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MasteringPhysics: Assignment Print View

Problem 3.73

In a Fourth of July celebration, a firecracker is launched from ground level with an initial velocity of 25.9

at 36.9 from the vertical. At its maximum height it explodes in a starburst into many fragments, two of which

travel forward initially at 24.2 at 45.1 with respect to the horizontal, both quantities measured relative to the original firecracker just before it exploded.

Part AWith what angles with respect to the horizontal do the two fragments initially move right after the explosion, as measured by a spectator standing on the ground?

ANSWER: , = 24.4,-24.4

Correct

Problem 3.74

In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 71.0 , to

his enemy's car, which is going 111 . The enemy's car is 15.4 in front of the hero's when he lets go of the grenade.

Part A

If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

ANSWER: = 80.8

Correct

Part BFind the magnitude of the velocity relative to the earth.

ANSWER: = 140

Correct

Problem 3.61

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=1451698 (1 of 18) [12/13/2010 7:14:39 PM]


Part AProve that a projectile launched at angle has the same horizontal range as one launched with the same speed at angle .

ANSWER: Answer Key:The range R is proportional to sin(2(90-a))=2sin(90-a)cos(90-a)=2cos(a)sin(a)=sin(2a).

Part B

A frog jumps at a speed of 2.4 and lands 18 from its starting point. At which angles above the horizontal could it have jumped?

Enter your answers numerically separated by a comma. Express your answer using two significant figures.

ANSWER: = 8.9,81

Correct

Exercise 4.30

A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. (Assume that the truck is accelerating to the right.)

Part ADraw clearly labeled free-body diagram for the box. (The bed of the truck is not frictionless.)

Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:

View Correct

Part B



Draw clearly labeled free-body diagram for the truck. (The bed of the truck is not frictionless.)

Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:

View All attempts used; correct answer displayed

Problem 4.58

The position of a training helicopter under test is given by

.

Part A

Find the net force on the helicopter at .

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

ANSWER: =

Correct

Exercise 5.15

A horizontal wire holds a solid uniform ball of mass in place on a tilted ramp that rises 35.0 above the horizontal. The surface of this ramp is perfectly smooth, and the wire is directed away from the center of the ball (the figure ).



Part ADraw a free-body diagram for the ball.

Draw the force vectors with their tails in the center of the ball. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:


Part BHow hard does the surface of the ramp push on the ball?

Express your answer in terms of the variable and appropriate constants.

ANSWER: =

Correct

Part CWhat is the tension in the wire?

Express your answer in terms of the variable and appropriate constants.

ANSWER: =

Correct



Problem 5.71

You are standing on a bathroom scale in an elevator in a tall building. Your mass is 72 kg. The elevator starts from rest and Itravels upward with a speed that varies with time according to .

Part A

When , what is the reading of the bathroom scale?

Express your answer using two significant figures.

ANSWER: 110 Correct

Problem 5.93

Block A, with weight , slides down an inclined plane S of slope angle 36.9 at a constant speed while plank B, with weight , rests on top of A. The plank is attached by a cord to the wall (the figure ).

Part ADraw a diagram of all the forces acting on block A.

Draw the force vectors with their tails at the center of the block A. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:




Part BIf the coefficient of kinetic friction is the same between A and B and between S and A, determine its value.

ANSWER: = 0.450

Correct

Exercise 5.10

A 1020- car is held in place by a light cable on a very smooth (frictionless) ramp, as shown in the figure . The cable makes an angle of 31.0 above the surface of the ramp, and the ramp itself rises at 25.0 above the horizontal.

Part ADraw a free-body diagram for the car.

Draw the force vectors with their tails at the front bumper of the car. The location and orientation of your vectors will be graded. The exact length of your vectors will not be graded.

ANSWER:


Part BFind the tension in the cable.

ANSWER: = 4930

Correct



Part CHow hard does the surface of the ramp push on the car?

ANSWER: = 6520

Correct

Exercise 5.13

A solid uniform 53.9- ball of diameter 34.0 is supported against a vertical frictionless wall using a thin 30.0- wire of negligible mass, as shown in the figure .

Part AMake a free-body diagram for the ball and use it to find the tension in the wire.

Draw the force vectors with their tails in the center of the ball. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:


Part B



ANSWER: = 567

Correct

Part CHow hard does the ball push against the wall?

ANSWER: = 205

Correct

Exercise 5.32

An 92 box of oranges is being pushed across a horizontal floor. As it moves, it is slowing at a constant rate

of 0.90 each second. The push force has a horizontal component of 20 and a vertical component of 25 downward.

Part ACalculate the coefficient of kinetic friction between the box and floor.


ANSWER: 0.24 Correct

Problem 5.89

Two objects with masses 5.40 and 1.20 hang 0.500 above the floor from the ends of a cord 7.20 long passing over a frictionless pulley. Both objects start from rest.

Part A

Find the maximum height reached by the 1.20 object.

ANSWER: =

1.32 All attempts used; correct answer displayed

above the floor

Problem 5.95: Banked Curve I



A curve with a 140 radius on a level road is banked at the correct angle for a speed of 20 .

Part A

If an automobile rounds this curve at 30 , what is the minimum coefficient of static friction between tires and road needed to prevent skidding?



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 BFind 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 10.71



The figure shows three identical yo-yos initially at rest on a horizontal surface. For each yo-yo, the string is pulled in the direction shown. In each case, there is sufficient friction for the yo-yo to roll without slipping. Draw the free-body diagram for each yo-yo.

Part A

Draw the force vectors with their tails at the points corresponding forces were applied. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:


Part B


ANSWER:




Part C


ANSWER:


Part DIn what direction will the first yo-yo rotate? (Try it!)

ANSWER: clockwisecounterclockwise

Correct

Part EIn what direction will the second yo-yo rotate? (Try it!)


Correct

Part FIn what direction will the third yo-yo rotate? (Try it!)


Correct

Part G



Explain your answers.

ANSWER: My Answer:

Exercise 10.8

A uniform spherical shell of mass 8.20 with diameter 45.0 has four small masses of mass 2.10 attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses .

Part AWhat friction torque is needed to reduce its angular speed from 76.0 to 45.0 in a time interval of 25.0 ?

ANSWER: = −6.35×10−2

Correct

Exercise 10.11

A solid, uniform cylinder with mass 8.20 and diameter 17.0 is spinning with angular velocity 205 on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction-brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is 0.334.

Part AWhat must the applied normal force be to bring the cylinder to rest after it has turned through 5.45 revolutions?

ANSWER: 7.02 Correct N

Problem 10.62



The mechanism shown in the figure is used to raise a crate of supplies from a ship's hold. The crate has total mass 56 . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.30 and a moment of inertia = 2.0 about the axle. The crate is suspended from the free end of the rope. One end of the axle pivots on frictionless bearings; a crank handle is attached to the other end. When the crank is turned, the end of the handle rotates about the axle in a vertical circle of radius 0.12 , the cylinder turns, and the crate is raised.

Part A

What magnitude of the force applied tangentially to the rotating crank is required to raise the crate with an

acceleration of 0.80 ? (You can ignore the mass of the rope as well as the moments of inertia of the axle and the crank.)


ANSWER: =

1.5 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 EA 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 10.13



A grindstone in the shape of a solid disk with diameter 0.540 and a mass of = 50.0 is rotating at = 840

. You press an ax against the rim with a normal force of = 250 , and the grindstone comes to rest in 7.90 .

Part AFind the coefficient of friction between the ax and the grindstone. You can ignore friction in the bearings.


Exercise 10.15

A textbook of mass 1.95 rests on a frictionless, horizontal surface. A cord attached to the book passes over a

pulley whose diameter is 0.200 , to a hanging book with mass 3.05 . The system is released from rest, and the books are observed to move a distance 1.20 over a time interval of 0.800 .

Part AWhat is the tension in the part of the cord attached to the textbook?


Part BWhat is the tension in the part of the cord attached to the book?

Take the free fall acceleration to be = 9.80 .


Part C



What is the moment of inertia of the pulley about its rotation axis?

Take the free fall acceleration to be = 9.80 .

ANSWER:2.97×10−2 Correct

Problem 10.58

While exploring a castle, Exena the Exterminator is spotted by a dragon who chases her down a hallway. Exena runs into a room and attempts to swing the heavy door shut before the dragon gets her. The door is initially perpendicular to the wall, so it must be turned through to close. The door has a height of 2.90 and a width of 1.15 , and its weight is 700 . You can ignore the friction at the hinges.

Part A

If Exena applies a force of 280 at the edge of the door and perpendicular to it, how much time does it take her to close the door?

Use 9.80 for the acceleration due to gravity.

ANSWER: = 0.554 Correct s

Exercise 10.16

A 12.0- box resting on a horizontal, frictionless surface is attached to a 5.00- weight by a thin, light wire that

passes over a frictionless pulley (the figure ). The pulley has the shape of a uniform solid disk of mass 2.50 and diameter 0.520 .

Part A



After the system is released, find the horizontal tension in the wire.

ANSWER: = 32.2 Correct

Part BAfter the system is released, find the vertical tension in the wire.


Part CAfter the system is released, find the acceleration of the box.


Part DAfter the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

Express your answers separated by a comma.

ANSWER: =

32.2,60.1 Answer Requested

Test Your Understanding 10.3: Rigid-Body Rotation about a Moving Axis

A uniform cylinder rolls up an incline without slipping. As it rolls uphill, its speed decreases. The surface of the incline and the cylinder are both perfectly rigid.

Part AWhich of the forces on the cylinder exert(s) a torque about the center of the cylinder?

ANSWER: the friction forcethe weight of the cylinder the normal forcemore than one of the abovenone of the above

Correct

Since the surface and incline are perfectly rigid, the normal force exerted by the incline on the cylinder is directed toward the cylinder's center. Hence, this force exerts zero torque about the center. The weight of



the cylinder acts at its center (because the cylinder is uniform), so this force also exerts zero torque around the center. The friction force acts tangential to the circumference of the cylinder, so it does exert a torque around the center.

Test Your Understanding 10.2: Torque and Angular Acceleration for a Rigid

BodyTwo blocks, a lightweight one of mass and a heavy one of mass , are connected by a very light flexible cord that passes over a pulley of mass , radius , and moment of inertia . The pulley (which is suspended from the ceiling) spins on frictionless bearings. The cord does not slip on the pulley. When released, the block of mass accelerates upward, the block of mass accelerates downward, and the pulley has a clockwise angular acceleration.

Part A

Which is the correct relationship among the weights of the two blocks and the tensions and on the two sides of the pulley?

ANSWER:

none of thesenot enough information given to decide

Correct

The net force on the block of mass must be downward so that this block accelerates downward, so must be greater than . The net torque on the pulley must be clockwise, so must be greater than

. Finally, the net force on the block of mass must be upward so that this block accelerates upward,

so must be greater than . Hence, .


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