Gravity, Force and Mass Assignment, Can someone please check it?

[kirsten_2009]

Homework Statement

Hello everyone!

I have this physics assignment I'm working on. It's 10 questions and I've answered them to the best of my abilities but I wanted to get valuable input from you guys and I have a couple of questions. I would really appreciate any help! Thanks in advance. PS: My answers and reasoning are in bold and my questions are in red. Please ignore the (1.) beside all the choices...I couldn't get rid of it.

1. A small car and a large truck collide head-on. During the collision, the small car experiences

1. A much larger force than the truck.
   A much larger change in momentum than the truck.
   A much larger acceleration than the truck.
   All of the above.
   None of the above.

(D) -All of the above- Because Force is related to mass, the larger truck would exert a larger force on
the small car because the large truck has more mass. Because it is exerting more Force on the small
car; the small car's motion would be affected more = change in momentum and because the car would
be pushed back harder; I assume it would have a drastic change in direction (not to mention speed)
which equals a change in acceleration.

2. Imagine that you could magically move the moon closer to Earth, so that the distance from Earth to moon is cut in half. This would cause the force that Earth exerts on the moon to be

1. halved.
   increased to four times its original value.
   reduced to 1/4 of its original value.
   doubled.
   Nonsense--Earth exerts no force on the moon.

(B) -Increased to four times its original value- Because gravity is inversely proportional to the square
of the distance between two objects. However, doesn't the mass of the objects also have an effect on
gravity? So, the Earth being that much larger than the moon and the moon being closer to Earth than
what it is already...wouldn't the gravitational pull of Earth be even greater than four times what it was
originally?

3. Suppose that the force of gravity between the sun and Earth suddenly stopped operating. What would happen?

1. Earth would fall directly inward, into the sun.
   Earth would fly directly outward from the sun.
   Earth would continue orbiting the sun, but objects on Earth would have no weight and would float into space.
   Earth would stop in its orbit around the sun, and remain motionless at its present position.
   Earth would move straight ahead, in a straight line, rather than orbiting the sun.

(E) -Earth would move straight ahead, in a straight line, rather than orbit the sun. Because the
Earth was actually just traveling through space at a constant velocity and no other forces acting on it
other than when it neared the sun; the sun's gravity curved it's path.

4. You are in distant space. A giant boulder, many times larger than you, is at rest in front of you. You tap the boulder lightly with a small hammer. What does the boulder do?

1. It accelerates during the tap, up to a slow speed [slower than walking speed], then keeps moving at that speed.
   It remains at rest.
   It accelerates during the tap, up to a high speed [faster than a fast-moving car], then keeps moving at that speed.
   It speeds up a little during the tap, but after the tap it soon [within a few minutes] slows down and comes to rest.
   It accelerates both during and after the tap.

(A) -It accelerates during the tap, up to a slow speed [slower than walking speed], then keeps
moving at that speed- Because there is no gravity, friction or air resistance in space; even a small tap
would provoke some sort of acceleration in the boulder. However, because the boulder is large, a small
hammer tap (a small Force) wouldn't cause it to accelerate much since force, acceleration and mass are
related and you would need more force to move an object with more mass...then, it would never stop
moving because there would be nothing to stop it.

5. An auto weighing 3000 Newtons has a forward drive force of 1000 Newtons. Air resistance on the car is 100 Newtons, and road resistance is 100 Newtons. The auto moves along a straight level road. The force due to gravity acting on the auto is

1. zero.
   3000 Newtons downward.
   4200 Newtons downward.
   800 Newtons upward.
   3000 Newtons upward.

(B) -3000 Newton's downward- O.K, so to be completely honest, I'm not too sure how I reached that
conclusion. What I did was pretty much a process of elimination. I figured that gravity only acts
"downward" because it's like a pull towards the center of Earth, so, I got rid of answers (a), (d), and (e).
Then I was left with (b) and (c) and I figured that you just don't add all the forces...because the direction of
the force matter and none of the forces are acting in opposition to that of gravity...I figured that the force of
gravity then just becomes it's weight.

6. Regarding the relation between acceleration, force, and mass, an object's acceleration is

1. proportional to the inverse of the height of the Empire State Building.
   inversely proportional to the force on it and proportional to the object's mass.
   proportional to the force on it and proportional to the object's mass.
   inversely proportional to the force on it and inversely proportional to the object's mass.
   proportional to the force on it and inversely proportional to the object's mass.

(E) –Proportional to the force on it and inversely proportional to the object’s mass- Because, not
just because my textbook says so but also because it makes sense. The more force you apply on an
object the faster it will go. Also, the larger or denser the object the more force required to accelerate it just
as much as a lighter object.

7. During this century, we have found that Newton's physics does not apply to

1. high speed objects.
   very strong gravitational forces.
   very small objects.
   All of the above.
   Nonsense--Newton's physics always applies.

(E) –Newton’s physics always applies- I don’t know…just going by what my book says.

8. Would you be richer if you had a hunk of gold whose weight is 1 Newton on the moon, or one whose weight is 1 Newton on Earth, and why?

1. 1 Newton on Earth, because then the gold's weight on Earth would be larger.
   1 Newton on Earth, because then the gold's mass would be larger.
   1 Newton on the moon, because then the gold's mass would be larger.
   1 Newton on the moon, because then the gold's weight on the moon would be larger.
   It wouldn't make any difference, because the amount of actual gold would be the same in both cases.

(D) -1 N on the moon, because then the gold’s weight on the moon would be larger- So, I’m not
sure if the question is just ambiguous or if I’m not understanding it correctly. If I look at it strictly from the
mass point of view then answer (e) is correct: an objects mass is constant no matter where it is in space
because its number of atoms doesn’t change. BUT, if we’re talking just about the “weight” (which is the
effect or pull of gravity on the mass) then wouldn’t 1 N of anything in the moon have to be much larger
(about 6x more) than on Earth in order to weight the same (1 N) because the pull of gravity is that much
less?

9. Astronauts in orbit around Earth feel weightless because

1. they must lose weight for the space program.
   they are in "free fall" around Earth.
   there is no gravity out there.
   they are moving with constant velocity.
   no forces at all are acting on them.

(E) –No forces at all are acting on them- Again, I’m not sure. I know that gravity still exists within the
orbit of Earth (actually it’s still quite strong) so it makes my answer (e) kind of contradictory but they “feel”
weightless because there is nothing “pushing up on them” (no contact forces) so they can’t “feel” gravity
though it’s still there….? If that reasoning is not correct, then I would go with (b) just because the rest of
the answers don’t make sense to me either…

10. If you somehow increased Earth's radius, without changing its mass, would this affect your weight?

1. Yes, your weight would increase.
   No, because the force of gravity on your body depends only on your mass and on Earth's total mass--it doesn't depend on Earth's size.
   Yes, your weight would decrease.
   No, because your weight always remains the same regardless of how you change the external surroundings.

(C) –Yes, your weight would decrease – Though, I am tempted to pick (b)…I decided to go with (c)
because if the Earth expanded its radius (the Earth uniformly expanded its radius –so really it’s the Earth diameter) then you’d be further away from the center and thus the pull of gravity would be less, which is what affects your weight not your mass…?

 

[Doc Al]

1. A small car and a large truck collide head-on. During the collision, the small car experiences

1. A much larger force than the truck.
   A much larger change in momentum than the truck.
   A much larger acceleration than the truck.
   All of the above.
   None of the above.

(D) -All of the above- Because Force is related to mass, the larger truck would exert a larger force on
the small car because the large truck has more mass. Because it is exerting more Force on the small
car; the small car's motion would be affected more = change in momentum and because the car would
be pushed back harder; I assume it would have a drastic change in direction (not to mention speed)
which equals a change in acceleration.

Careful! What does Newton's 3rd law have to say about this?

2. Imagine that you could magically move the moon closer to Earth, so that the distance from Earth to moon is cut in half. This would cause the force that Earth exerts on the moon to be

1. halved.
   increased to four times its original value.
   reduced to 1/4 of its original value.
   doubled.
   Nonsense--Earth exerts no force on the moon.

(B) -Increased to four times its original value- Because gravity is inversely proportional to the square
of the distance between two objects. However, doesn't the mass of the objects also have an effect on
gravity? So, the Earth being that much larger than the moon and the moon being closer to Earth than
what it is already...wouldn't the gravitational pull of Earth be even greater than four times what it was
originally?

Does the mass of the objects affect the gravitational force? Of course. But here the masses have not changed. The only thing that changes is the distance.

(Note: In general, it's not a good idea to cram too many questions into the same post!)

 

[theOrange]

Homework Statement

2. Imagine that you could magically move the moon closer to Earth, so that the distance from Earth to moon is cut in half. This would cause the force that Earth exerts on the moon to be

1. halved.
   increased to four times its original value.
   reduced to 1/4 of its original value.
   doubled.
   Nonsense--Earth exerts no force on the moon.

(B) -Increased to four times its original value- Because gravity is inversely proportional to the square
of the distance between two objects. However, doesn't the mass of the objects also have an effect on
gravity? So, the Earth being that much larger than the moon and the moon being closer to Earth than
what it is already...wouldn't the gravitational pull of Earth be even greater than four times what it was
originally?

7. During this century, we have found that Newton's physics does not apply to

1. high speed objects.
   very strong gravitational forces.
   very small objects.
   All of the above.
   Nonsense--Newton's physics always applies.

(E) –Newton’s physics always applies-I don’t know…just going by what my book says.

9. Astronauts in orbit around Earth feel weightless because

1. they must lose weight for the space program.
   they are in "free fall" around Earth.
   there is no gravity out there.
   they are moving with constant velocity.
   no forces at all are acting on them.

(E) –No forces at all are acting on them-Again, I’m not sure. I know that gravity still exists within the
orbit of Earth (actually it’s still quite strong) so it makes my answer (e) kind of contradictory but they “feel”
weightless because there is nothing “pushing up on them” (no contact forces) so they can’t “feel” gravity
though it’s still there….? If that reasoning is not correct, then I would go with (b) just because the rest of
the answers don’t make sense to me either…

2. I agree with your answer: "Increased to four times the original value."
Increase in mass does increase the gravity of the object, so yes the mass does have an effect on gravity. However when the moon is brought closer to Earth, the mass does not increase (it is constant). Therefore, only the distance is effecting the amount of gravity, not the mass.
Look back at the formula, see what is and is not changing.

7. Well look at what kind of physics has been developing lately, they talk about it all the time on Discovery channel. Where do the "traditional" laws of physics break down?

9. Think for one second on this one, which force is always acting on an object, no matter where you are in space? If you are on in an airplane and it suddenly goes downward accelerating at 9.81m/s^2, do you "feel" gravity or weightlessness?

 

[kirsten_2009]

Thank you! Yes, I received an email about not putting more than one question on a thread, ooops, sorry.

 

[Doc Al]

3. Suppose that the force of gravity between the sun and Earth suddenly stopped operating. What would happen?

1. Earth would fall directly inward, into the sun.
   Earth would fly directly outward from the sun.
   Earth would continue orbiting the sun, but objects on Earth would have no weight and would float into space.
   Earth would stop in its orbit around the sun, and remain motionless at its present position.
   Earth would move straight ahead, in a straight line, rather than orbiting the sun.

(E) -Earth would move straight ahead, in a straight line, rather than orbit the sun. Because the
Earth was actually just traveling through space at a constant velocity and no other forces acting on it
other than when it neared the sun; the sun's gravity curved it's path.

Good!

4. You are in distant space. A giant boulder, many times larger than you, is at rest in front of you. You tap the boulder lightly with a small hammer. What does the boulder do?

1. It accelerates during the tap, up to a slow speed [slower than walking speed], then keeps moving at that speed.
   It remains at rest.
   It accelerates during the tap, up to a high speed [faster than a fast-moving car], then keeps moving at that speed.
   It speeds up a little during the tap, but after the tap it soon [within a few minutes] slows down and comes to rest.
   It accelerates both during and after the tap.

(A) -It accelerates during the tap, up to a slow speed [slower than walking speed], then keeps
moving at that speed- Because there is no gravity, friction or air resistance in space; even a small tap
would provoke some sort of acceleration in the boulder. However, because the boulder is large, a small
hammer tap (a small Force) wouldn't cause it to accelerate much since force, acceleration and mass are
related and you would need more force to move an object with more mass...then, it would never stop
moving because there would be nothing to stop it.

Good!

5. An auto weighing 3000 Newtons has a forward drive force of 1000 Newtons. Air resistance on the car is 100 Newtons, and road resistance is 100 Newtons. The auto moves along a straight level road. The force due to gravity acting on the auto is

1. zero.
   3000 Newtons downward.
   4200 Newtons downward.
   800 Newtons upward.
   3000 Newtons upward.

(B) -3000 Newton's downward- O.K, so to be completely honest, I'm not too sure how I reached that
conclusion. What I did was pretty much a process of elimination. I figured that gravity only acts
"downward" because it's like a pull towards the center of Earth, so, I got rid of answers (a), (d), and (e).
Then I was left with (b) and (c) and I figured that you just don't add all the forces...because the direction of
the force matter and none of the forces are acting in opposition to that of gravity...I figured that the force of
gravity then just becomes it's weight.

Yes, the weight is the force of gravity. They tell you that up front! (You have to know that it acts downward, of course.)

 

[kirsten_2009]

I agree with your answer: "Increased to four times the original value."

Increase in mass does increase the gravity of the object, so yes the mass does have an effect on gravity. However when the moon is brought closer to Earth, the mass is not increase (it is constant). Therefore, only the distance is effecting the amount of gravity, not the mass.

Look back at the formula, see what is and is not changing.

Thank you! Yes that makes sense! :)

 

[kirsten_2009]

Good!Good!Yes, the weight is the force of gravity. They tell you that up front! (You have to know that it acts downward, of course.)

THANK-YOU! Yes, it makes sense.

 

[kirsten_2009]

Careful! What does Newton's 3rd law have to say about this?Does the mass of the objects affect the gravitational force? Of course. But here the masses have not changed. The only thing that changes is the distance.

(Note: In general, it's not a good idea to cram too many questions into the same post!)

Thank you for taking the time to look at my work. I reviewed Newton's third law and it states that for every action there is an equal and opposite reaction. Does that mean then, that both the truck and car experience the same force? But, that seems counter-intuitive (not that intuition is correct).

 

[Doc Al]

6. Regarding the relation between acceleration, force, and mass, an object's acceleration is

1. proportional to the inverse of the height of the Empire State Building.
   inversely proportional to the force on it and proportional to the object's mass.
   proportional to the force on it and proportional to the object's mass.
   inversely proportional to the force on it and inversely proportional to the object's mass.
   proportional to the force on it and inversely proportional to the object's mass.

(E) –Proportional to the force on it and inversely proportional to the object’s mass- Because, not
just because my textbook says so but also because it makes sense. The more force you apply on an
object the faster it will go. Also, the larger or denser the object the more force required to accelerate it just
as much as a lighter object.

Right answer, but careful with your reasoning. Size or density doesn't matter, only the mass and the net force.

7. During this century, we have found that Newton's physics does not apply to

1. high speed objects.
   very strong gravitational forces.
   very small objects.
   All of the above.
   Nonsense--Newton's physics always applies.

(E) –Newton’s physics always applies- I don’t know…just going by what my book says.

Better check your book! Newton's physics has been show to break down in certain areas. (See: Quantum mechanics and Relativity.)

8. Would you be richer if you had a hunk of gold whose weight is 1 Newton on the moon, or one whose weight is 1 Newton on Earth, and why?

1. 1 Newton on Earth, because then the gold's weight on Earth would be larger.
   1 Newton on Earth, because then the gold's mass would be larger.
   1 Newton on the moon, because then the gold's mass would be larger.
   1 Newton on the moon, because then the gold's weight on the moon would be larger.
   It wouldn't make any difference, because the amount of actual gold would be the same in both cases.

(D) -1 N on the moon, because then the gold’s weight on the moon would be larger- So, I’m not
sure if the question is just ambiguous or if I’m not understanding it correctly. If I look at it strictly from the
mass point of view then answer (e) is correct: an objects mass is constant no matter where it is in space
because its number of atoms doesn’t change. BUT, if we’re talking just about the “weight” (which is the
effect or pull of gravity on the mass) then wouldn’t 1 N of anything in the moon have to be much larger
(about 6x more) than on Earth in order to weight the same (1 N) because the pull of gravity is that much
less?

Right answer. Of course you want the most mass of gold. So a given hunk of gold, whose mass doesn't change going from moon to earth, will weigh less on the moon. That means it takes more gold (more mass) to weight 1 N on the moon than it does on earth.

 

[Doc Al]

Thank you for taking the time to look at my work. I reviewed Newton's third law and it states that for every action there is an equal and opposite reaction. Does that mean then, that both the truck and car experience the same force? But, that seems counter-intuitive (not that intuition is correct).

Yes! When car and truck collide, they exert equal and opposite forces on each other. Now, that same force will have a different effect on the small car versus the huge truck, but that's a different question.

 

[kirsten_2009]

Yes! When car and truck collide, they exert equal and opposite forces on each other. Now, that same force will have a different effect on the small car versus the huge truck, but that's a different question.

O.k...I see! So, based on the effects that one would have on the other...wouldn't the small car still experience a greater acceleration and change in momentum compared to the large truck? ...making the answer still "all of the above"?

 

[theOrange]

Homework Statement

10. If you somehow increased Earth's radius, without changing its mass, would this affect your weight?

1. Yes, your weight would increase.
   No, because the force of gravity on your body depends only on your mass and on Earth's total mass--it doesn't depend on Earth's size.
   Yes, your weight would decrease.
   No, because your weight always remains the same regardless of how you change the external surroundings.

(C) –Yes, your weight would decrease – Though, I am tempted to pick (b)…I decided to go with (c)
because if the Earth expanded its radius (the Earth uniformly expanded its radius –so really it’s the Earth diameter) then you’d be further away from the center and thus the pull of gravity would be less, which is what affects your weight not your mass…?

I agree with your answer.

 

[Doc Al]

9. Astronauts in orbit around Earth feel weightless because

1. they must lose weight for the space program.
   they are in "free fall" around Earth.
   there is no gravity out there.
   they are moving with constant velocity.
   no forces at all are acting on them.

(E) –No forces at all are acting on them- Again, I’m not sure. I know that gravity still exists within the
orbit of Earth (actually it’s still quite strong) so it makes my answer (e) kind of contradictory but they “feel”
weightless because there is nothing “pushing up on them” (no contact forces) so they can’t “feel” gravity
though it’s still there….? If that reasoning is not correct, then I would go with (b) just because the rest of
the answers don’t make sense to me either…

Answer E is incorrect, as you suspect. Astronauts in orbit still feel gravity--it's what is holding them in orbit. (The force of gravity is a bit smaller because they are further away, but still large.)

They feel "weightless" because they are in free fall. Nothing's pushing them up. Example: If you stood on a platform, it supports your weight. If that platform suddenly started falling (in free fall), you'd feel "weightless" as it would stop supporting you.

10. If you somehow increased Earth's radius, without changing its mass, would this affect your weight?

1. Yes, your weight would increase.
   No, because the force of gravity on your body depends only on your mass and on Earth's total mass--it doesn't depend on Earth's size.
   Yes, your weight would decrease.
   No, because your weight always remains the same regardless of how you change the external surroundings.

(C) –Yes, your weight would decrease – Though, I am tempted to pick (b)…I decided to go with (c)
because if the Earth expanded its radius (the Earth uniformly expanded its radius –so really it’s the Earth diameter) then you’d be further away from the center and thus the pull of gravity would be less, which is what affects your weight not your mass…?

Good. C is correct.

 

[Doc Al]

O.k...I see! So, based on the effects that one would have on the other...wouldn't the small car still experience a greater acceleration and change in momentum compared to the large truck? ...making the answer still "all of the above"?

The small car will experience a greater acceleration. But not a greater change in momentum. In a collision, momentum is conserved. Both car and truck will have equal and opposite changes in momentum, with the net change being zero.

 

[kirsten_2009]

Right answer, but careful with your reasoning. Size or density doesn't matter, only the mass and the net force.Better check your book! Newton's physics has been show to break down in certain areas. (See: Quantum mechanics and Relativity.)Right answer. Of course you want the most mass of gold. So a given hunk of gold, whose mass doesn't change going from moon to earth, will weigh less on the moon. That means it takes more gold (more mass) to weight 1 N on the moon than it does on earth.

So, I'm thinking that Newton's physics is having some trouble reconciling with quantum mechanics and how wavelike sub-atomic particles behave. I'm going with (c) -very small objects.

 

[kirsten_2009]

The small car will experience a greater acceleration. But not a greater change in momentum. In a collision, momentum is conserved. Both car and truck will have equal and opposite changes in momentum, with the net change being zero.

I just reviewed this in my book and although I didn't see it at first...I get what your saying and it makes sense. Goes to show how "feeling" that something is right can be completely deceiving. Honestly, thank-you so much for taking the time to look this over and helping me out! :)

 

[kirsten_2009]

I agree with your answer.

Thanks so much for looking this over!

 

[Doc Al]

So, I'm thinking that Newton's physics is having some trouble reconciling with quantum mechanics and how wavelike sub-atomic particles behave. I'm going with (c) -very small objects.

Careful! The realm of the very small is just one area where Newtonian physics breaks down.