Physics 209 Test 3

You have three bars of identical dimensions composed of steel ( Y=2.0 × 10^11 N/m2), titanium ( Y=1.2 × 10^11 N/m2), and tungsten (Y=3.6 × 10^11 N/m2). Which one compresses the least when used to support a large weight?

Tungsten The relation between the degree of stretching/compression, Young's modulus, and the applied force is F=Y(Lf-Lo/L) . Note that L , A , and F are the same for each material.

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, B Recall from Equation 9.6 that the moment of inertia of each particle is I=mr2, where m is its mass and r is the perpendicular distance of the particle from the axis. Using this equation, the moment of inertia of each particle is: A: 10m0r02, B: 8m0r02, C: 9m0r02.

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?

Both have the same total kinetic energy. As each hoop rolls down the incline, the total mechanical energy is conserved. Thus, the loss in potential energy is equal to the gain in the total kinetic energy (translational plus rotational). Because the hoops have the same mass and fall through the same vertical distance, they lose the same amount of potential energy. Moreover, both start from rest. Therefore, their total kinetic energies at the bottom are the same.

Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true?

Both points have the same instantaneous angular velocity.

What should be the frequency of the driving force acting on a mass attached to the end of a horizontal spring of spring constant (k) in order put the system into resonance?

[(1/2(pi)(squroot(k/m)]

A vertical spring is mounted to a table and compressed downward. A ball of mass (m) is placed on a spring (spring constant k ), the spring is released, and the ball is projected vertically upward. In which case would you expect the ball to reach the greatest maximum height?

Compress the spring twice as much

A lawn mower blade of length 0.50 m rotates about its center. Are the magnitudes of the linear displacement () and angular displacement () of one of the tips upon one complete rotation?

Displacement=0 m; angle theta= 2 rad

Suppose a mass is attached to the end of a horizontal oscillating spring of spring constant . Choose the answer that will double the frequency of oscillation.

Divide the mass by four, or quadruple the spring constant.

Suppose a mass is attached to the end of a horizontal oscillating spring of spring constant k. Choose the answer that will double the frequency of oscillation.

Divide the mass by four, or quadruple the spring constant.

Under what condition(s) is the angular momentum of a rotating body, such as a spinning ice skater, conserved?

Each external torque may be non-zero, but the sum of the torques must be zero. the angular momentum a system is conserved (remains constant) if the net external torque acting on the system is zero.

True or False: In an elastic collision, the kinetic energy of each object is the same both before and after the collision.

False It is the total kinetic energy of the system that is the same both before and after the collision.

True or False: In a two-dimensional collision, momentum can only be conserved in one dimension, not both.

False n a two-dimensional collision, where the sum of the external forces is equal to zero, the momentum in each dimension is conserved separately.

A ball is dropped from some height onto an unstrained vertical spring (mounted to a tabletop) and compresses it. Consider an instant where the spring has not yet brought the ball to a halt, but is still in the process of compressing. What types of energies are associated with the spring-ball system at that instant? Assume that the zero of gravitational energy is at the level of the tabletop.

Gravitational, kinetic, and elastic

A cloud of interstellar gas is rotating. Because the gravitational force pulls the gas particles together, the cloud shrinks, and, under the right conditions, a star may be formed. Would the angular velocity of the star be less than, greater than, or equal to the angular velocity of the rotating gas?

Greater than. The moment of inertia of the gas cloud will decrease as it shrinks. Therefore, the angular speed of the cloud will change accordingly to maintain a constant angular momentum.

A woman is sitting on a spinning piano stool with her arms folded. Ignore any friction in the spinning stool. When she extends her arms outward, which of the following is true? Her angular speed increases, and her angular momentum decreases. Her angular speed decreases, and her angular momentum increases. Her angular speed decreases, and her angular momentum remains constant. Her angular speed increases, and her angular momentum remains constant.

Her angular speed decreases, and her angular momentum remains constant. By extending her arms, here moment of inertia increases, therefore her angular speed must decrease to keep her angular momentum constant.

Exploding gunpowder in a cannon (mass ) propels a cannonball (mass ) forward. Simultaneously, the cannon recoils. Which of the following is true? Note that . I. The speeds of the cannonball and cannon are equal. II. The magnitudes of the momentum of the cannonball and cannon are equal. III. The kinetic energy of the cannonball and cannon are equal.

II only

Two objects have the same momentum. Which of the following is true? I. The masses of the objects are equal. II. The speeds of the objects are equal. III. The velocities of the objects are equal. IV. The direction of motion of each object is the same.

IV only- The direction of motion of each object is the same.

If you want to decrease the frequency of a simple pendulum by a factor of two you should ...

Increase the length by a factor of four

You are a passenger on a jetliner that is flying at constant velocity. You get up from your seat and walk toward the front of the plane. Because of this action, your forward momentum increases. What happens to the forward momentum of the plane itself?

It decreases.

What is the unit of strain?

It is a unitless quantity

Suppose a simple pendulum is submerged in water. If the mass is raised to a height above its lowest position and released, how many oscillations does it undergo if it is critically damped?

It will not oscillate at all.

A thin rod rotates at a constant angular speed. In case A the axis of rotation is perpendicular to the rod at its center. In case B the axis is perpendicular to the rod at one end. In which case, if either, are there points on the rod that have the same tangential speeds?

case A

An object on a spring is oscillating in simple harmonic motion. Suddenly friction appears and causes the energy of the system to be dissipated. The system now exhibits ____________.

damped harmonic motion

When the energy of the system is dissipated, the amplitude of the motion decreases. The motion is called

damped harmonic motion.

Review Conceptual Exercise 14 as an aid in answering this question. Suppose the ice cap at the South Pole melted and the water was distributed uniformly over the earth's oceans. Would the earth's angular velocity increase, decrease, or remain the same?

decrease

A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. Is the linear momentum of the satellite before the explosion less than, equal to, or greater than the total linear momentum of all the pieces after the explosion?

equal to remember that linear momentum is conserved

Conceptual Example 14 provides background for this question. A cloud of interstellar gas is rotating. Because the gravitational force pulls the gas particles together, the cloud shrinks, and, under the right conditions, a star may ultimately be formed. Would the angular velocity of the star be less than, equal to, or greater than the angular velocity of the rotating gas?

greater than

Sometimes, even with a wrench, one cannot loosen a nut that is frozen tightly to a bolt. It is often possible to loosen the nut by slipping one end of a long pipe over the wrench handle and pushing at the other end of the pipe. With the aide of the pipe, does the applied force produce a smaller torque, a greater torque, or the same torque on the nut?

greater torque

In which of the following is a tangential acceleration involved in the motion?

A 1-kg mass swinging freely at the end of a rope

The conservation of linear momentum is only applicable when the system of objects is an isolated system. Which one of the systems listed below is an isolated system?

A space probe is moving in deep space where gravitational and other forces on the probe are negligible. The system is the space probe.

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, B, C The torque applied to each rod is the same, but rod A has the smallest moment of inertia. Therefore it has the largest angular acceleration.

At atmospheric pressure you have identical spheres composed of copper ( B= 1.3 × 1011 N/m2), steel ( B=1.4 ×1011 N/m2), and osmium (B= 4.6 × 1011 N/m2). Which one has the largest volume when subjected to large pressure (much greater than atmospheric pressure)?

Osmium The relation between the degree of volume change, the bulk modulus, and the applied pressure is Pf-Po=-B(Vf-Vo/V). Note that (Pf-Po) and (V) are the same for each material.

The bicycle wheel in the figure is rotating clockwise at 60 rpm. After 2 minutes, it is rotating counterclockwise at 80 rpm. What is the direction of the change in the angular velocity of the wheel during that 2-minute period? Clockwise Counterclockwise Up Down Into the screen Out of the screen

Out of the screen

Vt=??

RW

Which of the following is true about a rigid body in dynamic equilibrium? The body cannot have translational or rotational motion of any kind. The body can have translational motion, but it cannot have rotational motion. The body cannot have translational motion, but it can have rotational motion. The body can have translational motion and rotational motion, as long as its translational and angular accelerations are equal to zero.

The body can have translational motion and rotational motion, as long as its translational and angular accelerations are equal to zero.

The piston of a shock absorber moves through oil in order to damp the motion of the car's chassis when it hits a bump. Holes in the piston head allow the oil to flow through it. Suppose the oil gets "stiffer" when it gets cold outside. Which one of the following do you expect in cold weather?

The degree of damping will be greater (the car will oscillate less when it hits bumps)

What is the natural frequency of a mass (m) hanging at the end of a massless string of length ?

m= squroot(g/L)

Momentum is a vector quantity that depends on what ?

magnitude and a direction.

he kinetic energy of an object depends on its what?

mass and speed.

A group of particles has a net momentum equal to zero? Which of the following must be true? I. The speed of each particle is zero. II. The velocity of each particle is zero. III. The mass of each particle must be equal. IV. The kinetic energy of each particle must be zero.

none are true

The earth rotates once per day about its axis, which is perpendicular to the plane of the equator and passes through the north geographic pole. Where on the earth's surface should you stand in order to have the smallest possible tangential speed?

on the north geographic pole or on the south geographic pole

Is kinetic energy a scalar or vector?

scalar

Suppose that a grandfather clock (a simple pendulum) is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you shorten or lengthen the pendulum to make the clock keep correct time?

shorten

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)?

solid sphere, cylinder, shell, hoop

Two circular cylinders have equal masses but one has twice the radius of the other. They are both placed with their circular faces on a flat surface. Which face, that with the larger or smaller radius, experiences the greatest stress?

The smaller one Incorrect. Note that the stress is equal to F/A . The magnitudes of the forces acting on each face (i.e., the weights) are equal, but the areas are not.

A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an inclined plane. All the objects have the same radius. They are all released at the same time and allowed to roll down the plane. Which object reaches the bottom first?

The solid sphere

Which one of the following statements describes the condition(s) for which a rigid body is in equilibrium?

The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero.

A deep space probe is rotating about a fixed axis with a constant angular acceleration. Which one of the following statements concerning the tangential acceleration of any point on the probe is true? The probe's tangential acceleration is constant in both magnitude and direction. The magnitude of the probe's tangential acceleration is zero m/s2. The tangential acceleration depends on the angular velocity of the probe. The tangential acceleration is to equal the centripetal acceleration of the probe. The tangential acceleration depends on the change in the probe's angular velocity.

The tangential acceleration depends on the change in the probe's angular velocity.

Object 1 is moving in the positive -direction. It collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision (see figure). What must be true about the total momentum of object 1 and object 2 in the -direction after the collision? The total momentum must be conserved separately in both the - and -direction. Since the total momentum in the -direction is equal to zero before the collision, the total momentum in the -direction after the collision must also be equal to zero.

The total momentum in the -direction after the collision will be equal to zero.

Young's modulus for steel is greater than that for a particular unknown material. What does this mean about how these materials compress when used in construction?

The unknown material compresses more easily than steel does.

Two identical cars are traveling at the same speed. One is heading due east and the other due north, as the drawing shows. Which statement is true regarding the kinetic energies and momenta of the cars?

They have the same kinetic energies, but different momenta. Kinetic energy, KE , is a scalar quantity and is the same for both cars. Momentum, mv, is a vector quantity that has a magnitude and a direction. The two cars have different directions, so they have different momenta.

Two objects have the same momentum. How do their velocities compare?

They must have the same directions but they could have different magnitudes.

A meter stick rotates about one end through an angle of 57.3°. What is the arc length traced out by the opposite end?

1 m

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 φ with respect to it. The angle can be 90˚, 45˚, or 0˚. Rank the values of φ according to the magnitude of the net torque (the sum of the torques) that the two forces produce, largest net torque first.

0˚, 45˚, 90˚ In the drawing, the two torques have opposite directions. One is clockwise while the other is counter-clockwise.

For sinple harmonic motion, which quantities are constant and which are variable?

The period=constant, but the average speed increases

An ice boat is coasting on a frozen lake. Friction between the ice and the boat is negligible, and so is air resistance. Nothing is propelling the boat. From a bridge someone jumps straight down into the boat, which continues to coast straight ahead. (a) Does the total horizontal momentum of the boat plus the jumper change? (b) Does the speed of the boat itself increase, decrease, or remain the same?

(a) no (b) decrease Linear momentum in the horizontal direction is conserved, so the total linear momentum in the horizontal direction remains the same. The speed of the boat must decrease to conserve momentum because the mass moving horizontally increases.

(a) Can a single object have a kinetic energy and no momentum? (b) Can a group of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero?

(a) no; (b) yes Kinetic energy is a scalar, but momentum is a vector. Even if the objects are moving, their total momenta could be zero because it's a vector. For example, two objects with the same mass and speed could be moving in opposite directions.

The space probe in the drawing is initially moving with a constant translational velocity and zero angular velocity. (a) When the two engines are fired, each generating a thrust of magnitude T, does the translational velocity increase, decrease, or remain the same? (b) Does the angular velocity increase, decrease, or remain the same?

(a) remain the same (b) increase

Is it possible (a) for a large force to produce a small, or even zero, torque and (b) for a small force to produce a large torque?

(a) yes (b) yes

A car of mass moving with a speed collides with an identical car that is at rest. After the collision, the cars stick together. Which of the following statements is FALSE?

- The collision is inelastic. Momentum is conserved, but kinetic energy is not.

What is the average angular velocity of the seconds hand of a clock?

-0.10 rad/s

A bicycle is turned upside down, the front wheel is spinning (see the drawing), and there is an angular acceleration. At the instant shown, there are six points on the wheel that have arrows associated with them. Which one of the following quantities could the arrows not represent?

Centripetal acceleration

A vertical spring is mounted to a table and compressed downward. A ball of mass (m) is placed on a spring (spring constant ), the spring is released, and the ball is projected vertically upward. In which case would you expect the ball to reach the greatest maximum height?

Compress the spring twice as much

A hoop of mass and radius and a solid cylinder of mass and radius are rolling along level ground with the same translational speed. Which object has the greater total kinetic energy? The hoop The solid cylinder Both have the same total kinetic energy

The hoop

A playground carousel is rotating counterclockwise on frictionless bearings about its center. A child walks from the center of the carousel to the outer edge. Which of the following is most likely to occur as a result of the child's movement?

The moment of inertia of the rotating system increases, which causes the angular velocity to decrease.

Which one of the following statements concerning the momentum of a system when the net force acting on the system has a positive value is true? The momentum of the system is increasing. The momentum of the system is decreasing. The momentum of the system is equal to zero kg · m/s. The momentum of the system has a constant value. The momentum of the system has a negative value.

The momentum of the system is increasing.

You have two springs. One has a greater spring constant than the other. You also have two objects, one with a greater mass than the other. Which object should be attached to which spring, so that the resulting spring-object system has the greatest possible period of oscillation?

The object with the greater mass should be attached to the spring with the smaller spring constant. Greater values for the mass m and smaller values for the spring constant k lead to greater values for the period.

A particle is oscillating in simple harmonic motion. The time required for the particle to travel through one complete cycle is equal to the period of the motion, no matter what the amplitude is. But how can this be, since larger amplitudes mean that the particle travels farther?

The period is constant, but the average speed increases, so the particle travels farther.

Tangential speed is equal to?

angular speed multiplied by the perpendicular distance from the axis of rotation.

A building is located on the earth's equator. As the earth rotates about its axis, which floor of the building has the greatest tangential speed? the first floor the tenth floor the twentieth floor

the twentieth floor The perpendicular distance from the axis of rotation to the floor is proportional to the tangential speed.

The greater the Young's Modulus, the harder it will be

to compress

A ball is attached to a vertical spring. The ball is initially supported at a height y so that the spring is neither stretched nor compressed. The ball is then released from rest and it falls to a height y - h before moving upward. Consider the following quantities: translational kinetic energy, gravitational potential energy, elastic potential energy. When the ball was at a height y - (h/2), which of the listed quantities has values other than zero joules?

translational kinetic, gravitational potential, and elastic potential energies

Is momentum a vector or scalar quantity?

vector

Which of the following sets of variables are suitable for direct substitution into the angular kinematic equations?

wx=0 rad/s, wx=5.0 rad/s, t=3.0 s

A wheel rotates with a constant angular speed ω. Which one of the following is true concerning the angular acceleration α of the wheel, the tangential acceleration aT of a point on the rim of the wheel, and the centripetal acceleration ac of a point on the rim?

α = 0 rad/s^2, aT = 0 m/s^2, and ac ≠ 0 m/^s2 Since the angular speed ω is constant, the angular acceleration α is zero, according to Equation 8.4. Since α = 0 rad/s2, the tangential acceleration aT is zero, according to Equation 8.10.Among other things, the centripetal acceleration ac cannot be zero. It cannot be zero, because it is proportional to the square of the angular speed, according to Equation 8.11, and the angular speed is not zero.

An electric clock is hanging on a wall. As you are watching the second hand rotate, the clock's battery stops functioning, and the second hand comes to a halt over a brief period of time. Which one of the following statements correctly describes the angular velocity ω and angular acceleration α of the second hand as it slows down?

ω is negative and α is positive. Counter-clockwise is the positive direction and clockwise is the negative direction.