Examples of gravitational force in the following topics:
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- When the bodies have spatial extent, gravitational force is calculated by summing the contributions of point masses which constitute them.
- For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.
- The portion of the mass that is located at radii $r>r_0$ exerts no net gravitational force at the distance $r_0$ from the center.
- That is, the individual gravitational forces exerted by the elements of the sphere out there, on the point at $r_0$, cancel each other out.
- Describe how gravitational force is calculated for the bodies with spatial extent
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- Gravitational energy is the potential energy associated with gravitational force, as work is required to move objects against gravity.
- Gravitational energy is the potential energy associated with gravitational force (a conservative force), as work is required to elevate objects against Earth's gravity.
- If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount.
- For the computation of the potential energy we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation (with respect to the distance r between the two bodies).
- Using that definition, the gravitational potential energy of a system of masses m and M at a distance r using gravitational constant G is:
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- The Law of Universal Gravitation states that the gravitational force between two points of mass is proportional to the magnitudes of their masses and the inverse-square of their separation, $d$:
- Finding the gravitational force between three-dimensional objects requires treating them as points in space.
- The gravitational force acting by a spherically symmetric shell upon a point mass inside it, is the vector sum of gravitational forces acted by each part of the shell, and this vector sum is equal to zero.
- So, the gravitational force acting upon point mass $m$ is:
- As in the case of hollow spherical shells, the net gravitational force that a solid sphere of uniformly distributed mass $M$ exerts on a body outside of it, is the vector sum of the gravitational forces acted by each shell of the sphere on the outside object.
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- Gravitational energy is the potential energy associated with gravitational force, such as elevating objects against the Earth's gravity.
- Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity.
- As the book is raised from the floor to the table, some external force works against the gravitational force.
- If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force.
- For the computation of the potential energy, we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to the distance $r$ between the two bodies.
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- The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation This attractive force always points inward, from one point to the other.
- While Newton was able to articulate his Law of Universal Gravitation and verify it experimentally, he could only calculate the relative gravitational force in comparison to another force.
- It wasn't until Henry Cavendish's verification of the gravitational constant that the Law of Universal Gravitation received its final algebraic form:
- $G$ represents the gravitational constant, which has a value of $6.674\cdot 10^{-11} \text{N}\text{(m/kg)}^2$.
- Because of the magnitude of $G$, gravitational force is very small unless large masses are involved.
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- Recall that the force of friction depends on both the coefficient of friction and the normal force.
- As always, the frictional force resists motion.
- If the frictional force is equal to the gravitational force the block will not slide down the incline.
- If the maximum frictional force is greater than the force of gravity, the sum of the forces is still 0.
- The force of friction can never exceed the other forces acting on it.
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- Here, external forces are forces from external sources, while internal forces are forces between particles in the system.
- For example, when we confine our system to the Earth and the Moon, the gravitational force due to the Sun would be external, while the gravitational force on the Earth due to the Moon (and vice versa) would be internal.
- Since the gravitational forces between the Earth and the Moon are equal in magnitude and opposite in direction, they will cancel out each other in the sum (see ).
- When there is no external force, the COM momentum is conserved.
- Proof: Since there is no external force, $M \cdot \bf{a}_{COM} = 0$.
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- Tides are the rise and fall of sea levels due to the effects of gravitational forces exerted by the moon and the sun when combined with the rotation of the Earth.
- The tidal force produced by the moon on a small particle located on Earth is the vector difference between the gravitational force exerted by the moon on the particle, and the gravitational force that would be exerted if it were located at the Earth's center of mass.
- Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
- On average, the solar gravitational force on the Earth is 179 times stronger than the lunar, but because the sun is on average 389 times farther from the Earth its field gradient is weaker.
- The solar tidal force is 46% as large as the lunar.
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- This value, though given in kilograms, is actually the non-SI unit of measure known as the kilogram-force.
- In scientific terms, 'weight' refers to the gravitational force acting on a given body.
- This measurement changes depending on the gravitational pull of the opposing body.
- For example, a person's weight on the Earth is different than a person's weight on the moon because of the differences in the gravitational pull of each body.
- In contrast, the mass of an object is an intrinsic property and remains the same regardless of gravitational fields.
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- Newton's universal law of gravitation states that every particle attracts every other particle with a force along a line joining them.
- Newton's universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them.
- The gravitational force is responsible for artificial satellites orbiting the Earth.
- Gravity supplies the centripetal force to mass $m$.
- (b) For any closed gravitational orbit, $m$ follows an elliptical path with $M$ at one focus.