pc1431 masteringphysics assignment 4
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Assignment 4: Linear MomentumDue: 2:00am on Saturday, October 9, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
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A Game of Frictionless Catch
Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined massof Chuck and his cart, , is identical to the combined mass of Jackie and her cart. Initially, Chuck
and Jackie and their carts are at rest.Chuck then picks up a ball of mass and throws it to Jackie, who catches it. Assume that the ball
travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball,his speed relative to the ground is . The speed of the thrown ball relative to the ground is .
Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relativeto the ground after she catches the ball is .
When answering the questions in this problem, keep the following in mind:The original mass of Chuck and his cart does not include the mass of the ball.
The speed of an object is the magnitude of its velocity. An object's speed will always be a nonnegativequantity.
Part A
Find the relative speed between Chuck and the ball after Chuck has thrown the ball.
Hint A.1 How to approach the problem
Hint not displayed
Express the speed in terms of and .
ANSWER: =
Correct
Make sure you understand this result; the concept of "relative speed" is important. In general, iftwo objects are moving in opposite directions (either toward each other or away from each other),the relative speed between them is equal to the sum of their speeds with respect to the ground. Iftwo objects are moving in the same direction, then the relative speed between them is theabsolute value of the difference of the their two speeds with respect to the ground.
Part B
What is the speed of the ball (relative to the ground) while it is in the air?
Hint B.1 How to approach the problem
Hint not displayed
Hint B.2 Initial momentum of Chuck, his cart, and the ball
Hint not displayed
Hint B.3 Find the final momentum of Chuck, his cart, and the thrown ball
Hint not displayed
Express your answer in terms of , , and .
ANSWER:
=
Correct
Part C
What is Chuck's speed (relative to the ground) after he throws the ball?
Hint C.1 How to approach the problem
Hint not displayed
Express your answer in terms of , , and .
ANSWER:
=
Correct
Part D
Find Jackie's speed (relative to the ground) after she catches the ball, in terms of .
Hint D.1 How to approach the problem
Hint not displayed
Hint D.2 Initial momentum
Hint not displayed
Hint D.3 Find the final momentum
Hint not displayed
Express in terms of , , and .
ANSWER:
=
Correct
Part E
Find Jackie's speed (relative to the ground) after she catches the ball, in terms of .
Hint E.1 How to approach the problem
Hint not displayed
Express in terms of , , and .
ANSWER:
=
Correct
A Girl on a Trampoline
A girl of mass kilograms springs from a trampoline with an initial upward velocity of
meters per second. At height meters above the trampoline, the girl grabs a box of mass
kilograms.
For this problem, use meters per
second per second for the magnitude of theacceleration due to gravity.
Part A
What is the speed of the girl immediately before she grabs the box?
Hint A.1 How to approach the problem
Hint not displayed
Hint A.2 Initial kinetic energy
Hint not displayed
Hint A.3 Potential energy at height
Hint not displayed
Express your answer numerically in meters per second.
ANSWER: = 4.98
Correct
Part B
What is the speed of the girl immediately after she grabs the box?
Hint B.1 How to approach the problem
Hint B.1 How to approach the problem
Hint not displayed
Hint B.2 Total initial momentum
Hint not displayed
Express your answer numerically in meters per second.
ANSWER: = 3.98
Correct
Part C
Is this "collision" elastic or inelastic?
Hint C.1 Definition of an inelastic collision
Hint not displayed
ANSWER:elastic
inelastic
Correct
In inelastic collisions, some of the system's kinetic energy is lost. In this case the kinetic energylost is converted to heat energy in the girl's muscles as she grabs the box, and sound energy.
Part D
What is the maximum height that the girl (with box) reaches? Measure with respect to the
top of the trampoline.
Hint D.1 How to approach the problem
Hint not displayed
Hint D.2 Finding
Hint not displayed
Hint D.3 Finding
Hint not displayed
Express your answer numerically in meters.
ANSWER: = 2.81
Correct
Filling the Boat
A boat of mass 250 is coasting, with its engine in neutral, through the water at speed 3.00
when it starts to rain. The rain is falling vertically, and it accumulates in the boat at the rate of 10.0 .
Part A
What is the speed of the boat after time 2.00 has passed? Assume that the water resistance is
negligible.
Hint A.1 How to approach the problem
Hint not displayed
Hint A.2 Find the momentum of the boat before it starts to rain
Hint not displayed
Hint A.3 Find the mass of the boat after it has started to rain
Hint not displayed
Express your answer in meters per second.
ANSWER: 2.78Correct
Part B
Now assume that the boat is subject to a drag force due to water resistance. Is the component of
the total momentum of the system parallel to the direction of motion still conserved?
ANSWER:yes
no
Correct
The boat is subject to an external force, the drag force due to water resistance, and therefore itsmomentum is not conserved.
Part C
The drag is proportional to the square of the speed of the boat, in the form . What is the
acceleration of the boat just after the rain starts? Take the positive axis along the direction of
motion.
Hint C.1 How to approach the problem
Hint not displayed
Hint C.2 Find the time rate of change of momentum of the boat
Hint not displayed
Express your answer in meters per second per second.
Express your answer in meters per second per second.
ANSWER: −1.80×10−2
Correct
Rocket Car
A rocket car is developed to break the land speed record along a salt flat in Utah. However, the safety ofthe driver must be considered, so the acceleration of the car must not exceed (or five times the
acceleration of gravity) during the test. Using the latest materials and technology, the total mass of thecar (including the fuel) is 6000 kilograms, and the mass of the fuel is one-third of the total mass of thecar (i.e., 2000 killograms). The car is moved to the starting line (and left at rest), at which time the rocketis ignited. The rocket fuel is expelled at a constant speed of 900 meters per second relative to the car,and is burned at a constant rate until used up, which takes only 15 seconds. Ignore all effects of frictionin this problem.
Part A
Find the acceleration of the car just after the rocket is ignited.
Hint A.1 How to approach the problem
The equation for the acceleration due to rocket propulsion is , where is the
exhaust speed. To use this equation, first find an expression for the rate of mass loss of the car.
Hint A.2 find the rate of mass change
Find the rate that the rocket car's mass is changing.
Express your answer to three significant figures.
ANSWER: = -133
Correct
Express your answer to two significant figures.
ANSWER: = 20
Correct
The driver of this car is experiencing just over , or two times the acceleration one normally
feels due to gravity, at the start of the trip. This is not much different from the accelerationtypically experienced by thrill seekers on a roller coaster, so the driver is in no danger on thisscore.
Part B
Find the final acceleration of the car as the rocket is just about to use up its fuel supply.
Hint B.1 What has changed?
Hint not displayed
Hint B.2 Find the final mass
Hint not displayed
Express your answer to two significant figures.
ANSWER: = 30
Correct
The driver of this car is experiencing just over , or three times the acceleration one normally
feels due to gravity, by the end of the trip. This is the maximum acceleration achieved during thetrip, and it is still very safe for the driver, who can easily withstand over with training.
Part C
Find the final velocity of the car just as the rocket is about to use up its fuel supply.
Hint C.1 Find the change in speed
Write an expression for the change in speed of the car from start to finish: . You will need
to make use of the differential equation for rocket motion
,
if you don't know the equation for velocity of a rocket.
Hint C.1.1 How to solve the differential equation
Hint not displayed
Express your answer in terms of the exhaust speed , the initial mass of the car (plus
fuel) , and the final mass of the car .
ANSWER: = Answer not displayed
Express your answer to two significant figures.
ANSWER: = 360
Correct
At the end of the trip, the driver is going a bit over Mach 1, or one times the speed of sound. Thisproblem was based loosely on the breaking of the sound barrier by the ThrustSSC team inOctober 1997.
Three-Block Inelastic Collision
A block of mass moving with speed undergoes a completely inelastic collision with a stationary
block of mass . The blocks then move, stuck together, at speed . After a short time, the two-block
system collides inelastically with a third block, of mass , which is initially stationary. The three blocks
then move, stuck together, with speed . All
three blocks have nonzero mass. Assume thatthe blocks slide without friction.
Part A
Find , the ratio of the velocity of the two-block system after the first collision to the velocity of
the block of mass before the collision.
Hint A.1 What physical principle to use
Hint not displayed
Express your answer in terms of , , and/or .
ANSWER: = Answer not displayed
Part B
Find , the ratio of the kinetic energy of the two-block system after the first collision to the
kinetic energy of the block of mass before the collision.
Hint B.1 Formula for kinetic energy
Hint not displayed
Express your answer in terms of , , and/or .
ANSWER: = Answer not displayed
Part C
Find , the ratio of the velocity of the three-block system after the second collision to the velocity
of the block of mass before the collisions.
Hint C.1 Total mass of the blocks
Hint not displayed
Express your answer in terms of , , and/or .
ANSWER: = Answer not displayed
Part D
Find , the ratio of the kinetic energy of the three-block system after the second collision to the
initial kinetic energy of the block of mass before the collisions.
Express your answer in terms of , , and/or .
ANSWER: = Answer not displayed
Part E
Suppose a fourth block, of mass , is included in the series, so that the three-block system with
speed collides with the fourth, stationary, block. Find , the ratio of the kinetic energy of all
the blocks after the final collision to the initial kinetic energy of the block of mass before any of
the collisions.
Hint E.1 How to approach the question
Hint not displayed
Express your answer in terms of , , , and/or .
ANSWER: = Answer not displayed
Conservation of Momentum in Two Dimensions Ranking Task
Part A
The figures below show bird's-eye views of six automobile crashes an instant before they occur. Theautomobiles have different masses and incoming velocities as shown. After impact, the automobiles remainjoined together and skid to rest in the direction shown by . Rank these crashes according to the angle ,
measured counterclockwise as shown, at which the wreckage initially skids.
Hint A.1 Conservation of momentum in two dimensions
Hint not displayed
Hint A.2 Determining the angle
Hint not displayed
Rank from largest to smallest. To rank items as equivalent, overlap them.
Rank from largest to smallest. To rank items as equivalent, overlap them.
ANSWER:
Answernotdisplayed
Surprising Exploding Firework
A mortar fires a shell of mass at speed . The shell explodes at the top of its trajectory (shown by a
star in the figure) as designed. However, rather than creating a shower of colored flares, it breaks into
just two pieces, a smaller piece of mass and a larger piece of mass . Both pieces land at
exactly the same time. The smaller piece lands perilously close to the mortar (at a distance of zero fromthe mortar). The larger piece lands a distance from the mortar. If there had been no explosion, the
shell would have landed a distance from the mortar. Assume that air resistance and the mass of the
shell's explosive charge are negligible.
Part A
Find the distance from the mortar at which the larger piece of the shell lands.
Hint A.1 Find the position of the center of mass in terms of
Hint not displayed
Hint A.2 Find the position of the center of mass in terms of
Hint not displayed
Express in terms of .
ANSWER: = Answer not displayed
Pucks on Ice
Two hockey players, Aaron and Brunnhilde, are pushing two pucks on a frictionless ice rink. The pucksare initially at rest on the starting line.Brunnhilde is pushing puck B, which has a massthree times as great as that of puck A, whichAaron is pushing. The players exert equalconstant forces of magnitude on their pucks,
directed horizontally, towards the finish line.They start pushing at the same time, and eachplayer pushes his or her puck until it crosses thefinish line, a distance away.
Part A
Which puck reaches the finish line first?
Hint A.1 Compute the relative acceleration of the pucks
Hint not displayed
ANSWER:Both pucks reach the finish line at the same time.
Puck A reaches the finish line first.
Puck B reaches the finish line first.
More information is needed to answer thisquestion.
Answer notdisplayed
Part B
Part B
Let be the magnitude of the kinetic energy of puck A at the instant it reaches the finish line.
Similarly, is the magnitude of the kinetic energy of puck B at the (possibly different) instant it
reaches the finish line. Which of the following statements is true?
Hint B.1 Determine the simplest way to answer this question
Hint not displayed
Hint B.2 Work done on puck A
Hint not displayed
Hint B.3 Work done on puck B
Hint not displayed
ANSWER:
You need more information to decide.
Answer not displayed
Part C
Part not displayed
A Rocket in Deep Space
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 15.6 .
Part A
What is the speed of the exhaust gas relative to the rocket?
Hint A.1 How to approach the problem
Hint not displayed
Hint A.2 The acceleration of the rocket
Hint not displayed
Hint A.3 Find the change in mass of the rocket
Hint not displayed
Express your answer numerically in kilometers per second.
ANSWER: = Answer not displayed
ANSWER: = Answer not displayed
A Relation Between Momentum and Kinetic Energy
Part A
A cardinal (Richmondena cardinalis) of mass 3.60×10−2 and a baseball of mass 0.144 have
the same kinetic energy. What is the ratio of the cardinal's magnitude of momentum to the
magnitude of the baseball's momentum?
Hint A.1 How to approach the problem
Hint not displayed
Hint A.2 Find a relationship between kinetic energy and momentum
Hint not displayed
ANSWER: = Answer not displayed
Part B
A man weighing 720 and a woman weighing 460 have the same momentum. What is the ratio of
the man's kinetic energy to that of the woman ?
Hint B.1 How to approach the problem
Hint not displayed
Hint B.2 Find a relationship between momentum and kinetic energy
Hint not displayed
ANSWER: = Answer not displayed
Collision at an Angle
Two cars, both of mass , collide and stick together. Prior to the collision, one car had been traveling
north at speed , while the second was traveling at speed at an angle south of east (as indicated
in the figure). After the collision, the two-car system travels at speed at an angle east of north.
Part A
Find the speed of the joined cars after the collision.
Hint A.1 Determine the conserved quantities
Hint not displayed
Hint A.2 The component of the final velocity in the east-west direction
Hint not displayed
Hint A.3 Find the north-south component of the final momentum
Hint not displayed
Hint A.4 Math help
Hint not displayed
Express your answer in terms of and .
ANSWER: = Answer not displayed
Part B
Part not displayed
Two Worlds on a String
Two balls, A and B, with masses and are connected by a taut, massless string, and are moving
along a horizontal frictionless plane. The distance between the centers of the two balls is . At a certain
instant, the velocity of ball B has magnitude and is directed perpendicular to the string and parallel to
the horizontal plane, and the velocity of ball A is zero.
Part A
Find , the tension in the string.
Hint A.1 Descibe the nature of the motion
Hint not displayed
Hint A.2 The key idea
Hint not displayed
Hint A.3 Find the velocity of the center of mass
Hint not displayed
Hint A.4 Find the rotational speed
Hint not displayed
Hint A.5 Find the radius of rotation
Hint not displayed
Hint A.6 Acceleration of ball B
Hint not displayed
Express in terms of , , , and .
ANSWER: = Answer not displayed
Score Summary:
Your score on this assignment is 93.8%.You received 37.5 out of a possible total of 40 points.
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