gravity lab experiment

4/7/13 Lab 9 (Gravity)

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Lab 9 (Gravity)

Due: 11:59pm on Sunday, March 24, 2013

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

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?

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:

PHY110ASPRING2013

Lab 9 (Gravity) Resources

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.

The velocity of the parachutist is not changing with time.

The velocity of the parachutist must be zero.

weight

gravity

force

mass

Signed in as Ellie Kamens Help Close



Correct

Mass 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?

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 thatthe planet 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:

The force of gravity is the same for each object.

The force of gravity is proportional to the object’s mass.

The force of gravity on an object in a vacuum is zero.

two times your weight on Earth

four times your weight on Earth

one-fourth your weight on Earth

the same as your weight on Earth

one-half your weight on Earth



Correct

Since 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 theSun would _________.

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:

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 forceof 100 N, what is the acceleration of the cart?


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

ANSWER:

Correct

Since 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.

one-fourth as strong

one-half as strong

the same strength

twice as strong

decrease by half

remain the same

double

quadruple

0.33 m/s/s

1 m/s/s

3 m/s/s

100 m/s/s



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

identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongestto weakest, of the gravitational force acting on the asteroid on the left.

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

The force of gravity follows an inverse square law, meaning that the strength of the force declines with the square of the distance betweentwo masses. 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:

Correct

Because the distance is the same for all five object pairs shown in Part A, the gravitational force depends only on the product of themasses. Moreover, notice that the asteroid on the left has the same mass in all five cases. With these facts in mind, you should beable to answer Part A.

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:

The acceleration of object B is three times that of object A.

The speeds of the two objects are equal after 2 seconds.

The speed of object A is three times that of object B after 3 seconds.

The accelerations of the two objects are equal.

the size of the larger mass in the pair

the size of the smaller mass in the pair

the product of the two object masses ( )

the sum of the two object masses ( )



Answer Requested

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 toPart B 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:

Correct

Newton’s third law tells us that every force has an equal and opposite reaction force, which means the objects attract each othergravitationally; therefore, the gravitational force acting on the object on the left is always equally strong as the gravitational force actingon the object on the right (considering only these two objects). With this idea in mind, think about how your ranking for Part A isrelated to the ranking for Part B.

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 left

the gravitational force exerted by the asteroids on the left will be equal for each pair of objects because all the asteroids have thesame mass

to 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



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 asthe gravitational 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 forPart 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 theasteroid on 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:

Correct

Newton’s second law of motion, F=ma, tells us that greater force means greater acceleration. With this idea in mind, think about howyour ranking for Part A is related to the ranking for Part C.

ANSWER:

mass

acceleration

distance

velocity



Correct

According to Newton’s second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exertedon it by 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 whichthe Moon 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.Therefore if mass is larger, acceleration must be smaller, and vice versa.

Understanding Mass and Weight

Fg divided by the mass of the Earth

Fg divided by the mass of the Moon

Fg divided by the acceleration of the Earth

Fg divided by the acceleration of the Moon

the Moon has a larger acceleration than Earth, because it has a smaller mass

Earth has a larger acceleration than the Moon, because it has a larger mass

the Moon and Earth both have equal accelerations, because the forces are equal



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 ofgravitation.

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 anobject's mass, 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 andits location.

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.

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

12.0 lbs

0.34 g

120 kg

1600 kN

0.34 m

411 cm

899 MN

12.0 lbs

0.34 g

120 kg

1600 kN

0.34 m

411 cm

899 MN



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 changesin the 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 recentbouts, 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 allowedto exceed 118 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:

NameMass( )

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 massequal to 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 only

weight only

both mass and weight

neither mass nor weight

mass increases; weight decreases

mass decreases; weight decreases

mass increases; weight increases

mass increases; weight remains the same

mass remains the same; weight decreases

mass remains the same; weight increases

mass remains the same; weight remains the same



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 theearth?

ANSWER:

ANSWER:

Correct

5.7

25%

50%

200%

400%

Tehar

Loput

Cremury

Suven

Pentune

Rams



Part H

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

ANSWER:

Correct

Of 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!

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 thedistance is marked to make it easier to see how the locations compare. Assume the spaceship has the same mass throughout the trip (that is, itis not burning any fuel). Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exertson the spaceship, from strongest to weakest.


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

ANSWER:

Correct

We say that gravity follows an inverse square law with distance, which means the force of gravity decreases with the square of thedistance. For example, doubling the distance weakens the force of gravity by a factor of four. If you think about it, this is the onlyinformation you need to complete Part A.

ANSWER:

mass increases; weight decreases

mass decreases; weight decreases

mass increases; weight increases

mass increases; weight remains the same

mass remains the same; weight decreases

mass remains the same; weight increases

mass remains the same; weight remains the same

increases with the square of their distance apart

increases in direct proportion to their distance apart

decreases with the square of their distance apart

decreases in direct proportion to their distance apart



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 thestrength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.


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:

Correct

We say that gravity follows an inverse square law with distance, which means the force of gravity decreases with the square of thedistance. For example, doubling the distance weakens the force of gravity by a factor of four. If you think about it, this is the onlyinformation you need to complete Part B.

ANSWER:

increases with the square of their distance apart

increases in direct proportion to their distance apart

decreases with the square of their distance apart

decreases in direct proportion to their distance apart



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, anasteroid with 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 toright based on the 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:

Correct

Nicely done! It’s good that you know that the gravitational force between two objects is related to the product of their masses andinversely related to the square of the distance between them. Think about how the strength of the gravitational force will change if themasses are kept the same and the distance is changed, or if the distance is kept the same but the masses are changed.

ANSWER:

add the two masses together, divide by their distance

multiply the two masses together, divide by their distance

square the two masses, divide by their distance

add the two masses together, divide by their distance squared

multiply the two masses, divide by their distance squared



Correct

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

Score Summary:

Your score on this assignment is 82.2%.You received 3.29 out of a possible total of 4 points.

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