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The trajectory of a projectile launched from a hilltop

The trajectory of a projectile is parabolic. Consider a simpler set-up, with ground-to-ground projection from the origin, the range is maximum when $\theta = 45^{\circ}$, as then the distance between ...
jIvitesha's user avatar
1 vote

Is gravitational potential energy of body by $mgh$ negative?

The key here is that it is the difference in potential energy that is important and this yields the same result in magnitude and sign, using using either equation. The potential energy is obtained by ...
KDP's user avatar
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0 votes

Is gravitational potential energy of body by $mgh$ negative?

Gravitation potential energy can have any sign you want: $$ U(h) = mgh + C $$ since you can add any constant $C$. Down is the direction of decreasing $U$, though, as the $m$ becomes more tightly bound ...
JEB's user avatar
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3 votes

Is gravitational potential energy of body by $mgh$ negative?

The two expressions have different locations for their energy zero points, that is why they disagree. $mgh$ is zero at wherever you have set $h=0$ to be with your coordinate system. Typically that is &...
Marius Ladegård Meyer's user avatar
7 votes
Accepted

How accurate does the ISS's velocity and altitude need to be to maintain orbit?

For a particular orbital period and altitude (or altitude and eccentricity, or eccentricity and period), there is exactly one velocity that produces the correct orbit. Of course the ISS doesn't have ...
controlgroup's user avatar
-1 votes

What would happen to the moon's orbit if we reduce (instantaneously) its mass?

I will assume moon's orbit around the earth is modelled as a Kepler problem. The moon's mass $m_m$ is about 80 times smaller than earth's mass $M_e$. But if you don't neglect it completely, reducing ...
Mateo's user avatar
  • 426
2 votes

What would happen to the moon's orbit if we reduce (instantaneously) its mass?

Mass is a conserved quantity. Having it simply disappear violates the known laws of physics. Once you have violated the laws of physics you can no longer ask what the laws of physics predict, since ...
Dale's user avatar
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0 votes

When an object is thrown towards the sky it starts to gain potential energy, why?

The push force makes the object move towards the sky and the pull force of gravity makes the object come down towards the Earth's surface. You are mistaken about this part. If you throw an object ...
KDP's user avatar
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2 votes
Accepted

Doubt on conservation of angular momentum for Kepler's laws

The definition of a plane can be written as $\vec{a}\cdot \vec{r} = 0$, where $\vec{a}$ is any vector perpendicular to the plane. In this case, you have a vector quantity $\vec{L}$, which is from its ...
ProfRob's user avatar
  • 133k
2 votes

Doubt on conservation of angular momentum for Kepler's laws

The angular momentum ${\bf L}$ of a point-like particle is proportional to the vector product of position ${\bf r}$ and velocity ${\bf v}$. It is a vector orthogonal to the plane containing ${\bf r}$ ...
GiorgioP-DoomsdayClockIsAt-90's user avatar
0 votes

When an object is thrown towards the sky it starts to gain potential energy, why?

Every body has total energy, which is the sum of its kinetic and potential energy .This total energy is always conserved for conservative forces. $ U=V+K$ Here U denotes total energy, V denotes ...
Ritesh Nandi's user avatar
0 votes

Why are fields described as force divided by mass or charge?

You are right in demanding a clear answer for this issue (in school, the teacher either can't answer or can't explain the thing). What is the difference between physics and philosophy if we are not ...
Andreas Klein's user avatar
0 votes

When an object is thrown towards the sky it starts to gain potential energy, why?

I think what you're missing is that potential energy can be negative. If you hold a ball and drop it from infinity, at the start the ball has no kinetic and no potential energy. When you drop it the ...
Alien from future's user avatar
1 vote

When an object is thrown towards the sky it starts to gain potential energy, why?

There are two ways to view the exchange of kinetic energy and potential energy. But before I do, I'd like to point out that your learning of physics will be much much easier if you drop the concept ...
Cort Ammon's user avatar
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2 votes

When an object is thrown towards the sky it starts to gain potential energy, why?

The object has energy, whether it is kinetic or potential. There is a point in its trajectory where the object is not moving, and this is at the highest point of its trajectory. At this point, it has ...
ABetheGammow's user avatar
3 votes

Has our knowledge of astrophysics and gravity reached the point where we can accurately calculate Lagrange points?

There are no true Lagrange points in the Solar System. Lagrange points represent solutions of the restricted three body problem, but the Solar System is a many body system. There are orbital regions ...
John Doty's user avatar
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0 votes

Local vs distant gravity effects where is the boundary line of effective control?

A helpful way into understanding this: calculate the acceleration due to gravity for the Earth due to the Sun and for the Moon due to the Sun. They're roughly the same, because it doesn't depend on ...
controlgroup's user avatar
1 vote

Local vs distant gravity effects where is the boundary line of effective control?

Two objects fall equally fast in a vacuum . Even if they are of different sizes and masses. Armstrong famously dropped a hammer and a hawk feather on the moon and they fell and hit the ground ...
Steeven's user avatar
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2 votes

Local vs distant gravity effects where is the boundary line of effective control?

so why is it that the moon hasn't yet been drawn away from earth and to sun You might ask, why is it that the earth hasn't been drawn to the sun? In the absence of drag, objects can remain in ...
BowlOfRed's user avatar
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81 votes
Accepted

Error concerning projectile motion in respected textbook?

I agree that the statement I made in the book is wrong: On a flat earth the time of flight is not affected by the initial horizontal velocity, only the horizontal distance is. I will post a correction ...
R Shankar's user avatar
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4 votes

Error concerning projectile motion in respected textbook?

As @RatulThakur points out, this is pretty clearly an error. ToF is not affected at all by horizontal velocity on a flat Earth, unless you're considering the aerodynamics of the object (there's a ...
controlgroup's user avatar
0 votes

Why is pressure in the outermost layer of a star lower than at its center?

Imagine you are sandwiched between two moon like objects each with mass M. The forces acting on you is $$F_{centre} = \frac{2 \times G\times M\times M}{D^2}$$ where D is the distance from the centre ...
KDP's user avatar
  • 6,182
5 votes

How much time does it take for an object to fall from space?

If the body has no angular momentum (no tangential speed with respect to Earth), what you want to solve is Newton's second law in this form: $$m \frac{\mathrm d^2h(t)}{\mathrm dt^2}=-\frac{GMm}{(R_{\...
Mauricio's user avatar
  • 5,578
2 votes

How much time does it take for an object to fall from space?

Assuming the fall is purely radial and neglecting any fancy rotation and coriolis effects, you would obtain a single differential equation: $$\frac{GM_e}{(R+h)^2} = -\frac{\mathrm{d}^2 h}{\mathrm{d}t^...
CompassBearer's user avatar
3 votes

How much time does it take for an object to fall from space?

The solution can be found on Wikipedia, the time $\rm t$ to fall from $\rm r_0$ to $\rm r_1$ is $$\rm t=\left(\sqrt{\frac{{r_1} \left(1-\frac{{r_1}}{{r_0}}\right)}{{r_0}}}+arccos\left(\sqrt{\frac{{r_1}...
Yukterez's user avatar
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3 votes
Accepted

Gravitational collapse - proof that energy dissipation is required?

The virial theorem tells us that for an isolated cloud (no external pressure, magnetic fields or rotation) that $$2K + \Omega = 0\ , $$ where $K$ is the kinetic energy of the cloud particles and $\...
ProfRob's user avatar
  • 133k
3 votes

How Can there be a Gravitational Potential when there is NO Gravitational Field?

You would be right, if you took your reference, at the center of the sphere, to be at a potential of 0. Throughout the sphere, you have a constant potential, which would remain 0. Generally, we take $...
ekl1pse's user avatar
  • 31
1 vote

Do objects really "fall" at the same rate?

The effect you cite is so tiny as to be unmeasurable. This is why in most such calculations it is neglected with no loss in accuracy.
niels nielsen's user avatar
3 votes

Do objects really "fall" at the same rate?

You are right in that if you release from some height objects of different masses at different times, the acceleration relative to the surface (which moves with the planet) will depend on the mass of ...
Pato Galmarini's user avatar
36 votes

Why is pressure in the outermost layer of a star lower than at its center?

Considering the only force keeping the star together is gravitational in nature, Gravity is also what's keeping our oceans stuck to the Earth's surface. Where's the pressure at its highest, near sea ...
Flater's user avatar
  • 890
4 votes

Why is pressure in the outermost layer of a star lower than at its center?

I believe you are confusing "force of gravity" with "pressure." The gravitational pull (or local acceleration $g$) is indeed zero at the center of the Sun, and a maximum elsewhere ...
RC_23's user avatar
  • 9,500
6 votes

Why is pressure in the outermost layer of a star lower than at its center?

Perhaps the confusion in the question arises because you are thinking of a rigid spherical shell of constant density, and you know that inside such a shell the gravitational field is zero? A ball of ...
C.M.O.B.'s user avatar
  • 119
7 votes

Why is pressure in the outermost layer of a star lower than at its center?

This is an exercise in hydrostatics. Imagine the sun consisting of a sphere of water. The deeper you go beneath the surface, the more water weight you have bearing down on you from above, and the ...
niels nielsen's user avatar
17 votes
Accepted

Why is pressure in the outermost layer of a star lower than at its center?

There is a lot of mass above the centre, pushing down on it. On the surface there is no mass above. Hence you get high pressure at the centre and zero at the surface.
Anders Sandberg's user avatar
0 votes

Why is work done by force $+mgh$ in the situation of throwing something up?

But the work done by the force that brings it above to point B is $+mgh$. I dont think its necessary. That will mean that the force making it move up is $+mg$ but it can also be something else. If ...
Bob D's user avatar
  • 73.7k
0 votes

Why is work done by force $+mgh$ in the situation of throwing something up?

System: particle. Two forces acting on the particle, gravitational attraction due to Earth, magnitude $mg$, downwards and external force exerted by you, magnitude $mg$, upwards. If the particles rises ...
Farcher's user avatar
  • 97.9k
-1 votes

Why is work done by force $+mgh$ in the situation of throwing something up?

I don't quite understand the question. You have a force $\vec{F}$ acting on the object to take it from A to B. This force is an external force, which goes against the force of gravity, and also this ...
JL14's user avatar
  • 67
1 vote

Why is work done by force $+mgh$ in the situation of throwing something up?

You are right, the work applied is not necessarily equal to $mgh$. To see this, let's look at energy conservation: $$K_0+U_0+W_{\text{n.c.}}=K_f+U_f$$ where $K_0$ and $K_f$ are the initial and final ...
BioPhysicist's user avatar
  • 57.2k
0 votes

Two particles rotating about their center of mass

The center of mass is the geometric point of a rigid solid which acts as if all forces were acting on it. It is "indifferent" if that point in space coincides with a place where there is ...
JL14's user avatar
  • 67
0 votes

What is the relationship between gravitation, centripetal and centrifugal force on the Earth?

In this case, the centripetal force is the gravitational force. "Centripetal" and "gravitational" refer to two different aspects of the force: Gravitational refers to the source ...
Carmeister's user avatar
5 votes

What is the relationship between gravitation, centripetal and centrifugal force on the Earth?

The expression 'centrifugal force' can in most circumstances be understood as: 'a centripetal force is required'. In the case of the spinning Earth: At the equator the measured gravitational ...
Cleonis's user avatar
  • 21.4k
3 votes
Accepted

What is the relationship between gravitation, centripetal and centrifugal force on the Earth?

Rotating reference frames can be tricky. Some of the trickery is that we typically only use them when it simplifies the math. This can make it tricky to separate the effects of the frame from the ...
Cort Ammon's user avatar
  • 50.2k
5 votes

What is the relationship between gravitation, centripetal and centrifugal force on the Earth?

When confused, ditch centrifugal. Let us go back to the basics. The original Newton's 2nd Law (N2L) states that $$ \begin{align} \tag1\sum\vec F&=\frac{\mathrm d\vec p}{\mathrm dt}\\ \tag2\sum\vec ...
naturallyInconsistent's user avatar
0 votes

Regarding the objects in free fall in the ISS

In the ISS, people can push themselves in a direction and move. What caused that direction? Did the astronaut push themselves from a place? Please explain this in a simple way from Newton's Laws. Yes,...
gandalf61's user avatar
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