Keplers Law berkeley review Passage 5 Section 2

[harkkam]

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Guys I have a question on number 33 on passage 5 of section 2 in the berkeley Physics.

The question reads. "Assuming this solar system consists only of the Sun and the planet, the net force on the planet points"

A. Towards the Sun
B. Away from the sun
C. in the direction of the planets velocity
D. In the direction opposite the planets velocity

I picked B but the correct answer is A.

The reason I selected B was that the earth feels two forces or so I thought. There is a Force tangential that points in the direction of the velocity on a centripetal motion path and there is a force gravitational pointing toward the sun and the vector sum of the two is somewhere in between not directly pointed at the sun.

However the answer choices say that there is only one force pointing inward that is the force gravitational. What happened to the force tangential?

 

[puravida85]

In this situation, the tang. force you are describing is a velocity force that is only a vector because of the idea that every second it changes direction, not because it is changing speed. a = v2 -v1 / delta t. If you add the vector velocities from time 1 and time 2, you'll notice a net vector pointed towards the center of the circle. In any case, don't focus on a single velocity vector to tell you net force because net force = m*a. The vectors create a net acceleration towards the center and therefore any object in uniform circular motion is undergoing a net force towards the center. In your case, the planet's acceleration is going directly towards the center of the sun. It only deviates when the object is changing speed, for example if it was also slowing down, than the net force would than not be towards the center but a little off. So the keyword in the question anyhow is NET FORCE.

 

[harkkam]

Hmm so if I understand you correctly.

Since the velocity vector is only changing direction it does nothing to change the magnitude of the speed of the planet. Hence a=0 from the force tangential. The only net force being produced is the one pointing toward the sun.

That makes sense if the orbit is perfectly circular, however in the book they said that all real orbits are elliptical and that at certain points of the orbit the earth travels faster than it does at other points.

So I thought that so there must be a Force tangential.

But I think even if it is elliptical orbit, their is no net tangential force and the only force is gravitational.

 

[dingyibvs]

Guys I have a question on number 33 on passage 5 of section 2 in the berkeley Physics.

The question reads. "Assuming this solar system consists only of the Sun and the planet, the net force on the planet points"

A. Towards the Sun
B. Away from the sun
C. in the direction of the planets velocity
D. In the direction opposite the planets velocity

I picked B but the correct answer is A.

The reason I selected B was that the earth feels two forces or so I thought. There is a Force tangential that points in the direction of the velocity on a centripetal motion path and there is a force gravitational pointing toward the sun and the vector sum of the two is somewhere in between not directly pointed at the sun.

However the answer choices say that there is only one force pointing inward that is the force gravitational. What happened to the force tangential?

You're missing one thing here: since the orbit is elliptical, then a force pointing toward the sun isn't always perfectly perpendicular to the planet's velocity. In other words, having a tangential component to a planet's direction NO LONGER contradicts with the fact that the force and acceleration point toward the sun. It'll only be contradictory in a perfectly circular motion.

 

[harkkam]

You're missing one thing here: since the orbit is elliptical, then a force pointing toward the sun isn't always perfectly perpendicular to the planet's velocity. In other words, having a tangential component to a planet's direction NO LONGER contradicts with the fact that the force and acceleration point toward the sun. It'll only be contradictory in a perfectly circular motion.

Im sorry man, but I dont understand that 🙁

I drew a diagram and yes you're right that the centripital force doesnt always lie perpendicular to the tangental velocity. But how does that make it the ONLY force pointing at the sun?

Wouldnt having another force point it a bit away?

 

[lorenzomicron]

Im sorry man, but I dont understand that 🙁

I drew a diagram and yes you're right that the centripital force doesnt always lie perpendicular to the tangental velocity. But how does that make it the ONLY force pointing at the sun?

Wouldnt having another force point it a bit away?

There isno other The only force is the one of gravity, which is directed perpendicular and inwards to the sun at every point. The velocity is tangential but there is no tangential force.

Think about it, where would this other force come from?
All forces, at least for this reason, are either physical or field. I can see no other force in the system.

So, the net force points inward to the sun. The way it works is that the velocity points out on a straight line (ideal orbit but nearly the same for the ellipse as well), the acceleration at every points causes the velocity to change a little inwards, in the manner of addition such that
V = dxi/dt + integral(acentripetal)dt.

But yeah, the maths doesnt matter really. All that is needed is that the acceleration changes the direction of the velocity, and the only acceleration is this inward centripetal acceleration.

 

[UCB05]

If there were a force pointing the same general direction as the tangential velocity vector, what is causing it? The centripetal force is gravitational, sun<->planet, and causes radial acceleration. In a system consisting only of the sun and planet, what else is there in the system that will cause a force vector parallelish to the planet's velocity? Just because a planet has a tangential velocity doesn't imply there has to be a force to maintain it.

I'm sure you've seen a diagram that shows, say, a satellite orbiting in a circular orbit. The only force in this case is perpendicular to velocity and maintains radial acceleration at constant tangential velocity. In an elliptical orbit where the planet's velocity is not perfectly perpendicular to the centripetal force, the x and y (and z) vectors of the single gravitational force accelerates the planet, causing the orbital velocity to be different at various points along the orbit, but there is still only that one force pointing at the sun which causes it.

 

[lorenzomicron]

If there were a force pointing the same general direction as the tangential velocity vector, what is causing it? The centripetal force is gravitational, sun<->planet, and causes radial acceleration. In a system consisting only of the sun and planet, what else is there in the system that will cause a force vector parallelish to the planet's velocity? Just because a planet has a tangential velocity doesn't imply there has to be a force to maintain it.

I'm sure you've seen a diagram that shows, say, a satellite orbiting in a circular orbit. The only force in this case is perpendicular to velocity and maintains radial acceleration at constant tangential velocity. In an elliptical orbit where the planet's velocity is not perfectly perpendicular to the centripetal force, the x and y (and z) vectors of the single gravitational force accelerates the planet, causing the orbital velocity to be different at various points along the orbit, but there is still only that one force pointing at the sun which causes it.

And to build on this farther, ideally, in a circle, the velocity tangential always has the same magnitude. In a non-ideal ellipse, the velocity changes somewhat because the distance changes from the sun and things like that which causes different magnitudes of acceleration in different ways, basically, though its a little more complicated than that actually.

 

[Excelsius]

Guys I have a question on number 33 on passage 5 of section 2 in the berkeley Physics.

The question reads. "Assuming this solar system consists only of the Sun and the planet, the net force on the planet points"

A. Towards the Sun
B. Away from the sun
C. in the direction of the planets velocity
D. In the direction opposite the planets velocity

I picked B but the correct answer is A.

The reason I selected B was that the earth feels two forces or so I thought. There is a Force tangential that points in the direction of the velocity on a centripetal motion path and there is a force gravitational pointing toward the sun and the vector sum of the two is somewhere in between not directly pointed at the sun.

However the answer choices say that there is only one force pointing inward that is the force gravitational. What happened to the force tangential?

Actually the answer is much simpler than what is discussed here. Think force-body diagrams. How many forces are there in nature? There are four that we know of: Gravitational, Electromagnetic, Strong Nuclear, Weak Nuclear. The last two do not appear on MCAT - so strike that. Electromagnetic is involved only when the bodies are charged - so strike that too since the earth or the sun are not charged particles. What does it leave us? Gravity. So what does gravity do? It is pulling two objects together. Therefore, this case, the force body diagram would show a force on earth directly pulling it towards the sun - imagine an apple on the surface of the earth, the earth is like an apple on the surface of the sun. That's all you need to know.

Now, as far as centripetal force is concerned, a lot of people are confused by it. Centripetal force is not a force per se. In other words, there is nothing acting on Earth besides gravity. Centripetal force is simply the result of gravity. So if you were to solve something, you would say that the gravitational force is equal to centripetal force, and not gravitational force plus centripetal force. It's just like when you are solving problems with F=ma. It is equal, not plus. Same is true for F=mv^2/r. The only real force is on the left side of the equation.

Finally, the centripetal force is directed to the center of the curved path, which in this case is still the sun. These are the details, but you could answer the problem correctly if you knew the first paragraph alone.

 

[harkkam]

Actually the answer is much simpler than what is discussed here. Think force-body diagrams. How many forces are there in nature? There are four that we know of: Gravitational, Electromagnetic, Strong Nuclear, Weak Nuclear. The last two do not appear on MCAT - so strike that. Electromagnetic is involved only when the bodies are charged - so strike that too since the earth or the sun are not charged particles. What does it leave us? Gravity. So what does gravity do? It is pulling two objects together. Therefore, this case, the force body diagram would show a force on earth directly pulling it towards the sun - imagine an apple on the surface of the earth, the earth is like an apple on the surface of the sun. That's all you need to know.

Now, as far as centripetal force is concerned, a lot of people are confused by it. Centripetal force is not a force per se. In other words, there is nothing acting on Earth besides gravity. Centripetal force is simply the result of gravity. So if you were to solve something, you would say that the gravitational force is equal to centripetal force, and not gravitational force plus centripetal force. It's just like when you are solving problems with F=ma. It is equal, not plus. Same is true for F=mv^2/r. The only real force is on the left side of the equation.

Finally, the centripetal force is directed to the center of the curved path, which in this case is still the sun. These are the details, but you could answer the problem correctly if you knew the first paragraph alone.

Thanks that was great man

 

[dingyibvs]

Im sorry man, but I dont understand that 🙁

I drew a diagram and yes you're right that the centripital force doesnt always lie perpendicular to the tangental velocity. But how does that make it the ONLY force pointing at the sun?

Wouldnt having another force point it a bit away?

No, gravity is the only force acting on it, where would another force come from?

 

[apumic]

Your "other force" is a pseudoforce ("centrifugal force"). It does not exist but would be "felt" (by a person examining the apparent acting forces from the planet's perspective) due to the changing velocity vector (due to the actual centripetal force and resulting centripetal acceleration). Recall that Newton's Laws can only be applied if there is no acceleration occurring in the reference frame; that is, you cannot apply these laws relative to a frame of reference in which there is acceleration occurring. Remember that anything moving in circular motion is being pulled inward. If there were another force acting outward (of equal but opposite magnitude), what would happen to the planet? (Answer: it'd fly straight out of the solar system!)