portfolio 2 - activity 1 mastering physics

13/9/2015 Portfolio 2 - Activity 1

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3778740 1/18

Portfolio 2 - Activity 1Due: 11:59pm on Sunday, September 13, 2015

To understand how points are awarded, read the Grading Policy for this assignment.

Ranking Task: Newton's Law of Gravity

Part A

Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distanceis marked to make it easier to see how the locations compare. Assume the spaceship has the same mass throughout the trip (that is, it is not burningany fuel). Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship,from strongest to weakest.

Hint 1. What does the strength of gravity depend on?

For the situations shown, the two objects we are concerned with are Earth and the spaceship, which both have constant masses. Therefore, thestrength of gravity between them: __________.

ANSWER:

ANSWER:

Correct

Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as thespaceship gets farther from Earth.

Part B

The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strengthof the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.

increases with the square of their distance apartincreases in direct proportion to their distance apartdecreases with the square of their distance apartdecreases in direct proportion to their distance apart




For the situations shown, the two objects we are concerned with are the Moon and the spaceship, which both have constant masses.Therefore, the strength of gravity between them __________.

ANSWER:

ANSWER:

Correct

Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as thespaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity.

Part C

The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroidwith M=2 has twice the mass of one with M=1 and a distance of d=2 is twice as large as a distance of d=1. Rank each pair from left to right based onthe strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.

Hint 1. How do we calculate the gravitational force between two objects?

To calculate the gravitational force between two objects we __________, and then multiply by the gravitational constant .

ANSWER:

increases with the square of their distance apartincreases in direct proportion to their distance apartdecreases with the square of their distance apartdecreases in direct proportion to their distance apart

G



ANSWER:

Correct

You have correctly taken into account both the masses of the asteroids and the distances between them.

Motion and Gravity Tutorial

Work through the tutorial by clicking the image or link below, then answer the questions below.Motion and Gravity

Part A

A parachutist is falling toward the ground. The downward force of gravity is exactly equal to the upward force of air resistance. Which statement istrue?

add the two masses together, divide by their distancemultiply the two masses together, divide by their distancesquare the two masses, divide by their distanceadd the two masses together, divide by their distance squaredmultiply the two masses, divide by their distance squared

http://media.pearsoncmg.com/aw/aw_0media_physics/hewitttutorials/motiongravity/motiongravity.html

http://media.pearsoncmg.com/aw/aw_0media_physics/hewitttutorials/motiongravity/motiongravity.html



Hint 1. Newton’s second law

Use Newton’s second law to determine the parachutist’s acceleration.

ANSWER:

Correct

Since the net force on the parachutist is zero, the parachutist is not accelerating.

Part B

A kilogram is a measure of an object’s ________.

Hint 1. Mass versus weight

A kilogram is not a measure of force.

ANSWER:

CorrectMass is measured in kilograms in the metric system.

Part C

Why would a bowling ball and a small marble fall down to the surface of the Moon at the same rate?


How does the acceleration of an object depend on the object’s mass and the net force acting on it?

ANSWER:

Correct

The object’s acceleration is equal to the force of gravity divided by its mass, and the force of gravity is proportional to the mass; therefore, thebowling ball and the marble fall with the same acceleration.

Part D

If you stood on a planet having a mass four times that of Earth, and a radius two times that of Earth, how much would you weigh on that planet?

The velocity of the parachutist must be zero.The velocity of the parachutist is not changing with time.The velocity of the parachutist is increasing with time. Review Lesson 1 in the tutorial for additional help.The velocity of the parachutist is decreasing with time.

forceweightgravitymass

The force of gravity is proportional to the object’s mass.The force of gravity is the same for each object.The force of gravity on an object in a vacuum is zero.



Hint 1. Force of gravity due to a planet

The person’s weight (force of gravity) on a planet is proportional to the mass of the planet and inversely proportional to the square of theplanet’s radius.

ANSWER:

Correct

Weight is inversely proportional to the square of the planet’s radius. Therefore, even though the planet is four times as massive, the fact that theplanet has twice the radius exactly offsets the effect of the higher mass.

Part E

Imagine that Earth had an identical twin planet, “Farth”, which is twice as far away from the Sun as Earth is. Compared to the force of gravity thatEarth exerts on the Sun, how strong is the force of gravity that Farth exerts on the Sun?

Hint 1. Force of gravity

The force of gravity is inversely proportional to the square of the distance between the two objects.

ANSWER:

CorrectSince Farth is twice as far from the Sun, the force of gravity is one fourth as strong.

Part F

Suppose the Sun suddenly shrunk, reducing its radius by half (but its mass remaining the same). The force of gravity exerted on the Earth by the Sunwould _________.

Hint 1. Force of gravity

Does the force of gravity depend on the radius of an object, or the distance away from the object?

ANSWER:

the same as your weight on Earthone-half your weight on Earthtwo times your weight on Earthone-fourth your weight on Earthfour times your weight on Earth

one-fourth as strongone-half as strongthe same strengthtwice as strong

decrease by halfremain the samedoublequadruple



Correct

Since the distance between the Sun’s center and Earth’s center doesn’t change when the Sun shrinks, the force of gravity doesn’t change.

Part G

If one person is pushing to the right on a 300-kg cart with a force of 200 N, and another person is pushing to the left on the same cart with a force of100 N, what is the acceleration of the cart?


Use Newton’s second law to solve for the acceleration of the cart, .

ANSWER:

CorrectSince the net force on the cart is 100 N, the acceleration is .

Part H

Object A has three times as the mass of object B. Identical forces are exerted on the two objects. Which statement is true?


From Newton’s second law, the acceleration is equal to the force divided by the mass.

ANSWER:

Correct

Since object A is three times more massive, from , its acceleration is three times lower than that of object B.

Ranking Task: Gravity and Newton's Laws

Part A

The following five diagrams show pairs of astronomical objects that are all separated by the same distance . Assume the asteroids are all identicaland relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest,of the gravitational force acting on the asteroid on the left.


The force of gravity follows an inverse square law, meaning that the strength of the force declines with the square of the distance between twomasses. But if the distances between pairs of objects are all the same, as in Part A, then the strength of gravity depends only on __________.

ANSWER:

a = F/m

0.33 m/s/s1 m/s/s3 m/s/s100 m/s/s

a = F/m = 100/300 m/s/s = 0.33 m/s/s

The accelerations of the two objects are equal.The speeds of the two objects are equal after 2 seconds.The acceleration of object B is three times that of object A.The speed of object A is three times that of object B after 3 seconds.

a = F/m

d



Hint 2. Comparative masses for the objects shown

Here are some comparisons for the masses of the objects on the right:• The Sun’s mass is about 330,000 times the mass of the Earth.

• Earth’s mass is about 80 times the mass of the Moon.

• The Moon’s mass is about a million times that of a typical small asteroid.

• A typical small asteroid has a mass at least a million trillion trillion trillion times that of a hydrogen atom.With this information and an understanding of the factors that determine the strength of gravity, you should be able to complete Part A.

ANSWER:

Correct

Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the sameasteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to PartB to explore what happens if we instead ask about the gravitational force acting on the object on the right.

Part B

The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength,from strongest to weakest, of the gravitational force acting on the object on the right.

Hint 1. How can Newton’s third law help you solve this problem?

ANSWER:

the size of the larger mass in the pairthe size of the smaller mass in the pairthe product of the two object masses ( )the sum of the two object masses ( )

×M1 M2

+M1 M2



ANSWER:

Correct

Newton’s third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be exactly the same as thegravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A.

Part C

The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroidon the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.

Hint 1. How can Newton’s second law help you solve this problem?

According to Newton’s second law, the greater the force exerted on an object, the greater the object’s _____.

ANSWER:

ANSWER:

According to Newton’s third law __________.

the strength of the force that the object on the left exerts on the object on the right has to be exactly the same (but in an oppositedirection) as the force the object on the right exerts on the object on the leftthe gravitational force exerted by the asteroids on the left will be equal for each pair of objects because all the asteroids have thesame massto find the force on the object on the right, you just have to divide the asteroid mass by the mass of the object on the right

massaccelerationdistancevelocity



Correct

According to Newton’s second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on itby the object on the right. That is why the ranking here is the same as the ranking for Part A.

Part D

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which theMoon exerts on Earth. Therefore, according to Newton’s second law of motion __________.

Hint 1. How can Newton’s second law help you solve this problem?

Newton’s second law of motion states that force equals mass times acceleration, or F=ma. Suppose you have already calculated thegravitational force, which we will call Fg , attracting Earth and the Moon. Then the amount of acceleration of Earth due to this force is__________.

ANSWER:

ANSWER:

Correct

Newton’s second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Thereforeif mass is larger, acceleration must be smaller, and vice versa.

Fg divided by the mass of the EarthFg divided by the mass of the MoonFg divided by the acceleration of the EarthFg divided by the acceleration of the Moon

the Moon has a larger acceleration than Earth, because it has a smaller massEarth has a larger acceleration than the Moon, because it has a larger massthe Moon and Earth both have equal accelerations, because the forces are equal



Understanding Mass and Weight

Learning Goal:

To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton's law of gravitation.

The concepts of mass and weight are often confused. In fact, in everyday conversations, the word "weight" often replaces "mass," as in "My weight isseventy-five kilograms" or "I need to lose some weight." Of course, mass and weight are related; however, they are also very different.

Mass, as you recall, is a measure of an object's inertia (ability to resist acceleration). Newton's 2nd law demonstrates the relationship among an object'smass, its acceleration, and the net force acting on it: . Mass is an intrinsic property of an object and is independent of the object's location.

Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: , where is the weight of an object, is the mass of that object, and is the local acceleration due to gravity (in other words, the strength of

the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and itslocation.

Part A

Which of the following quantities represent mass?

Check all that apply.

ANSWER:

Correct

Part B

Which of the following quantities would be acceptable representations of weight?

Check all that apply.

ANSWER:

Correct

Weight is a force and is measured in newtons (or kilonewtons, meganewtons, etc.) or in pounds (or tons, megatons, etc.).

Using the universal law of gravity, we can find the weight of an object feeling the gravitational pull of a nearby planet. We can write an expression , where is the weight of the object, is the gravitational constant, is the mass of that object, is mass of the planet, and is the

distance from the center of the planet to the object. If the object is on the surface of the planet, is simply the radius of the planet.

= maFnet

w = mg w m g

12.0 lbs0.34 g120 kg1600 kN0.34 m411 cm899 MN

12.0 lbs0.34 g120 kg1600 kN0.34 m411 cm899 MN

w = GmM/r2 w G m M rr



Part C

The gravitational field on the surface of the earth is stronger than that on the surface of the moon. If a rock is transported from the moon to the earth,which properties of the rock change?

ANSWER:

Correct

Part D

An object is lifted from the surface of a spherical planet to an altitude equal to the radius of the planet. As a result, which of the following changes inthe properties of the object take place?

ANSWER:

Correct

Punch Taut is a down-on-his-luck heavyweight boxer. One day, he steps on the bathroom scale and "weighs in" at 236 lb. Unhappy with his recent bouts,Punch decides to go to a different planet where he would weigh in at 118 lb so that he can compete with the bantamweights who are not allowed to exceed118 lb. His plan is to travel to Xobing, a newly discovered star with a planetary system. Here is a table listing the planets in that system:

Name Mass( )

Radius( )

Tehar 2.1 0.80

Loput 5.6 1.7

Cremury 0.36 0.30

Suven 12 2.8

Pentune 8.3 4.1

Rams 9.3 4.0

In this table, the mass and the radius of each planet are given in terms of the corresponding properties of the earth. For instance, Tehar has a mass equalto 2.1 earth masses and a radius equal to 0.80 earth radii.

Part E

If acceleration due to gravity on the earth is , which formula gives the acceleration due to gravity on Loput?

Hint 1. What equations to use

Combine and .

ANSWER:

mass onlyweight onlyboth mass and weightneither mass nor weight

mass increases; weight decreasesmass decreases; weight decreasesmass increases; weight increasesmass increases; weight remains the samemass remains the same; weight decreasesmass remains the same; weight increasesmass remains the same; weight remains the same

Mearth Rearth

g

w = mg w = GmM/r2



Correct

Part F

If the acceleration due to gravity on the earth is 9.8 , what is the acceleration due to gravity on Rams?

Express your answer in meters per second squared and use two significant figures.

ANSWER:

Correct

Part G

Which planet should Punch travel to if his goal is to weigh in at 118 lb? Refer to the table of planetary masses and radii given to determine youranswer.

Hint 1. Determine the percentage difference in weight

To make the scale read 118 lb, the 236-lb Punch has to travel to a planet where the gravitational field is what percentage of that on the earth?

ANSWER:

ANSWER:

Correct

Part H

After Punch Taut travels to Pentune, what actually happens to his mass and his weight?

g 1.75.6

g 1.72

5.6

g 1.72

5.62

g 5.61.7

g 5.62

1.72

g 5.61.72

m/s2

5.7 m/s2

25%50%200%400%

TeharLoputCremurySuvenPentuneRams



ANSWER:

CorrectOf course, the "weight classes" in boxing are really "mass classes": It is the relative mass of the boxers that matters. The masses and theweights of the athletes are directly proportional--as long as everyone is on the same planet!

Interactive Figure: Weight in an Elevator

Explore the Interactive Figure to help you with the following set of questions. If you need more help, click on "How To Use" for more information.

Do not click any buttons on the figure at this point. Start with the questions and follow the instructions therein. When told to do so, you can usethe “Mass” slider to set the mass of the person in the elevator. You can also set the “Acceleration” slider to the desired positive or negativevalue. Then click either the “Real down” or “Real up” buttons to make the elevator move down or up, respectively. If you wish to restart theelevator, click the “Start” button.

Part A

Predict how the upward force exerted on the feet by the scale will compare to the weight of the person if the elevator is moving upward at a constantspeed.


If the speed is constant, what is the acceleration? Based on this acceleration, according to Newton’s second law, what is the net force? Giventhis value of the net force, which is a combination of the weight and the upward force, what is the upward force?

ANSWER:

Correct

mass increases; weight decreasesmass decreases; weight decreasesmass increases; weight increasesmass increases; weight remains the samemass remains the same; weight decreasesmass remains the same; weight increasesmass remains the same; weight remains the same

The upward force on the feet will exceed the weight.The upward force on the feet will be equal to the weight.The upward force on the feet will be less than the weight.



Part B

Predict how the upward force exerted on the feet by the scale will compare to the weight if the elevator is moving downward at a constant speed.


If the speed is constant, what is the acceleration? Based on this acceleration, according to Newton’s second law, what is the net force? Giventhis value of the net force, which is a combination of the weight and the upward force, what is the upward force?

ANSWER:

Correct

Part C

Predict how the upward force exerted on the feet by the scale will compare to the weight if the elevator is accelerating upward.


According to Newton’s second law, the net force is in the direction of the acceleration. The net force is a combination of the weight and theupward force.

ANSWER:

Correct

Part D

Predict how the upward force exerted on the feet by the scale will compare to the weight if the elevator is accelerating downward.


According to Newton’s second law, the net force is in the direction of the acceleration. The net force is a combination of the weight and theupward force.

ANSWER:

Correct

Visual Activity: Exploring a Person’s Weight in a Moving Elevator

First, launch the animation below. Explore the animation to help you with the following set of questions. Notice that when the elevator is stationary, we seethe person’s “normal weight” (weight at rest) of 140 lbs. Click other buttons to see what happens to the person’s weight when the elevator is moving.

The upward force on the feet will be equal to the weight.The upward force on the feet will exceed the weight.The upward force on the feet will be less than the weight.

The upward force on the feet will be equal to the weight.The upward force on the feet will exceed the weight.The upward force on the feet will be less than the weight.

The upward force on the feet will exceed the weight.The upward force on the feet will be equal to the weight.The upward force on the feet will be less than the weight.



Part A

Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward withincreasing speed, your weight will be __________.

Hint 1. How do you know if you are accelerating?

If you are in an elevator that is accelerating upward, you will feel __________ while the elevator __________.

ANSWER:

ANSWER:

Correct

Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making yourweight greater than your normal (at rest) weight.

Part B

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this timewhen the elevator is moving upward with decreasing speed, your weight will be __________.

Hint 1. In which direction is the acceleration?

Suppose you throw a ball straight up. It begins going upward fairly fast (as fast as you throw it), but it gradually slows down until it comes to astop at the top of its flight, and then starts heading back down. During the time that the ball is still on its upward path but with a slowing speed,its acceleration is _____.

ANSWER:

a downward force/moves upward with increasing speeda downward force/moves upward at constant speedlight-headed/ floor drops away from you

greater than your normal weight at restequal to your normal weight at restless than your normal weight at rest

downwardupwardzero



ANSWER:

CorrectEven though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward; the situation is ratherlike that of a ball that is still on its way up after you throw it, even though it is being pulled downward with the acceleration of gravity. Because theacceleration of the elevator is downward, your weight is lower than normal.

Part C

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion wouldyour weight also be greater than your normal weight?

Hint 1. What is your acceleration in free-fall?

As you can see in the animation, you become weightless in free-fall. What kind of acceleration do you have in free-fall on Earth?

ANSWER:

ANSWER:

Correct

When the elevator is moving downward, a downward acceleration would mean an increasing downward speed. Therefore, as your answer correctlystates, an upward acceleration would mean a decreasing downward speed.

Part D

If you are standing on a scale in an elevator, what exactly does the scale measure?

Hint 1. How does your mass change while you accelerate upward?

True or False? While you accelerate upward, you have more mass than when you are stationary.

ANSWER:

Hint 2. How does the gravitational attraction exerted on you by Earth change while you accelerate downward ?

True or False? While you accelerate downward, Earth exerts a smaller-than-normal gravitational attraction on you.

ANSWER:

greater than your normal weight at restequal to your normal weight at restless than your normal weight at rest

downward acceleration, meaning your downward speed continually gets fasterupward acceleration, meaning your downward speed continually gets slowerzero acceleration, meaning you move downward with constant speed

The elevator moves upward with constant velocity.The elevator moves downward with constant velocity.The elevator moves upward while slowing in speed.The elevator moves downward while slowing in speed.The elevator moves downward while increasing in speed.

TrueFalse



ANSWER:

Correct

You probably recognize that neither your mass nor the gravitational force exerted on you change when you are in an elevator. The scale measuresthe force that is exerted on it, which in an elevator is a combination of the force due to your normal weight and a force due to the elevator’sacceleration.

Video: Apparent Weightlessness

Watch the video and then answer the following questions.

Part A

How does the gravity in the Space Shuttle compare with the gravity on Earth’s surface?

Hint 1. Gravity and the distance from the center of the Earth

Gravity depends on how far one is from the center of the Earth. The Earth has a diameter of about 6400 km. The satellites are approximately200 kilometers above Earth’s surface.

ANSWER:

Correct

Part B

Why does the gravity in the Space Shuttle compare with the gravity on Earth the way it does?

TrueFalse

your massthe force you exert on the scalethe gravitational force exerted on you by Earth

The gravity in the Space Shuttle is much larger than the gravity on Earth’s surface.The gravity in the Space Shuttle is much smaller than the gravity on Earth’s surface.The gravity in the Space Shuttle is approximately equal to the gravity on the surface of the Earth.



Hint 1. Gravity and the distance from the center of the Earth

Gravity depends on how far one is from the center of the Earth. The Earth has a diameter of about 6400 km. The satellites are about 200kilometers above Earth’s surface.

ANSWER:

Correct

Part C

Why do the astronauts in the Space Shuttle float around?

Hint 1. Free fall and apparent weightlessness

The astronauts experience apparent weightlessness because they, along with the Space Shuttle, are in free fall toward the Earth as they arecircling the Earth.

ANSWER:

Correct

The Space Shuttle is much farther away from the center of the Earth than the surface of the Earth.The Space Shuttle is about the same distance from the center of the Earth than from the surface of the Earth.The Space Shuttle is much closer to the center of the Earth than the surface of the Earth.

There is no gravity in the Space Shuttle because it is completely enclosed and shielded from the effects of gravity due to the Earth.There is no gravity in the Space Shuttle because it is too far away from the center of the Earth.The Space Shuttle is in free fall, so the shuttle and the astronauts inside it are continuously falling toward the Earth. They thus experienceapparent weightlessness.

portfolio 2 - activity 1 mastering physics

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