113

MasteringPhysics: Assignment Print View

Problem 8.92: Energy SharingAn object with mass , initially at rest, explodes into two fragments, one with mass and the other with mass , where .

Part A

If energy is released in the explosion, how much kinetic energy does each fragment have immediately after the collision?

Express your answers in terms of the variables , , and . Enter your answers separated by a comma.

ANSWER: =

Correct

Part B

What percentage of the total energy released does each fragment get when fragment has four times the mass of the other?

Enter your answers numerically separated by a comma.

ANSWER: = 20.0,80.0

Correct

Problem 8.104

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=1471642 (1 of 22) [12/13/2010 7:17:08 PM]


A 12.0- shell is launched at an angle of 55.0 above the horizontal with an initial speed

of 150 . When it is at its highest point, the shell exploded into two fragments, one three times heavier than the other. The two fragments reach the ground at the same time. Assume that air resistance can be ignored. If the heavier fragment lands back at the same point from which the shell was launched, where will the lighter fragment land and how much energy was released in the explosion?

Part A

ANSWER: = 8630 Correct from the launch point

Part B

ANSWER: = 5.33×105

Correct

Test Your Understanding 8.1: Momentum and Impulse

Part A

Rank the following situations in order of the magnitude of the impulse of the net force, from largest value to smallest value.

ANSWER:

View Answer Requested



The impulse of the net force is equal to the average net force multiplied by the

time interval during which that force acts:

The impulse of the net force is also equal to the change in momentum of the object on which the force acts:

The equation tells us that for a 200- object whose velocity changes

from 20 west to zero, the magnitude of is

This value is the same no matter how long it takes the momentum to change. This same equation tells us that for a 400- object whose velocity changes from 10

south to 15 south, the magnitude of is

For a 400- object whose velocity changes from 20 south to 25 south, the

magnitude of is

The equation tells us that if a 300- net force acts on an object for

15 , the magnitude of is

This is independent of the mass of the object on which the net force acts.

Exercise 8.40



You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 77.0 , is given a push and slides

eastward. Abigail, with mass 51.0 , is sent sliding northward. They collide, and after the

collision Sam is moving at 30.0 north of east with a speed of 6.80 and Abigail is

moving at 22.0 south of east with a speed of 10.0 .

Part AWhat was the speed of each person before the collision? Sam's speed:

ANSWER: = 12.0

Correct

Part BAbigail's speed:

ANSWER: = 1.39

Correct

Part CBy how much did the total kinetic energy of the two people decrease during the collision?

ANSWER: =

-1290 Answer Requested

Exercise 8.41



Blocks (mass 4.00 ) and (mass 12.00 ) move on a frictionless, horizontal

surface. Initially, block is at rest and block is moving toward it at 10.0 . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let be the direction of the initial motion of .

Part AFind the maximum energy stored in the spring bumpers and the velocity of each block at that time. Find the maximum energy.

ANSWER: = 150 Correct

Part B

Find the velocity of .

ANSWER: =

2.50 All attempts used; correct answer displayed

Part C


ANSWER: =

2.50 Answer Requested

Part DFind the velocity of each block after they have moved apart. Find the velocity of .

ANSWER: = -5.00

Correct



Part E


ANSWER: = 5.00

Correct

Exercise 8.59

A rocket is fired in deep space, where gravity is negligible. In the first second it ejects of

its mass as exhaust gas and has an acceleration of 15.1 .

Part AWhat is the speed of the exhaust gas relative to the rocket?

ANSWER: = 2.42 Correct

Exercise 8.62

Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible.

Part A

If the rocket ejects gas at a relative speed of 1400 and you want the rocket's speed eventually to be 1.00×10−3 , where is the speed of light, what fraction of the initial mass of the rocket and fuel is not fuel?

ANSWER: = 8.65×10−94 Correct

Part B



What is this fraction if the final speed is to be 3900 ?

ANSWER: = 6.17×10−2 Correct

Problem 8.80

A 15.00 lead sphere is hanging from a hook by a thin wire 3.70 long, and is free to

swing in a complete circle. Suddenly it is struck horizontally by a 4.00 steel dart that embeds itself in the lead sphere.

Part AWhat must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

ANSWER: = 64.0 Correct

Problem 8.81

An 8.00 ball, hanging from the ceiling by a light wire 115 long, is struck in an elastic

collision by a 2.20 ball moving horizontally at 4.50 just before the collision.

Part AFind the tension in the wire just after the collision.

ANSWER: = 105 Correct

Problem 8.91



Jack and Jill are standing on a crate at rest on the frictionless, horizontal surface of a frozen pond. Jack has a mass of 74.3 , Jill has a mass of 44.6 , and the crate has a mass

of 15.9 . They remember that they must fetch a pail of water, so each jumps horizontally from the top of the crate. Just after each jumps, that person is moving away from the crate with a speed of 4.40 relative to the crate.

Part AWhat is the final speed of the crate if both Jack and Jill jump simultaneously and in the same direction? (Hint: Use an inertial coordinate system attached to the ground.)

ANSWER: = 3.88

Correct

Part BWhat is the final speed of the crate if Jack jumps first and then a few seconds later Jill jumps in the same direction?

ANSWER: =


Part CWhat is the final speed of the crate if Jill jumps first and then Jack, again in the same direction?

ANSWER: =


Problem 8.103



A fireworks rocket is fired vertically upward. At its maximum height of 75.0 , it explodes and breaks into two pieces, one with mass = 1.45 and the other with mass

= 0.200 . In the explosion, 840 of chemical energy is converted to kinetic energy of the two fragments.

Part AWhat is the speed of each fragment just after the explosion?


ANSWER: , = 11.9,85.9

Correct

Part BIt is observed that the two fragments hit the ground at the same time. What is the distance between the points on the ground where they land? Assume that the ground is level and air resistance can be ignored.

ANSWER: = 382

Correct

Problem 8.112

A rocket is in outer space, far from any planet, when the rocket engine is turned on, the mass of the rocket as a function of time is

.

Assume that rocket ejects mass with a relative speed of 2400 .

Part A



Calculate and graph the velocity of the rocket as a function of time from to .

ANSWER:

View Answer Requested

Part B

A 80- astronaut lies on a reclined chair during the firing of the rocket. What is the maximum net force exerted by the chair on the astronaut during the firing?

Express your answer using two significant figures.

ANSWER: = 6400

Correct

Part CHow does your answer compare with her weight on earth?


ANSWER: =


Problem 8.106: Center-of-Mass Coordinate System.



Puck (mass ) is moving on a frictionless, horizontal air table in the direction with velocity and makes an elastic, head-on collision with puck (mass ), which is initially at rest. After the collision, both pucks are moving along the x-axis.

Part ACalculate the velocity of the center of mass of the two-puck system before the collision.

Express your answer in terms of the variables , , and .

ANSWER:

Correct

Part BConsider a coordinate system whose origin is at the center of mass and moves with it. Is this an inertial reference frame?

ANSWER: yesno

Correct

Part C

What are the initial velocities and of the two pucks in this center-of-mass reference frame?

Express your answers in terms of the variables , , and , separated by a comma.

ANSWER:

=

Correct

Part D



What is the total momentum in this center-of-mass reference frame?

Express your answer in terms of the variables , , and .

ANSWER: =

0.00×100 Answer Requested

Part EUse conservation of momentum and energy, applied in the center-of-mass reference frame, to relate the final momentum of each puck to its initial momentum and thus the final velocity of each puck to its initial velocity. Your results should show that a one-dimensional, elastic collision has a very simple description in center-of-mass coordinates.

ANSWER: My Answer:

Part F

Let = 0.500 , = 0.200 , and = 8.00 . Find the center-of-mass

velocities and , apply the simple result found in part (d).

ANSWER: , =

2.29,-5.71 All attempts used; correct answer displayed

Part GTransform back to velocities in a stationary frame to find the final velocities of the pucks.

ANSWER: , =

3.43,11.4 Answer Requested

Problem 8.108: Binding Energy of the Hydrogen Molecule



When two hydrogen atoms of mass combine to form a diatomic hydrogen molecule , the potential energy of the system after they combine is , where is a positive

quantity called the binding energy of the molecule.

Part AShow that in a collision that involves only two hydrogen atoms, it is impossible to form an

molecule because momentum and energy cannot simultaneously be conserved. (Hint: If you can show this to be true in one frame of reference, then it is true in all frames of reference. Can you see why?)

ANSWER: My Answer:

Part B

An molecule can be formed in a collision that involves three hydrogen atoms. Suppose

that before such a collision, each of the three atoms has speed 3000 , and they are

approaching at 120 angles so that at any instant, the atoms lie at the corners of an equilateral triangle. Find the speeds of the molecule and of the single hydrogen atom

that remains after the collision. The binding energy of is , and the

mass of the hydrogen atom is .


ANSWER: = 1.22×104,2.44×104

Correct

Exercise 10.52



The earth precesses once every 26000 years and spins on its axis once a day.

Part AEstimate the magnitude of the torque that causes the precession of the earth, take

and . Make the estimate by assuming (i) the earth is a uniform sphere and (ii) the precession of the earth is like that of the gyroscope. In this model, the precession axis and rotation axis are perpendicular. Actually, the angle between these two axes for the earth is only this affects the calculated torque by about a factor of 2.

ANSWER: =

5.39×1022 All attempts used; correct answer displayed

Problem 10.60: Balancing Act

Attached to one end of a long, thin, uniform rod of length and mass is a small blob of clay of the same mass .

Part ALocate the position of the center of mass of the system of rod and clay.

Express your answer in terms of some or all of the variables , , and .

ANSWER: =

Correct from the end with the clay

Part B



You carefully balance the rod on a frictionless tabletop so that it is standing vertically, with the end without the clay touching the table. If the rod is now tipped so that it is a small angle away from the vertical, determine its angular acceleration at this instant. Assume that the end without the clay remains in contact with the tabletop.

Express your answer in terms of some or all of the variables , , , and .

ANSWER: =

Correct

Part CYou again balance the rod on the frictionless tabletop so that it is standing vertically, but now the end of the rod with the clay is touching the table. If the rod is again tipped so that it is a small angle away from the vertical, determine its angular acceleration at this instant. Assume that the end with the clay remains in contact with the tabletop.

Express your answer in terms of some or all of the variables , , , and .

ANSWER: =

Correct

Part DHow does the angular acceleration in part C compare to the angular acceleration in part B?

ANSWER: greatersmallerequal

Correct

Part E



A pool cue is a tapered wooden rod that is thick at one end and thin at the other. You can easily balance a pool cue vertically on one finger if the thin end is in contact with your finger; this is quite a bit harder to do if the thick end is in contact with your finger. Explain why there is a difference.

ANSWER: My Answer:

Exercise 10.41: The spinning figure skater

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center . When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 9.0 . When outstretched, they span 1.7 ; when wrapped, they form a cylinder of radius 23 . The moment of inertia about the rotation axis of the remainder of his body is constant and equal to .

Part A

If his original angular speed is 0.50 , what is his final angular speed?


ANSWER: = 1.5

Correct

Exercise 10.45



A small 15.0- bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 50.0 and is 100 in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 15.0 relative to the table.

Part AWhat is the angular speed of the bar just after the frisky insect leaps?

ANSWER: = 0.135

Correct

Exercise 10.49

The rotor (flywheel) of a toy gyroscope has mass 0.130 . Its moment of inertia about its

axis is . The mass of the frame is 2.70×10−2 . The gyroscope is supported on a single pivot with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.10 .

Part AFind the upward force exerted by the pivot.

ANSWER: = 1.54

Correct



Part BFind the angular speed with which the rotor is spinning about its axis, expressed in rev/min.

ANSWER: =

1640 All attempts used; correct answer displayed

Problem 10.85

A 4.90 ball is dropped from a height of 14.5 above one end of a uniform bar that

pivots at its center. The bar has mass 5.00 and is 5.60 in length. At the other end of

the bar sits another 6.00 ball, unattached to the bar. The dropped ball sticks to the bar after the collision.

Part AHow high will the other ball go after the collision?

ANSWER: =


Problem 10.86

A uniform rod of mass 3.20×10−2 and length 0.430 rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.180 , are mounted so that they can slide along the rod. They are initially held by catches at positions a distance 4.60×10−2 on each side from the center of the rod, and the system is rotating at an angular velocity 31.0 . Without otherwise changing the system, the catches are released, and the rings slide outward along the rod and fly off at the ends.

Part A



What is the angular speed of the system at the instant when the rings reach the ends of the rod?

ANSWER: =


Part BWhat is the angular speed of the rod after the rings leave it?

ANSWER: = 2.27

Correct

Problem 10.91

A 530.0 bird is flying horizontally at 2.50 , not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 below the top (the figure ). The bar is uniform, 0.780 long, has a mass of 1.30 , and is hinged at its base. The collision stuns the bird so that it just drops to the ground afterward (but soon recovers to fly happily away).

Part A



What is the angular velocity of the bar just after it is hit by the bird?

ANSWER: = 2.66

Correct

Part BWhat is the angular velocity of the bar just as it reaches the ground?

ANSWER: = 6.69

Correct

Problem 10.92

A small block with mass 0.240 is attached to a string passing through a hole in a frictionless, horizontal surface (see the figure ). The block is originally revolving in a circle with a radius of 0.760 about the hole with a tangential speed of 4.10 . The string is then pulled slowly from below, shortening the radius of the circle in which the block revolves. The breaking strength of the string is 25.0 .

Part AWhat is the radius of the circle when the string breaks?

ANSWER: 0.453 Correct m



Problem 10.93

A horizontal plywood disk with mass 7.20 and diameter 1.10 pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.01 to the disk. A 1.30 , battery-driven model train rests on the tracks. To demonstrate conservation of angular momentum, you switch on the train's engine. The train moves counterclockwise, soon attaining a constant speed of 0.600 relative to the tracks.

Part AFind the magnitude and direction of the angular velocity of the disk relative to the earth.

ANSWER: =

0.277 All attempts used; correct answer displayed

Part B

ANSWER: counterclockwiseclockwise

Correct

Exercise 10.47



A thin, uniform, metal bar, 2 long and weighing 80 , is hanging vertically from the ceiling by a frictionless pivot. Suddenly it is struck 1.3 below the ceiling by a small 3-kg ball, initially traveling horizontally at 11 . The ball rebounds in the opposite direction with

a speed of 6 .

Part AFind the angular speed of the bar just after the collision.

ANSWER: = 6.09

Correct

Part BDuring the collision, why is the angular momentum conserved but not the linear momentum?

ANSWER: My Answer:


113

Documents

Transcript of 113