.
Consider again the record in Problem 3. If it plays music for 20 min, how far does a point on the edge travel in meters?Data from Problems 3.An old-fashioned (vinyl) record rotates at a constant rate
The angular speed of the shaft of a car’s engine is 360 rad/s. How many revolutions does it complete in 1 hour?
An old-fashioned (vinyl) record rotates at a constant rate of 33 rpm. (a) What is its angular speed in rad/s? (b) If the record has a radius of 18 cm, what is the linear speed of a point on
The shaft on an engine turns through an angle of 45 rad. (a) How many revolutions does the shaft make? (b) What is this angle in degrees?
An angle has a value of 85°. What is the angle in radians?
In Section 8.6, we found that for a uniform baseball bat, the sweet spot is a distance L/6 from the center of the bat. A real bat is not uniform; it is much thinner in the handle than in the barrel
Consider a wheel that rolls without slipping such as the wheel in Figure 8.34. We have seen that slipping is prevented by the force of static friction between the wheel and the pavement. Can this
Explain why it is easier (it requires a smaller force) to open a large jar than a small one.
Bodybuilders do an exercise called “curls” in which they lift a weight by bending at the elbow. Explain why the torque on the elbow is largest when the arm is horizontal.
A force of magnitude F is applied to a rod at various spots and at various angles (Fig. Q8.16). In which case, (1), (2), or (3), is the magnitude of the torque largest? Smallest?Figure Q8.16 Hinge 3)
A tree has two large branches that grow out horizontally from the trunk in opposite directions. One branch has length L and diameter d, whereas the other has length L/2. If the magnitude of the
A tree has a large branch that grows horizontally out from the trunk. If the branch doubles in length and doubles in diameter, by what factor does the torque on the branch due to gravity increase?
A tennis racket possesses a sweet spot in close analogy to that of a baseball bat. One might expect that rackets are designed so that the sweet spot is in the center of the strings. Somewhat
In about 200 BCE, Archimedes made the statement, “Give me a lever long enough and a place to stand, and I will move the Earth.” Assume he can exert a force equal to his weight on the Earth (about
Three types of levers. Levers can be classified as first, second, or third class, depending on how the load force (F(vector)L) and effort force (F(vector)E) are configured with respect to the pivot
Two meter sticks, one with a weight attached to its end, are held with one of their ends in the corner formed by the floor and a wall as depicted in Figure Q8.10. If the ends of the meter sticks are
A snap of the wrist will usually detach a paper towel from a roll. Why does that almost always work for a full roll, yet an almost empty roll often gives much more than a single sheet?
A mechanic???s toolbox contains the two wrenches and two screwdrivers shown in Figure Q8.8. While working on her vintage car, the mechanic comes across a stubborn and rusted bolt. Which wrench would
Two golfers team up to win a golf tournament and are awarded a solid gold golf club. To divide their winnings, they balance the club on a finger and then cut the club into two pieces at the balance
In our analysis of a rollover car accident in Example 8.6, we treated the car in a very simplified way. Develop a more realistic model of a car with special attention to the height of its center of
The tree in Figure Q8.5 experiences a large torque due to the force of gravity, yet it is in static equilibrium. What additional torque balances the torque due to gravity?Figure Q8.5 50°
According to Table 8.2, the moment of inertia for a rod that rotates about an axis perpendicular to the rod and passing through one end is I = ML2/3; if the axis passes through the center of the rod,
A hoop and a disk have the same radius and the same moment of inertia. What is the ratio of their masses?
Two disks, each of mass m, have radii R and 2R and are mounted on axles that pass through their centers. (a) Which disk has the larger moment of inertia? (b) If a force of magnitude F is applied at
Explain why placing your hands behind your head rather than placing them on your stomach makes sit-ups more difficult.
Match each of the examples of motion in Problem 22 to one of the velocity???time graphs shown in Figure P2.23. Figure P2.23 ? t Case 1 Case 2 t Case 3 Case 4
A railroad car (m = 3000 kg) is coasting along a level track with an initial speed of 25 m/s. A load of coal is then dropped into the car as sketched in Figure 7.19.? (a) Treat the railroad car plus
An airplane is sent on a rescue mission to help a stranded explorer near the South Pole. The plane cannot land, but instead drops a supply package of mass m = 60 kg while it is flying horizontally
Figure P7.45 shows several arrangements of blocks. In cases 1 through 3, the blocks all have the same mass, but in case 4, one of the blocks has a mass twice that of the other two blocks. Find the
Estimate the location of the center of mass of the thin metal plate in Figure P7.46. Assume the grid lines are spaced 1 cm apart in both the x and y directions. Figure P7.46 ? -y- +5 =5. 5.
Consider the Sun and the Earth as a “system” of two “particles.” The center of mass of this system lies a distance L from the center of the Sun. Find L and compare it to the radius of the Sun.
A block of wood (Mblock = 5.2 kg) rests on a horizontal surface for which the coefficient of kinetic friction is 0.28. A bullet (mbullet = 32 g) is shot along the horizontal direction and quickly
Consider again the collision between two hockey pucks in Figure P7.24, but now they do not stick together. Their speeds before the collision are v1i= 20 m/s and v2i= 15 m/s. It is found that after
Consider the motion of the two ice skaters in Figure 7.28 and assume they have masses of 60 kg and 100 kg. If the larger skater has moved a distance of 12 m from his initial position, where is the
A person of mass 90 kg standing on a friction less, horizontal surface fires a bullet of mass 40 g in a horizontal direction. After the bullet has traveled a distance of 50 m, what distance has the
Consider the motion of an apple and the Earth as the apple falls to the ground. If the apple begins at the top of a tree of height 15 m, how much does the Earth move?
A bomb that is initially at rest at the origin explodes and breaks into two pieces of mass m1= 1500 kg and m2= 2500 kg as shown in Figure P7.50. If piece 1 has a velocity of +35 m/s directed along x,
A hand grenade is thrown with speed v0= 30 m/s, as sketched in Figure P7.51, just prior to exploding. It breaks into two pieces of equal mass after the explosion. One piece has a final velocity of 40
The ballistic pendulum. A bullet of mass m = 30 g is fired into a wooden block of mass M = 5.0 kg as shown in Figure P7.52. The block is attached to a string of length 1.5 m. The bullet is embedded
A rock of mass 30 g strikes a car windshield while the car is traveling on a highway. Estimate the force of the rock on the windshield. You will need to estimate the collision time (i.e., the time
Two particles of mass 2.3 kg and mass 4.3 kg that are free to move on a horizontal track are initially held at rest so that they compress a spring as shown in Figure P7.54. The spring has a spring
A tennis ball of mass 0.12 kg is dropped vertically onto a hard concrete floor from a height of 1.5 m. The ball then bounces up to some maximum height h. If the ball bounces up to a height h = 1.0 m,

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