Physics Chapter on Gravitational Forces

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Questions and Answers

What principle does the law of areas derive from?

Conservation of angular momentum (correct)

Conservation of kinetic energy

Conservation of linear momentum

Conservation of potential energy

In the context of the described law, which force applies to the motion of the planet around the Sun?

A radial force (correct)

A linear force

An outward centripetal force

A tangential force

What is the relationship between the speed of the moon and its time period?

V is proportional to T

V is independent of T

V is inversely proportional to T (correct)

V is equal to T

How is the acceleration due to gravity at the moon's orbit characterized compared to that on Earth's surface?

It is smaller than the acceleration on the surface Signup and view all the answers

What does the equation ∆A / ∆t = L / (2m) signify in the context of planetary motion?

The area swept per time is constant Signup and view all the answers

What is represented by L in the equation ∆A / ∆t = L / (2m)?

Angular momentum Signup and view all the answers

What characterizes the gravitational force described in the content?

It is attractive and directed along –r Signup and view all the answers

What role does the distance play in the gravitational force acting on the planet?

The force decreases with distance Signup and view all the answers

What is the force of attraction between a hollow spherical shell of uniform density and a point mass located outside the shell?

It acts as if the mass is concentrated at the center of the shell. Signup and view all the answers

When a point mass is located inside a hollow spherical shell of uniform density, what can be said about the force of attraction on it?

It is non-existent. Signup and view all the answers

How is the resultant gravitational force calculated for a hollow spherical shell acting on a point mass outside it?

The components of forces perpendicular to the line are canceled out. Signup and view all the answers

In the case of three equal masses placed in a triangle and a mass at the centroid, what does the force exerted at the centroid depend on?

The mass of the three equal masses. Signup and view all the answers

What happens to the gravitational forces caused by different regions of a hollow spherical shell when summed?

Only the components along the line between the center and the mass remain. Signup and view all the answers

What is a characteristic property of the gravitational attraction of a hollow spherical shell on an external point mass in terms of uniform density?

It is effectually as if it's concentrated at the center. Signup and view all the answers

If a hollow spherical shell has a mass of 'M', what is the effective gravitational force it exerts on a point mass located at its center?

Zero Newtons. Signup and view all the answers

Regarding gravitational forces, what is the outcome of placing a point mass at the centroid of three equal masses placed at the vertices of a triangle?

The point mass experiences equal forces from all three sides, resulting in zero net force. Signup and view all the answers

What does the principle of superposition imply regarding the forces acting on the point mass inside the spherical shell?

The forces cancel each other completely. Signup and view all the answers

What was the result of doubling the mass at vertex A in the gravitational system described?

The forces acting on the point mass become unbalanced. Signup and view all the answers

Who first determined the value of the gravitational constant experimentally?

Henry Cavendish Signup and view all the answers

Why is the equation for gravitational force between an extended object and a point mass not directly applicable?

The forces from each point mass do not act in the same direction. Signup and view all the answers

What is the resultant gravitational force represented as when considering the contributions from multiple masses?

FR = FGA + FGB Signup and view all the answers

In Cavendish's experiment, what causes the bar AB to rotate?

Torque reversing direction due to mass repositioning. Signup and view all the answers

What method is suggested for calculating the total force exerted by an extended object on a point mass?

Applying calculus to add up the forces vectorially. Signup and view all the answers

Which direction do the various forces exerted by the regions of the spherical shell act towards?

Forces may act in different directions and not in unison. Signup and view all the answers

What equation represents the gravitational force on a mass m located at a height h above the Earth's surface?

F(h) = GMEm/(RE + h)^2 Signup and view all the answers

What is the escape speed from the surface of the Earth?

11.2 km s–1 Signup and view all the answers

How is the acceleration experienced by a mass m at height h above the Earth's surface represented mathematically?

g(h) = F(h)/m Signup and view all the answers

What happens to the gravitational force acting on a particle located inside a uniform spherical shell?

It is zero Signup and view all the answers

What is the relationship between gravitational force (F) and mass (m) illustrated in this content?

F = mg Signup and view all the answers

What value does the acceleration g(h) approach for small heights compared to the Earth’s radius?

It approaches the Earth's gravitational acceleration g Signup and view all the answers

Which quantity is NOT conserved when considering the motion of an object under gravitational influence?

Linear momentum Signup and view all the answers

What is the nature of the total energy E of a bound system in gravitational terms according to this content?

Total energy can be negative for closed orbits Signup and view all the answers

What does Kepler's third law state about planets in circular orbits?

The squares of the orbital periods are proportional to the cubes of the semi-major axes Signup and view all the answers

Why does an astronaut experience weightlessness in a space satellite?

The astronaut is in free fall along with the satellite Signup and view all the answers

What is the form of potential energy V of a mass m in a gravitational field as given in the context?

V = -GMm/a Signup and view all the answers

In the equations provided, which variable represents the radius of the Earth?

RE Signup and view all the answers

What is the gravitational potential energy between two particles separated by a distance r?

$V = –G\frac{m_1m_2}{r}$ Signup and view all the answers

What type of orbit is characterized as a closed orbit in the context of gravitational energy?

Elliptical orbit Signup and view all the answers

What does the conservation of angular momentum lead to?

Kepler's second law Signup and view all the answers

For a particle inside a homogeneous solid sphere, how does the gravitational force act on it?

It acts toward the center Signup and view all the answers

Which symptom is most likely to affect an astronaut while in space?

Swollen face Signup and view all the answers

At what point from the center of the Earth is the gravitational force on a rocket zero, given the mass of the sun and Earth?

1.0 × 10^11 m Signup and view all the answers

If a body weighs 63 N on Earth's surface, what will be its weight at a height equal to half the Earth's radius?

31.5 N Signup and view all the answers

How far would a rocket travel before returning to Earth if fired vertically at 5 km s-1?

600 km Signup and view all the answers

What is the speed of a projectile far away from Earth if it is projected with three times the escape speed?

33.6 km s-1 Signup and view all the answers

If a body weighs 250 N on the surface of the Earth, how much would it weigh halfway to the Earth's center?

125 N Signup and view all the answers

How far is Saturn from the Sun if a Saturn year is 29.5 times an Earth year, given that Earth is 1.5 × 10^8 km from the Sun?

4.49 × 10^8 km Signup and view all the answers

What energy must be expended to remove a satellite from Earth's gravitational influence at a height of 400 km?

2.4 × 10^8 J Signup and view all the answers

Study Notes

Gravitation

Gravity is a fundamental force of attraction between any two objects with mass
All objects on Earth are pulled towards the Earth's center
Galileo demonstrated that all objects accelerate towards Earth at the same rate regardless of their mass
Early models of planetary motion placed Earth at the center (geocentric)
Later, Copernicus proposed a Sun-centered model (heliocentric)
Kepler's laws describe planetary motion:
- Planets orbit the Sun in elliptical orbits, not circles
- A line joining a planet and the Sun sweeps out equal areas during equal intervals of time
- The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit
Newton's law of universal gravitation:
- Every object attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. (F = Gm₁m₂/r²)
- G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N⋅m²/kg²)

Kepler's Laws

Law of Orbits: Planets move in elliptical orbits with the Sun at one focus.
Law of Areas: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Law of Periods: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Universal Law of Gravitation

The gravitational force between two masses m₁ and m₂ separated by a distance r is given by F = G(m₁m₂)/r².

Acceleration due to gravity

The acceleration due to gravity (g) is the acceleration experienced by an object in free fall near the surface of a massive body like Earth.
The value of g varies slightly depending on location on Earth
On Earth’s surface, g is approximately 9.8 m/s²
The value of g decreases as you move further above or below the surface of Earth.

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Description

Test your understanding of gravitational forces and planetary motion with this quiz focused on key principles of physics. Explore the law of areas, the relationship between speed and time period of celestial bodies, and the characteristics of gravitational force in various contexts. This quiz is essential for students studying gravitational concepts in physics.