Physics test 3

An ice skater with rotational inertia I0 is spinning with angular speed 0. She pulls her arms in, thereby increasing her angular speed to 4 0. Her rotational inertia is then a. I0 b. I0/2 c. 2I0 d. I0/4 e. 4I0

D

Block A has a mass m and block B has a mass 2m. Block A is pressed against a spring to compress the spring by a distance x. It is then released such that the block eventually separates from the spring and it slides across a surface where the friction coefficient is μk. The same process is applied to block B. Which one of the following statements concerning the distance that each block slides before stopping is correct? a) Block A slides one-fourth the distance that block B slides. b) Block A slides one-half the distance that block B slides. c) Block A slides the same distance that block B slides. d) Block A slides twice the distance that block B slides. e) Block A slides four times the distance that block B slides.

D

A block is attached to a horizontal spring. On top of this block rests another block. The two-block system slides back and forth in simple harmonic motion on a frictionless horizontal surface. At one extreme end of the oscillation cycle, when the blocks come to a momentary halt, the top block is lifted vertically upward, without disturbing the bottom block. What happens to the amplitude and the angular frequency of the ensuing motion? a. The amplitude remains the same, and the angular frequency increases. b. The amplitude increases, and the angular frequency remains the same. c. Both the amplitude and the angular frequency increase. d. Both the amplitude and the angular frequency decrease e. Boththeamplitudeandtheangularfrequencyremainthesame.

A

A block is attached to a horizontal spring. On top of this block rests another block. The two-block system slides back and forth in simple harmonic motion on a frictionless horizontal surface. At one extreme end of the oscillation cycle, when the blocks come to a momentary halt, the top block is lifted vertically upward, without disturbing the bottom block. What happens to the amplitude and the angular frequency of the ensuing motion? a. The amplitude remains the same, and the angular frequency increases. b. The amplitude increases, and the angular frequency remains the same. c. Both the amplitude and the angular frequency increase. d. Boththeamplitudeandtheangularfrequencydecrease e. Both the amplitude and the angular frequency remain the same.

A

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring's unstrained position by a distance x0 and given an initial speed of v0 as it is released. Which one of the following parameters must be known in addition to x0 and v0 to determine the amplitude of the subsequent simple harmonic motion? a) period b) spring constant c) mass of the block d) the direction of the initial velocity of the block e) the direction of the initial displacement of the block

A

A constant torque of 20 N·m acts on a flywheel. If the flywheel makes 25 complete revolutions, how much work as been done by the torque on the flywheel? a. 1000 J b. 500 J c. -500 J d. -1000 J e. 250 J

A

A force of 250 N is applied to a hydraulic jack piston that is 0.02 m in diameter. If the piston that supports the load has a diameter of 0.15 m, approximately how much mass can be lifted by the jack? Ignore any difference in height between the pistons. a. 1400 kg b. 700 kg c. 2800 kg d. 5600 kg e. 250 kg

A

A glass beaker, filled to the brim with water, is resting on a scale. A solid block is then placed in the water, causing some of it to spill over. The water that spills is wiped away, and the beaker is still filled to the brim. How do the initial readings and final readings on the scale compare if the block is made from wood (whose density is less than that of water)? Iron (whose density is greater than that of water)? a. The initial reading is less than the final reading b. The initial reading is greater than the final reading c. The initial reading is the same as the final reading.

A

A solid sphere of radius R rotates about an axis that is tangent to the sphere with an angular speed . Under the action of internal forces, the radius of the sphere increases to 2R. What is the final angular speed of the sphere? a) W/4 b) W/2 c) W d) 2W e) 4W

A

A steel ball is hung from a vertical ideal spring where it oscillates in simple harmonic motion with an amplitude of 0.157 m and an angular frequency of rad/s. Which one of the following expressions represents the acceleration, in m/s2, of the ball as a function of time? a) a = 1.55 cos(3.14t) b) a = 1.55 cos2(3.14t) c) a = 0.157 cos(3.14t) d) a = 0.493 cos2(3.14t) e) a = 0.493 cos(3.14t)

A

A woman is sitting on the spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. As she extends her arms outward, the MOMENT OF INERTIA a. Increases b. Decreases c. Remains the same

A

An interesting method for exercising a dog is to have it walk on the rough surface of a circular platform that freely rotates about its center as shown. When the dog begins walking near the outer edge of the platform as shown, how will the platform move, if at all? Assume the bearing on which the platform can rotate is frictionless. a) When the dog walks clockwise, the platform will rotate counterclockwise when viewed from above. b) When the dog walks clockwise, the platform will rotate clockwise when viewed from above. c) When the dog walks clockwise or counterclockwise, the platform will not rotate.

A

At the surface of Mars, the acceleration due to gravity is 3.71 m/s2. On Earth, a pendulum that has a period of one second has a length of 0.248 m. What is the length of a pendulum on Mars that oscillates with a period of one second? a) 0.0940 m b) 0.143 m c) 0.248 m d) 0.296 m e) 0.655 m

A

Consider the following three objects, each of the same mass and radius: (1) a solid sphere (2) a solid disk (3) a hoop All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline? a) 1, 2, 3 b) 2, 3, 1 c) 3, 1, 2 d) 3, 2, 1 e) All three reach the bottom at the same time.

A

In snowy regions of the world, the local people may wear snow shoes below their normal shoes or boots. These snow shoes have a much larger area than a regular shoe or boot. How does a snow shoe improve a hiker's ability to walk across a snowy region? a) The hiker's weight is distributed over the area of the snow shoes, which reduces the pressure on the snow below and minimizes sinking into the snow. b) The snow shoes increase the normal force of the snow on the hiker. c) The snow shoes increase the upward pressure of the snow on the hiker. d) The snow shoes compact the snow making it harder to sink into it. e) The hiker's weight is reduced by wearing large area snow shoes.

A

In the figure, the block has a kinetic energy of 3 J and the spring has an elastic potential energy of 2 J when the block is at x = +2.0 cm. What is the elastic potential energy when the block is at x = -2.0 cm? Note: xm is the amplitude. Ignore the effects of friction. a. 2J b. 3J c. 4J d. 5J e. 6J

A

In the figure, the block has a kinetic energy of 3 J and the spring has an elastic potential energy of 2 J when the block is at x = +2.0 cm. What is the elastic potential energy when the block is at x = -2.0CM? Note: xm is the amplitude. Ignore the effects of friction. a. 2J b. 3J c. 4J d. 5J e. 6J

A

Suppose the thin hoop and a solid disk in the figure have the same mass and radius. The same force F is applied tangentially to the edge of each object as shown and each object begins to rotate about their center of mass. Which object has the greater ROTATIONAL INERTIA? Note: you can solve this problem without using the equations in table 10-2. a. Thin hoop b. Solid disk c. Tie

A

The corner of a rectangular piece of wood is attached to a rod that is free to rotate as shown. The length of the longer side of the rectangle is 4.0 m, which is twice the length of the shorter side. Two equal forces with magnitudes of 22 N are applied to two of the corners. What is the magnitude of the net torque on the block and direction of rotation, if any? a) 44 Nm, clockwise b) 44 Nm, counterclockwise c) 88 Nm, clockwise d) 88 Nm, counterclockwise e) zero Nm, no rotation

A

The drawing shows three containers filled to the same height with the same fluid. In which container, if any, is the pressure at the bottom greatest? a. All three containers have the same pressure at the bottom. b. ContainerC,becauseitsbottomhastheleastsurfacearea. c. Container B, because it has the least volume of fluid. d. Container A, because its bottom has the greatest surface area. e. Container A, because it has the greatest volume of fluid.

A

The input piston and output plunger of a hydraulic car lift are at the same level, as shown in the drawing. The cross-sectional area of the input piston is 12 cm2, while that of the output plunger is 1200 cm2. The F1 applied to the input piston has a magnitude of 130 N. What is the weight W of the car? Neglect the weight of the piston and plunger. a. 13,000N b. 130,000 N c. 156,000 N d. 1,560 N e. 1.3N

A

Three massless rods (A, B, and C) are free to rotate about an axis at their left end (see the drawing). The same force is applied to the right end of each rod. Objects with different masses are attached to the rods, but the total mass (3m) of the objects is the same for each rod. Rank the angular acceleration of the rods, largest to smallest. a. A, B, C b. B, C, A c. C, B, A d. B, A, C e. none of these

A

Two thin rods of length L are rotating with the same angular speed about axes that pass perpendicularly through one end. Rod A is massless but has a particle of mass M attached to its free end. Rod B has a mass M, which is distributed uniformly about its length. Which rod has the greater kinetic energy? a. Rod A b. Rod B c. Both rods have the same kinetic energies.

A

A 0.2-kg block is held in place by a force 𝐹 that results in a 0.10-m compression of a spring beneath the block. The spring constant is 100 N/m. The force F is removed, and the block moves upward. Assuming the mass of the spring is negligible compared to that of the block, what is the gravitational potential energy of the block when it reaches maximum height? Set gravitational potential energy equal to zero when the block is held in place by the force 𝐹. a. 0.2J b. 0.5J c. 1.0J d. 2J e. Not enough information

B

A 1.0-m long steel bar is suspended from a rope from the ceiling as shown. The rope is attached to the bar at its mid-point. A force F1 directed at an angle is applied at one end. At the other end, a force F2 is applied perpendicular to the bar. If the magnitudes of the two forces are equal, for which one of the following values of the angle will the net torque on the bar have the smallest magnitude? The net torque is the sum of the torques on the bar. a) 0 b) 90 c) 135 d) 180 e) 270

B

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring's unstrained position by a distance x0 = 0.050 m and released from rest. The period of the subsequent periodic motion of the block is 0.64 s. At what distance from the unstrained position is the speed of the block equal to 0.30 m/s? a) 0.050 m b) 0.040 m c) 0.030 m d) 0.020 m e) 0.010 m

B

A bowling ball is rolling without slipping at constant speed toward the pins on a lane. What percentage of the ball's total kinetic energy is translational kinetic energy? a) 50% b) 71% c) 46% d) 29% e) 33%

B

A force F is applied to a spring, resulting in a displacement x. If the magnitude of F is reduced by a factor of 2, then the displacement a. Decreases by a factor of 4 b. Decreases by a factor of 2 c. Remainsthesame d. Increases by a factor of 2 e. Increases by a factor of 4

B

A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an incline. All the objects have the same radius. They are then released at the same time. What is the order in which they reach the bottom (fastest first)? a) shell, hoop, cylinder, solid sphere b) solid sphere, cylinder, shell, hoop c) hoop, cylinder, shell, solid sphere d) cylinder, shell, solid sphere, hoop

B

A pressure gauge is taken up a mountain where the atmospheric pressure outside is 9.0x104 Pa. What is the height h of the mercury in the tube? The density of mercury is 13,600 kg/m3. Use g = 10 m/s2 A. 0.151 m B. 0.662 m C. 0.713 m D. 0.760 m E. 6.62m

B

A simple pendulum on earth has a period of 6 s. What is the approximate period of this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that of earth? a. 2.4s b. 6.0s c. 36s d. 1.0s e. 15s

B

A solid cylinder of radius 0.35 m is released from rest from a height of 1.8 m and rolls down the incline as shown. What is the angular speed of the cylinder when it reaches the horizontal surface? a. 34 rad/s b. 14 rad/s c. 67 rad/s d. This cannot be determined because the mass is unknown e. 8.2 rad/s

B

A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane. Which one of the following statements is necessarily true? a. The hollow sphere will reach the bottom with the greater kinetic energy. b. The solid sphere will reach the bottom first. c. The solid sphere will reach the bottom with the greater kinetic energy. d. The hollow sphere will reach the bottom first. e. Both spheres will reach the bottom at the same time.

B

A star is rotating about an axis that passes through its center. When the star "dies," the balance between the inward pressure due to the force of gravity and the outward pressure from nuclear processes is no longer present and the star collapses inward; and its radius decreases with time. Which one of the following choices best describes what happens as the star collapses? a) The angular velocity of the star remains constant. b) The angular momentum of the star remains constant. c) The angular velocity of the star decreases. d) The angular momentum of the star decreases. e) Both angular momentum and angular velocity increase.

B

A string is wrapped around a pulley of radius 0.05 m and moment of inertia 0.2 kg m2. If the string is pulled with a force F , the resulting angular acceleration of the pulley is 2 rad/s2. Determine the magnitude of the force F . a. 0.4 N b. 8N c. 16N d. 2N e. 40N

B

A woman is sitting on the spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. As she extends her arms outward, the ANGULAR VELOCITY a. Increases b. Decreases c. Remains the same

B

Consider the drawing. A rope is wrapped around one-third of the circumference of a solid disk of radius R = 2.2 m that is free to rotate about an axis that passes through its center. The force applied to the rope has a magnitude of 35 N; and the disk has a mass M of 7.5 kg. Assuming the force is applied horizontally as shown and the disk is initially at rest, determine the amount of rotational work done until the time when the end of the rope reaches the top of the disk? a) 140 N b) 160 N c) 180 N d) 210 N e) 250 N

B

Consider the mercury U-shaped tube manometer shown. Which one of the following choices is equal to the gauge pressure of the gas enclosed in the spherical container? The acceleration due to gravity is g and the density of mercury is . a) pgc b) -pgb c) pga d) Patm + pgb e) Patm -pgc

B

Figure 10-27 shows three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other. In disks 1 and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disk, either at the outer edge or at the interface of the two materials as shown. For which of the following disks, is the ANGULAR ACCELERATION about center the greatest? a. 1 b. 2 c. 3 d. 1 and 3 tie e. 1 and 2 tie

B

In the figure, the block has a kinetic energy of 3 J and the spring has an elastic potential energy of 2 J when the block is at x = +2.0 cm. What is the elastic potential energy when the block is at x = -xm? Note: xm is the amplitude. Ignore the effects of friction. a. 2J b. 3J c. 4J d. 5J e. 6J

B

Suppose the thin hoop and a solid disk in the figure have the same mass and radius. The same force F is applied tangentially to the edge of each object as shown and each object begins to rotate about their center of mass. Which object experiences the greater ANGULAR ACCELERATE? Note: you can solve this problem without using the equations in table 10-2. a. Thin hoop b. Solid disk c. Tie

B

Two solid cylinders are rotating about an axis that passes through the center of both ends of each cylinder. Cylinder A has three times the mass and twice the radius of cylinder B, but they have the same rotational kinetic energy. What is the ratio of the angular velocities, A/B, for these two cylinders? a) 0.25 b) 0.29 c) 1.0 d) 0.50 e) .86

B

Two solid disks, which are free to rotate independently about the same axis that passes through their centers and perpendicular to their faces, are initially at rest. The two disks have the same mass, but one of has a radius R and the other has a radius 2R. A force of magnitude F is applied to the edge of the larger radius disk and it begins rotating. What force must be applied to the edge of the smaller disk so that the angular acceleration is the same as that for the larger disk? Express your answer in terms of the force F applied to the larger disk. a) 0.25F b) 0.50F c) F d) 1.5F e) 2F

B

While excavating the tomb of Tutankhamen (d. 1325 BC), archeologists found a sling made of linen. The sling could hold a stone in a pouch, which could then be whirled in a horizontal circle. The stone could then be thrown for hunting or used in battle. Imagine the sling held a 0.050-kg stone; and it was whirled at a radius of 1.2 m with an angular speed of 2.0 rev/s. What was the angular momentum of the stone under these circumstances? a) 0.14 kg m2/s b) 0.90 kg m2/s c) 1.2 kg m2/s d) 2.4 kg m2/s e) 3.6 kg m2/s

B

oe has volunteered to help out in his physics class by sitting on a stool that easily rotates. As Joe holds the dumbbells out as shown, the professor temporarily applies a sufficient torque that causes him to rotate slowly. Then, Joe brings the dumbbells close to his body and he rotates faster. Why does his speed increase? a) By bringing the dumbbells inward, Joe exerts a torque on the stool. b) By bringing the dumbbells inward, Joe decreases the moment of inertia. c) By bringing the dumbbells inward, Joe increases the angular momentum. d) By bringing the dumbbells inward, Joe increases the moment of inertia. e) By bringing the dumbbells inward, Joe decreases the angular momentum.

B

A 4.0-m board is resting directly on top of a 4.0-m long table. The weight of the board is 340 N. An object with a weight of 170 N is placed at the right end of the board. What is the maximum horizontal distance that the board can be moved toward the right such that the board remains in equilibrium? a) 0.75 m b) 1.0 m c) 1.3m d) 1.5 m e) 2.0m

C

A 60.0-kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia to one-half its initial value. What is the skater's final angular speed? a. 4.5 rad/s b. 9.0 rad/s c. 12 rad/s d. 3.0 rad/s e. 18 rad/s

C

A meter stick is pivoted at the 0.50-m line. A 3.0-kg object is hung from the 0.15-m line. Where should a 5.0-kg object be hung to achieve equilibrium (the meter stick oriented horizontal and motionless)? a. 0.24-m line b. 0.06-m line c. 0.56-m line d. 0.71-m line e. A 5.0-kg object cannot be placed anywhere on the meter stick to result in equilibrium in this system

D

A beaker is filled to the brim with water. A solid object of mass 3.00 kg is lowered into the beaker so the object is fully submerged in the water (see the drawing). During this process, 2.00 kg of water flows over the rim and out of the beaker. What is the buoyant force that acts on the submerged object, and, when released, does the object rise, sink, or remain in place? a. 30 N. The object rises b. 20 N. The object rises c. 30 N. The object sinks d. 20 N. The object remains in place e. 20 N. The object sinks

C

A hollow cylinder is rotating about an axis that passes through the center of both ends. The radius of the cylinder is r. At what angular speed must the this cylinder rotate to have the same total kinetic energy that it would have if it were moving horizontally with a speed v without rotation? a) W= V2/2R b) W=V/R SR2 c) W=V/R d) W=V/2R e) W=V2/R2

C

A mass is attached to a spring and executes simple harmonic motion. At time t = 0, the object is a distance A from the unstrained position and the instantaneous speed is zero. If T is the period, the next time after t = 0 that the object will be a distance A from the unstrained position is a. T/4 b. T/3 c. T/2 d. T/6 e. T

C

A pirate's treasure chest lies 20 m below the surface of a lake. What is the magnitude of the force that acts on the rectangular top that is 0.75 m x 0.425 m? Assume that atmospheric pressure is 1.0x105 Pa and the acceleration due to gravity is 10 m/s2. The density of water is 1000 kg/m3. a. 3.2x104 N b. 6.4x104 N c. 9.6x104 N d. 2.0x105 N e. 3.0x105 N

C

A string is wrapped around a pulley of radius 0.05 m and moment of inertia 0.2 kgm . If the string is pulled with a force 𝐹, the resulting angular acceleration of the pulley is 2 rad/s2. Determine the magnitude of 𝐹. a. 0.4 N b. 2 N c. 8 N d. 16 N e. 40 N

C

A woman is sitting on the spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. As she extends her arms outward, the ANGULAR MOMENTUM a. Increases b. Decreases c. Remains the same

C

An ideal spring is hung vertically from a device that displays the force exerted on it. A heavy object is then hung from the spring and the display on the device reads W, the weight of the spring plus the weight of the object, as both sit at rest. The object is then pulled downward a small distance and released. The object then moves in simple harmonic motion. What is the behavior of the display on the device as the object moves? a) The magnitude of the force remains constant during oscillation. b) The magnitude of the force varies between W and +W during oscillation. c) The magnitude of the force varies between a value of W+kx and W-kx during oscillation. d) The magnitude of the force varies between a value near zero newtons and 2W during oscillation. e) The magnitude of the force varies between W and 2W during oscillation.

C

An object with a triangular cross-section is free to rotate about the axis represented by the black dot shown. Four forces with identical magnitudes are exerted on the object. Which one of the forces, if any, exerts the largest torque on the object? a) 1 b) 2 c) 3 d) 4 e) The same torque is exerted by each force.

C

As a pendulum swings in simple harmonic motion at the surface of the Earth, the angle the pendulum makes relative to its equilibrium position is given by (t) = (0.140 rad) cos (5.72t) where t is in seconds. What is the length of this pendulum? a) 0.140 m b) 0.250 m c) 0.300 m d) 0.439 m e) 0.801 m

C

At a given instant an object has an angular velocity. It also has an angular acceleration due to torques that are present. Therefore, the angular velocity is changing. If all the torques are suddenly removed, the angular velocity a. Increases b. Decreases c. Remain the same.

C

Consider the three situations shown in the figure. Three forces act on the triangular object in different ways. Two of the forces have magnitude F and one of the forces has a magnitude 2F. In which case(s), if any, will the object be in equilibrium? In each case, the forces may act at the center of gravity or at the center of a corner. a) A only b) B only c) C only d) A and C e) A and B

C

In the produce section of a supermarket, five pears are placed on a spring scale. The placement of the pears stretches the spring and causes the dial to move from zero to a reading of 2.0 kg. If the spring constant is 450 N/m, what is the magnitude of the displacement of the spring due to the weight of the pears? a. 0.088 m b. 0.0088 m c. 0.044 m d. 0.0044 m e. 0.018 m

C

Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare? a) The maximum speed of A is one fourth that of object B. b) The maximum speed of A is one half that of object B. c) The maximum speed of A is the same as that of object B. d) The maximum speed of A is two times that of object B. e) The maximum speed of A is four times that of object B.

C

Suppose the thin hoop and a solid disk in the figure have the same mass and radius. The same force F is applied tangentially to the edge of each object as shown and each object begins to rotate about their center of mass. The NET TORQUE is greater on which object? Note: you can solve this problem without using the equations in table 10-2. a. Thin hoop b. Solid disk c. Tie

C

The drawing shows a graph of displacement x versus time t for simple harmonic motion of an object on a horizontal spring. Which of the following answers correctly gives the magnitude v of the velocity and the magnitude a of the acceleration at POINT A. a. v = maximum and a = maximum b. v=0 and a=0 c. v=maximum and a=0 d. v=0 and a=maximum

C

The drawing shows an overhead view of a horizontal bar that is free to rotate about an axis perpendicular to the page. Two forces act on the bar, and they have the same magnitude. However, one force is perpendicular to the bar, and the other makes an angle with respect to it. For which value of will the magnitude of the net torque (the sum of the torques) be the SMALLEST? a. 0 b. 45 c. 90 d. 180 e. 270

C

A torque of 170 N·m does 4700 J of work on a rotating flywheel. If the flywheel's initial kinetic energy is 1500 J, what is its final kinetic energy? a. 1500 J b. 3200 J c. 4700 J d. 6200 J e. Cannot be determined

D

The figure shows an overhead view of a meter stick that can pivot about the point ԦԦ indicated, which is to the left of the stick's midpoint. Two horizontal forces, 𝐹 and 𝐹 , ԦԦ are applied to the stick. Only 𝐹 is shown. Force 𝐹 is perpendicular to the rod and applied at the right end. If the torque on the rod is zero, a. 𝐹2 points upward and has a larger magnitude than 𝐹1 b. 𝐹2 points upward and has a smaller magnitude than 𝐹1 c. 𝐹2 points downward and has a larger magnitude than 𝐹1 d. 𝐹2 points downward and has a smaller magnitude than 𝐹1 e. 𝐹2 points upward and has the same magnitude as that of F1

C

Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia I and is spinning with angular velocity . The second disc has rotational inertia 2I and is spinning in the same direction as the first disc with angular velocity 2 as shown. The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of a. 𝜔 3 b. 3𝜔 c. (5𝜔)/3 d. 𝜔 7/3 e. 𝜔

C

Two hoops, starting from rest, roll down identical inclined planes. The work done by nonconservative forces, such as air resistance, is zero (Wnc = 0 J). Both have the same mass M, but, as the drawing shows, one hoop has twice the radius as the other. The moment of inertia for each hoop is I = Mr2, where r is its radius. Which, if either, has the greater total kinetic energy (translational plus rotational) at the bottom of the incline? a) Large hoop b) Small hoop c) Both tie

C

Two objects, A and B, have the same volume and are completely submerged in a liquid, although A is deeper than B. Which object, if either, experiences the greater buoyant force? a. A b. B c. The buoyant forces on A and B are the same

C

Which one of the following graphs correctly represents the restoring force F of an ideal spring as a function of the displacement x of the spring from its unstrained length? a / b v c \ d ^ e >

C

Which one of the following statements describes the condition(s) for which a rigid body is in equilibrium? a. Each external torque may not be non-zero, but the sum of the torques must be zero. b. Each external force may be non-zero, but the sum of the forces must be zero. c. The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero. d. Only internal forces can be present. e. Each external torque acting on the body must be zero.

C

9.4.4. A long board is free to rotate about the pivot shown in each of the four configurations shown. Weights are hung from the board as indicated. In which of the configurations, if any, is the net torque about the pivot axis the largest? a) 1 b) 2 c) 3 d) 4 e) The net torque is the same for all four situations.

D

A certain merry-go-round is accelerated from rest and attains an angular speed of 1.2 rad/s in the first 18 seconds. If the net applied torque is 1200 Nm, what is the moment of inertia of the merry-go- round? a. 500 kgm2 b. 1400 kgm2 c. 9000kgm2 d. 18000 kgm2 e. This cannot be determined since the radius is not specified.

D

A disk has a rotational inertia of 6 kg·m2 and a constant angular acceleration of 2 rad/s2. If it starts from rest the work done during the first 5 s by the net torque acting on it is a. 0 b. 30J c. 60J d. 300 J e. 600 J

D

Figure 10-27 shows three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other. In disks 1 and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disk, either at the outer edge or at the interface of the two materials as shown. For which of the following disks, is the ROTATIONAL INERTIA about center the greatest? a. 1 b. 2 c. 3 d. 1 and 3 tie e. 1 and 2 tie

D

In a classroom demonstration, a physics professor lies on a "bed of nails." The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board. While the professor is lying down, nearly one thousand nails make contact with his body. Which one of the following choices provides the best explanation as to why the professor is not harmed by the bed of nails? a) The nails are not as sharp as nails typically used in construction. b) The professor is wearing special clothes that are not easily penetrated by nails. c) The professor's skin has been caloused after years of doing the demonstration, so nails no longer penetrate the skin. d) The professor's weight is distributed over all of the nails in contact with the professor's body, so the pressure exerted a nail at any location is too small to penetrate the skin. e) The force due to gravity on the professor is balanced by the upward force of the nails, as explained by Newton's third law of motion, so the professor doesn't accelerate downward.

D

In designing a spring loaded cannon, determine the spring constant required to launch a 2.00-kg ball with an initial speed of 1.20 m/s from a position where the spring is displaced 0.150 m from its equilibrium position. a) 16.0 N/m b) 32.0 N/m c) 64.0 N/m d) 128 N/m e) 180 N/m

D

In the figure, the block has a kinetic energy of 3 J and the spring has an elastic potential energy of 2 J when the block is at x = +2.0 cm. What is the kinetic energy when the block is at x = 0? Note: xm is the amplitude. Ignore the effects of friction. a. 2J b. 3J c. 4J d. 5J e. 6J

D

The drawing shows a graph of displacement x versus time t for simple harmonic motion of an object on a horizontal spring. Which of the following answers correctly gives the magnitude v of the velocity and the magnitude a of the acceleration at POINT B. a. v = maximum and a = maximum b. v = 0 and a = 0 c. v = maximum and a = 0 d. v = 0 and a = maximum

D

The drawing shows a graph of displacement x versus time t for simple harmonic motion of an object on a horizontal spring. Which of the following answers correctly gives the magnitude v of the velocity and the magnitude a of the acceleration at POINT B. a. v = maximum and a = maximum b. v=0 and a=0 c. v=maximum and a=0 d. v=0 and a=maximum

D

Three objects are attached to a massless rigid rod that has an axis of rotation as shown. Assuming all of the mass of each object is located at the point shown for each, calculate the moment of inertia of this system. a. 3.1 kg m2 b. 5.3 kg m2 c. 7.2 kg m2 d. 9.1 kg m2 e. 1.3 kg m2

D

Which one of the following statements is true concerning an object executing simple harmonic motion? a. The object's acceleration is never zero. b. The object's velocity is never zero. c. The object's maximum acceleration is equal to its maximum velocity. d. The object's velocity is zero when its acceleration is a maximum. e. The object's velocity is never zero.

D

You are using a wrench in an attempt to loosen a nut by applying a force as shown. But this fails to loosen the nut. Which one of the following choices is most appropriate for loosening this tough nut? a) Tie a rope of length 2L to the wrench at the same location and apply the same force as shown. b) Place a pipe of length 2L over the handle of the wrench and apply the same force to the opposite end (farthest from the nut). c) Double the force you applied at length L. d) Doubling the length or doubling the force will have the same result, but doubling the length is easier. e) Continue applying the same force as in the drawing and eventually the nut will loosen.

D

You would like to use a simple pendulum to determine the local value of the acceleration due to gravity, g. Consider the following parameters: (1) pendulum length, (2) mass of the object at the free end of the pendulum, (3) the period of the pendulum as it swings in simple harmonic motion, (4) the amplitude of the motion. Which of these parameters must be measured to find a value for g? a) 1 only b) 2 only c) 3 and 4 only d) 1 and 3 only e) 1, 2, and 4 only

D

1.5-kg ball is tied to the end of a string. The ball is then swung at a constant angular velocity of 4 rad/s in a horizontal circle of radius 2.0 m. What is the torque on the stone? a) 18 Nm b) 29 Nm c) 36 Nm d) 59 Nm e) zero Nm

E

A 1.0-kg wheel in the form of a solid disk rolls along a horizontal surface with a speed of 6.0 m/s. What is the total kinetic energy of the wheel? a. 9.0 J b. 36J c. 54J d. 18J e. 27J

E

A 1.5-kg ball is tied to the end of a string. The ball is then swung at a constant angular velocity of 4 rad/s in a horizontal circle of radius 2.0 m. What is the torque on the ball? a) 18 Nm b) 29 Nm c) 36 Nm d) 59 Nm e) zero Nm

E

A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 0.6 kg. Its volume is 5.0 m3. The density of air is 1.3 kg/m3. Will the balloon rise, fall, or remain stationary; and why? a. The balloon will rise because its density is greater than that of air. b. The balloon will remain stationary because its density is less than that of air. c. The balloon will fall because the downward buoyant force is greater than the upward buoyant force. d. The balloon will rise because the upward buoyant force is greater than its weight. e. The balloon will fall because the upward buoyant force is less than its weight.

E

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring's unstrained position by a distance x0 and given an initial speed of v0 as it is released. Which one of the following statements concerning the amplitude of the subsequent simple harmonic motion is true? a) The amplitude will depend on whether the initial velocity of the block is in the +x or the x direction. b) The amplitude will be less than x0. c) The amplitude will be equal to x0. d) The amplitude will be greater than x0. e) The amplitude will depend on whether the initial position of the block is in the +x or the x direction relative to the unstrained position of the spring.

E

A steel ball is hung from a vertical ideal spring where it oscillates in simple harmonic motion with a period T. At time t = 0 s, the ball is at its maximum displacement, A, from its equilibrium position. In terms of the period, at what time will the ball be at y = 0.75A? a) 0.33T b) 0.25T c) 0.19T d) 0.15T e) 0.12T

E

An ideal spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. The object is then lifted and held to a height y +A, where A << y. Which one of the following statements concerning the total potential energy of the object is true? a) The total potential energy will be equal to zero joules. b) The total potential energy will decrease and be equal to the gravitational potential energy of the object. c) The total potential energy will decrease and be equal to the elastic potential energy of the spring. d) The total potential energy will decrease and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object. e) The total potential energy will increase and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object.

E

Five simple pendulums are shown in the drawings. The lengths of the pendulums are drawn to scale, and the masses are either m or 2m, as shown. Which one has the smallest angular frequency of oscillation?

E

The drawing shows an overhead view of a horizontal bar that is free to rotate about an axis perpendicular to the page. Two forces act on the bar, and they have the same magnitude. However, one force is perpendicular to the bar, and the other makes an angle with respect to it. For which value of will the magnitude of the net torque (the sum of the torques) be the LARGEST? a. 0 b. 45 c. 90 d. 180 e. 270

E

The drawing shows three objects rotating about a vertical axis. The mass of each object is given in terms of m0, and its perpendicular distance from the axis is specified in terms of r0. Rank the three objects according to their moments of inertia, largest to smallest. a. C, A, B b. B, A, C c. B, C, A d. A, B, C e. A, C, B

E

The figure shows three particles of mass m that have been glued to a rod of negligible mass. The distance between each mass and the axis of rotation can be put in terms of d (see diagram). What is the moment of inertia of the assembly? a. 𝐼=6𝑚𝑑 b. 𝐼 = 3𝑚𝑑2 c. 𝐼=6𝑚𝑑2 d. 𝐼 = 9𝑚𝑑2 e. 𝐼=14𝑚𝑑2

E

shows three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other. In disks 1 and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disk, either at the outer edge or at the interface of the two materials as shown. For which of the following disks, is the TORQUE about the disk center the greatest? a. 1 b. 2 c. 3 d. 1 and 3 tie e. 1 and 2 tie

E

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring's unstrained position by a distance x0 and given an initial speed of v0 as it is released. Which one of the following statements concerning the amplitude of the subsequent simple harmonic motion is true? a) The amplitude will depend on whether the initial velocity of the block is in the +x or the x direction. b) The amplitude will be less than x0. c) The amplitude will be equal to x0. d) The amplitude will be greater than x0. e) The amplitude will depend on whether the initial position of the block is in the +x or the x direction relative to the unstrained position of the spring.

e