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MasteringPhysics: Assignment Print View

Problem 6.60Two blocks are connected by a very light string passing over a massless and frictionless pulley (Figure ). The 20.0- block moves 75.0 to the right and the 12.0- block moves 75.0 downward.

Part A

Find the total work done on 20.0- block if there is no friction between the table and the 20.0- block.

ANSWER: = 5.62

Correct

Part B

Find the total work done on 12.0- block if there is no friction between the table and the 20.0- block.

ANSWER: = 3.38

Correct

Part C

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=1466066 (1 of 23) [12/13/2010 7:15:56 PM]


Find the total work done on 20.0- block if =0.500 and =0.325 between the table and the 20.0- block.

ANSWER: = 2.58

Correct

Part D

Find the total work done on 12.0- block if and between the table and the 20.0- block.

ANSWER: = 1.54

Correct

Problem 6.78: Pushing a Cat

Your cat "Ms." (mass 7.00 ) is trying to make it to the top of a frictionless ramp 2.00 long and inclined upward at 30.0 above the horizontal. Since the poor cat can't get any traction on the ramp, you push her up the entire length of the ramp by exerting a constant 100 force parallel to the ramp.

Part A

If Ms. takes a running start so that she is moving at 2.40 at the bottom of the ramp, what is her speed when she reaches the top of the incline? Use the work-energy theorem.

ANSWER: = 6.58 Correct

Problem 6.94



Six diesel units in series can provide 13.4 of power to the lead car of a freight train.

The diesel units have total mass . The average car in the train has mass

and requires a horizontal pull of 2.8 to move at a constant 27 on level tracks.

Part AHow many cars can be in the train under these conditions?

ANSWER: = 177 Correct

Part BThis would leave no power for accelerating or climbing hills. Show that the extra force needed to accelerate the train is about the same for a 0.10 acceleration or a 1.0% slope (slope angle =arctan 0.010).

ANSWER: My Answer:

Part C

With the 1.0% slope, show that an extra 2.9 of power is needed to maintain the

27 speed of the diesel units.

ANSWER: My Answer:

Part D

With 2.9 less power available, how many cars can the six diesel units pull up a 1.0%

slope at a constant 27 ?

Express your answer using two significant figures.

ANSWER: = 36 Correct



Exercise 6.6

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.4×106 , one an angle 17 west of north and the other an angle 17 east of north, as they pull the tanker a distance 0.90 toward the north.

Part AWhat is the total work they do on the supertanker?


ANSWER: =

2.4×109 Answer Requested

Exercise 6.31

A child applies a force parallel to the -axis to a 5.00- sled moving on the frozen

surface of a small pond. As the child controls the speed of the sled, the -component of the force she applies varies with the -coordinate of the sled as shown in figure . Suppose the sled is initially at rest at =0. You can ignore friction between the sled and the surface of the pond.

Part A



Use the work-energy theorem to find the speed of the sled at 2.0 .

ANSWER: =

1.00 Answer Requested

Part BUse the work-energy theorem to find the speed of the sled at 10.0 .

ANSWER: =

4.69 All attempts used; correct answer displayed

Exercise 6.41

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 39.0 above the horizontal. The glider has mass 9.00×10−2 . The

spring has 650 and negligible mass. When the spring is released, the glider travels a maximum distance of 1.60 along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring.

Part AWhat distance was the spring originally compressed?

ANSWER: = 5.23×10−2

Correct

Part BWhen the glider has traveled along the air track 0.600 from its initial position against the compressed spring, is it still in contact with the spring?

ANSWER: YesNo

Correct



Part CWhat is the kinetic energy of the glider at this point?

ANSWER: = 0.555

Correct

Problem 6.80

A physics professor is pushed up a ramp inclined upward at an angle 28.0 above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 81.0 . He is pushed a distance 2.85 along the incline by a group of students who together exert a constant horizontal force of 597 . The professor's

speed at the bottom of the ramp is 2.15 .

Part AUse the work-energy theorem to find his speed at the top of the ramp.


Problem 6.85

On an essentially frictionless, horizontal ice rink, a skater moving at 5.0 encounters a

rough patch that reduces her speed by 48 due to a friction force that is 23 of her weight.

Part AUse the work-energy theorem to find the length of this rough patch.


ANSWER: =

4.0 All attempts used; correct answer displayed



Exercise 7.36 An object moving in the -plane is acted on by a conservative force described by the potential-energy function , where is a positive constant.

Part A

Derive an expression for the force expressed in terms of the unit vectors and .

Express your answer in terms of the given quantities.

ANSWER:

=

Correct

Problem 7.68

A variable force is maintained tangent to a frictionless, semicircular surface . By slowly

varying the force, a block with weight is moved, and the spring to which it is attached is stretched from position 1 to position 2. The spring has negligible mass and force constant . The end of the spring moves in an arc of radius .

Part A



Calculate the work done by the force .

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

ANSWER:

=

All attempts used; correct answer displayed

Test Your Understanding 7.5: Energy Diagrams

This graph shows the potential energy of a particle moving along the -axis.

Part A



Rank the following points along the -axis in order of the -component of force on the particle at that point, from most positive to most negative.

ANSWER:

View All attempts used; correct answer displayed

The -component of force is the negative derivative of the potential energy function:

Hence the -component of force is most positive at point A, where the potential energy function has the most negative (downward) slope. The -component of force is also positive at point E, but the curve there is less steep than at point A. At points

, D, and , the curve is flat, so the -component of force is zero. At point the curve has a positive (upward) slope, so the -component of force at that point is negative. The curve has an even steeper positive slope at point G, so the -component of force is even more negative there.

Exercise 7.19

A spring of negligible mass has force constant = 1600 .

Part A

How far must the spring be compressed for an amount 3.30 of potential energy to be stored in it?


ANSWER: 6.4×10−2 Correct m

Part B



You place the spring vertically with one end on the floor. You then drop a book of mass 1.30 onto it from a height of 0.900 above the top of the spring. Find the maximum distance the spring will be compressed.

Take the free fall acceleration to be 9.80 . Express your answer using two significant figures.

ANSWER: 0.13 Correct m

Problem 7.51: Bungee Jump

A bungee cord is 30.0 long and, when stretched a distance , it exerts a restoring force of magnitude . Your father-in-law (mass 90.0 ) stands on a platform 45.0 above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 420 .

Part AWhen you do this, what distance will the bungee cord that you should select have stretched?


Problem 7.54



You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1520 will move with speed 2.2 at the top of a ramp that slopes downward at

an angle 22.0 . The ramp will exert a 569 force of kinetic friction on each crate, and the maximum force of static friction also has this value. At the bottom of the ramp, each crate will come to rest after compressing a spring a distance . Each crate will move a total distance of 7.7 along the ramp; this distance includes . Once stopped, a crate must not rebound back up the ramp.

Part A

Calculate the maximum force constant of the spring that can be used in order to meet the design criteria.

ANSWER: =

1710 Answer Requested

Problem 7.73

A wooden block with mass 1.80 is placed against a compressed spring at the bottom of a slope inclined at an angle of 26.0 (point ). When the spring is released, it projects the block up the incline. At point , a distance of 7.25 up the incline from , the block is

moving up the incline at a speed of 7.50 and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is = 0.50. The mass of the spring is negligible.

Part ACalculate the amount of potential energy that was initially stored in the spring.

Take free fall acceleration to be 9.80 .

ANSWER: = 164

Correct

Problem 9.80



A uniform, solid disk with mass and radius is pivoted about a horizontal axis through its center. A small object of the same mass is glued to the rim of the disk.

Part AIf the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when the small object is directly below the axis.

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

ANSWER:

=

Correct

Problem 9.84

Exactly one turn of a flexible rope with mass is wrapped around a uniform cylinder with mass and radius . The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder. The cylinder starts with angular speed . After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder.

Part AFind the angular speed of the cylinder at this time. You can ignore the thickness of the rope. (Hint: Use Equation .)

Express your answer in terms of the variables m, M, R, and appropriate constants.

ANSWER:

=

Correct

Part B



Find the linear speed of the lower end of the rope at this time.

Express your answer in terms of the variables m, M, R, and appropriate constants.

ANSWER:

=

Answer Requested

Problem 9.86

The pulley in the figure has radius 0.160 and a moment of inertia 0.480 . The rope does not slip on the pulley rim.

Part AUse energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.


Problem 9.87



You hang a thin hoop with radius over a nail at the rim of the hoop. You displace it to the side (within the plane of the hoop) through an angle from its equilibrium position and let it go.

Part AWhat is its angular speed when it returns to its equilibrium position? (Hint: Use Equation

.)

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

ANSWER:

=

Correct

Problem 9.98: Neutron Stars and Supernova Remnants

The Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light years from the earth (the figure ). It is the remnant of a star that underwent a supernova explosion, seen on earth in 1054 a.d. Energy is released by the Crab Nebula at a rate of about

, about times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every 0.0331 , and this period is increasing by for each second of time that elapses.

Part A



If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, find the moment of inertia of the neutron star.


ANSWER: = 1.1×1038

Correct

Part BTheories of supernovae predict that the neutron star in the Crab Nebula has a mass about 1.4 times that of the sun. Modeling the neutron star as a solid uniform sphere, calculate its radius in kilometers.


ANSWER: = 9.9

Correct

Part CWhat is the linear speed of a point on the equator of the neutron star?


ANSWER: = 1.9×106

Correct

Part DCompare to the speed of light.

Express your answer in terms of .Express your answer using two significant figures.

ANSWER: =

Correct

Part E



Assume that the neutron star is uniform and calculate its density.


ANSWER: = 6.9×1017

Correct

Exercise 9.48

We wrap a light, flexible cable around a thin-walled, hollow cylinder with mass and radius . The cylinder is attached to the axle by spokes of a negligible moment of inertia.The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass and release the object with no initial velocity at a distance above the floor. As the block falls, the cable unwinds without stretching or slipping, turning the cylinder.

Part AFind the speed of the hanging mass just as it strikes the floor.

Give your answer in terms of given quantities.

ANSWER:

=

Correct

Part BUse energy concepts to explain why the answer to part A is different from the speed found

in case of solid cylinder,which is .

ANSWER: My Answer:

Exercise 9.44



You need to design an industrial turntable that is 51.0 in diameter and has a kinetic energy of 0.230 when turning at 40.0 ( ).

Part AWhat must be the moment of inertia of the turntable about the rotation axis?

ANSWER: = 2.63×10−2

Correct

Part BIf your workshop makes this turntable in the shape of a uniform solid disk, what must be its mass?

ANSWER: = 0.808

Correct

Exercise 9.42

An airplane propeller is 1.93 in length (from tip to tip) with mass 130 and is rotating

at 2300 ( ) about an axis through its center. You can model the propeller as a slender rod.

Part AWhat is its rotational kinetic energy?

ANSWER: = 1.17×106

Correct

Part B



Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0 of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in ?

ANSWER: = 2650

Correct

Exercise 9.45

The flywheel of a gasoline engine is required to give up 750 of kinetic energy while its

angular velocity decreases from 880 to 410 .

Part AWhat moment of inertia is required?


Exercise 9.49

A frictionless pulley has the shape of a uniform solid disk of mass 2.50 and radius 10

. A 1.10 stone is attached to a very light wire that is wrapped around the rim of the pulley (the figure ), and the system is released from rest.



Part A

How far must the stone fall so that the pulley has 3.30 of kinetic energy?

ANSWER: = 0.576

Correct

Part BWhat percent of the total kinetic energy does the pulley have? .

ANSWER: = 53.2

Correct

Problem 9.70

Engineers are designing a system by which a falling mass imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (the figure ). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71

. In the earth tests, when is

set to 13.0 and allowed to fall through 5.50 , it gives 150.0 of kinetic energy to the drum.

Part A



If the system is operated on Mars, through what distance would the 13.0- mass have to fall to give the same amount of kinetic energy to the drum?

ANSWER: = 14.5

Correct

Part B

How fast would the 13.0- mass be moving on Mars just as the drum gained 150.0 of kinetic energy?

ANSWER: = 9.20

Correct

Problem 9.83

A stick with a mass of 0.170 and a length of 1.00 is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released.

Part AAs it swings through the vertical, calculatethe change in gravitational potential energy that has occurred.

ANSWER: = -0.834 Correct

Part BAs it swings through the vertical, calculate the angular speed of the stick.


Part C



As it swings through the vertical, calculate the linear speed of the end of the stick opposite the axis.


Part DFind the ratio of the speed of a particle that has fallen a distance of 1.00 , starting from rest, to the speed from part (C).

ANSWER: 0.816 Answer Requested

Exercise 10.24

A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance above the bottom of the bowl. The left half of the bowl is rough enough to cause the marble to roll without slipping, but the right half has no friction because it is coated with oil.

Part AHow far up the smooth side will the marble go, measured vertically from the bottom?

Express your answer in terms of .

ANSWER: =

Correct

Part BHow high would the marble go if both sides were as rough as the left side?

Express your answer in terms of .

ANSWER: =

Correct



Problem 10.56

A uniform hollow disk has two pieces of thin light wire wrapped around its outer rim and is supported from the ceiling (the figure ). Suddenly one of the wires breaks, and the remaining wire does not slip as the disk rolls down.

Part AUse energy conservation to find the speed of the center of this disk after it has fallen a distance of 1.20 .

ANSWER: = 3.74

Correct

Problem 10.75: Rolling Stones

A solid, uniform spherical boulder starts from rest and rolls down a 50.0-m high hill, as shown in the figure . The top half of the hill is rough enough to cause the boulder to roll



without slipping, but the lower half is covered with ice and there is no friction.

Part AWhat is the translational speed of the boulder when it reaches the bottom of the hill?

ANSWER: = 29.0

Correct


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