##### Document Text Contents

Page 1

Assignment 1

Due: 11:59pm on Friday, November 25, 2011

Note: To understand how points are awarded, read your instructor's Grading Policy.

[Switch to Standard Assignment View]

Block on an Incline

A block lies on a plane raised an angle from the horizontal. Three forces act upon the block:

, the force of gravity; , the normal force; and , the force of friction. The coefficient of friction

is large enough to prevent the block from sliding .

Part A

Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes?

ANSWER:

only

only

only

and

and

and

and and

Correct

Part B

Which forces lie along the axes of the coordinate system b, in which the y axis is vertical?

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Page 2

ANSWER:

only

only

only

and

and

and

and and

Correct

Now you are going to ignore the general rule (actually, a strong suggestion) that you should pick

the coordinate system with the most vectors, especially unknown ones, along the coordinate

axes. You will find the normal force, , using vertical coordinate system b. In these coordinates

you will find the magnitude appearing in both the x and y equations, each multiplied by a

trigonometric function.

Part C

Because the block is not moving, the sum of the y components of the forces acting on the block

must be zero. Find an expression for the sum of the y components of the forces acting on the

block, using coordinate system b.

Hint C.1 Find the y component of

Hint not displayed

Hint C.2 Find the y component of

Hint not displayed

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

ANSWER:

Correct

Part D

Because the block is not moving, the sum of the x components of the forces acting on the block

must be zero. Find an expression for the sum of the x components of the forces acting on the

block, using coordinate system b.

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Page 5

28 days. The Moon makes large orbits around the center of mass of the Earth-Moon

system, whereas the center of the Earth makes small orbits.

Part C

Calculate the location of the center of mass of the Earth-Moon-Sun system during a full Moon.

A full Moon occurs when the Earth, Moon, and Sun are lined up as shown in the figure. Use a

coordinate system in which the center of

the sun is at and the Earth and

Moon both lie along the positive x

direction.

Hint C.1 Calculating the center of mass

Hint not displayed

Express your answer in kilometers to three significant figures.

ANSWER:

=

456

Correct

The equatorial radius of the Sun is 695,000 . As you can see, the center of mass for

the Sun-Earth-Moon system is well within the Sun. However, if you were to find the center

of mass of the Jupiter-Sun system, you would find that it is slightly above the surface of the

Sun at 780,000 from the center of the Sun. A distant alien civilization would not be able

to see Jupiter directly, because it is far too faint, but they would be able to see the Sun

move back and forth as it orbited the center of mass with Jupiter. Because the sun is

"wobbling," alien scientists would be able to infer that there was a planet around the Sun.

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This is one of the methods that human scientists are using to identify planets around other

stars.

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 from the 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:

=

Correct

Rocket Car

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Page 10

Hint not displayed

Hint A.4 Compute the sum of horizontal forces

Hint not displayed

Express the required force in terms of given quantities.

ANSWER:

=

Correct

Part B

The solution for has a singularity (that is, becomes infinitely large) at a certain angle . For any

angle , the expression for will be negative. However, a negative applied force would

reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable

solution. In fact, the increased normal force at these large angles makes the force of friction too large to

move the lawnmower at all.

Find an expression for .

Hint B.1 How to approach the problem

Hint not displayed

ANSWER:

=

Correct

You should have found that , the force required to push the lawnmower at constant speed, was

.

Note that this expression becomes infinite when the denominator equals zero:

,

or

.

(The phrase " has a singularity at angle " means that " goes to infinity at a certain

angle .")

It's not too hard to understand what this means. Suppose you were pushing straight down on the

lawnmower ( degrees). It obviously wouldn't move. But, according to the equation for ,

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when you plug in degrees, you get a negative force (which doesn't make sense).

The more vertical you push, the harder it gets to move the lawnmower. At , it gets

impossible to move it. The force required to move it goes to infinity; you have to push infinitely hard.

Score Summary:

Your score on this assignment is 109.2%.

You received 15.49 out of a possible total of 16 points, plus 1.98 points of extra credit.

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

11 af 11 21-01-2012 01:14

Assignment 1

Due: 11:59pm on Friday, November 25, 2011

Note: To understand how points are awarded, read your instructor's Grading Policy.

[Switch to Standard Assignment View]

Block on an Incline

A block lies on a plane raised an angle from the horizontal. Three forces act upon the block:

, the force of gravity; , the normal force; and , the force of friction. The coefficient of friction

is large enough to prevent the block from sliding .

Part A

Consider coordinate system a, with the x axis along the plane. Which forces lie along the axes?

ANSWER:

only

only

only

and

and

and

and and

Correct

Part B

Which forces lie along the axes of the coordinate system b, in which the y axis is vertical?

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

1 af 11 21-01-2012 01:14

Page 2

ANSWER:

only

only

only

and

and

and

and and

Correct

Now you are going to ignore the general rule (actually, a strong suggestion) that you should pick

the coordinate system with the most vectors, especially unknown ones, along the coordinate

axes. You will find the normal force, , using vertical coordinate system b. In these coordinates

you will find the magnitude appearing in both the x and y equations, each multiplied by a

trigonometric function.

Part C

Because the block is not moving, the sum of the y components of the forces acting on the block

must be zero. Find an expression for the sum of the y components of the forces acting on the

block, using coordinate system b.

Hint C.1 Find the y component of

Hint not displayed

Hint C.2 Find the y component of

Hint not displayed

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

ANSWER:

Correct

Part D

Because the block is not moving, the sum of the x components of the forces acting on the block

must be zero. Find an expression for the sum of the x components of the forces acting on the

block, using coordinate system b.

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

2 af 11 21-01-2012 01:14

Page 5

28 days. The Moon makes large orbits around the center of mass of the Earth-Moon

system, whereas the center of the Earth makes small orbits.

Part C

Calculate the location of the center of mass of the Earth-Moon-Sun system during a full Moon.

A full Moon occurs when the Earth, Moon, and Sun are lined up as shown in the figure. Use a

coordinate system in which the center of

the sun is at and the Earth and

Moon both lie along the positive x

direction.

Hint C.1 Calculating the center of mass

Hint not displayed

Express your answer in kilometers to three significant figures.

ANSWER:

=

456

Correct

The equatorial radius of the Sun is 695,000 . As you can see, the center of mass for

the Sun-Earth-Moon system is well within the Sun. However, if you were to find the center

of mass of the Jupiter-Sun system, you would find that it is slightly above the surface of the

Sun at 780,000 from the center of the Sun. A distant alien civilization would not be able

to see Jupiter directly, because it is far too faint, but they would be able to see the Sun

move back and forth as it orbited the center of mass with Jupiter. Because the sun is

"wobbling," alien scientists would be able to infer that there was a planet around the Sun.

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

5 af 11 21-01-2012 01:14

Page 6

This is one of the methods that human scientists are using to identify planets around other

stars.

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 from the 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:

=

Correct

Rocket Car

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6 af 11 21-01-2012 01:14

Page 10

Hint not displayed

Hint A.4 Compute the sum of horizontal forces

Hint not displayed

Express the required force in terms of given quantities.

ANSWER:

=

Correct

Part B

The solution for has a singularity (that is, becomes infinitely large) at a certain angle . For any

angle , the expression for will be negative. However, a negative applied force would

reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable

solution. In fact, the increased normal force at these large angles makes the force of friction too large to

move the lawnmower at all.

Find an expression for .

Hint B.1 How to approach the problem

Hint not displayed

ANSWER:

=

Correct

You should have found that , the force required to push the lawnmower at constant speed, was

.

Note that this expression becomes infinite when the denominator equals zero:

,

or

.

(The phrase " has a singularity at angle " means that " goes to infinity at a certain

angle .")

It's not too hard to understand what this means. Suppose you were pushing straight down on the

lawnmower ( degrees). It obviously wouldn't move. But, according to the equation for ,

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

10 af 11 21-01-2012 01:14

Page 11

when you plug in degrees, you get a negative force (which doesn't make sense).

The more vertical you push, the harder it gets to move the lawnmower. At , it gets

impossible to move it. The force required to move it goes to infinity; you have to push infinitely hard.

Score Summary:

Your score on this assignment is 109.2%.

You received 15.49 out of a possible total of 16 points, plus 1.98 points of extra credit.

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignm...

11 af 11 21-01-2012 01:14