Inertial mass and gravitational mass are two of the most basic concepts in physics, explaining properties of matter but different in their measurement phenomenon. Inertial mass is the definition of resistance that an object poses for changes in its motion once a force is applied on it. It quantifiesRead more
Inertial mass and gravitational mass are two of the most basic concepts in physics, explaining properties of matter but different in their measurement phenomenon.
Inertial mass is the definition of resistance that an object poses for changes in its motion once a force is applied on it. It quantifies the difficulty to accelerate an object. For instance, a more massive object with greater inertial mass will require much more force to achieve acceleration of equal magnitude to a less massive object. This concept was deeply placed in Newton’s second law of motion and measured in dynamic experiments involving motion and force.
On the contrary, the gravitational mass sets the intensity of interaction an object exhibits with the gravitational field. It expresses the degree to which an object experiences the force of gravitation by being at a given distance from some other heavy body such as Earth or the Sun. Gravitational mass is normally gauged by either gravitation between objects or its weight within a gravitational field of known strength.
Interestingly, inertial and gravitational masses are observed to be equal experimentally. It means they give the same numerical value for the same object. This is a principle of Einstein’s general theory of relativity, suggesting that gravitational force and acceleration can’t be distinguished in certain situations. Although they are conceptually different, the equality of these masses simplifies our understanding of motion and gravity in the universe.
The total mechanical energy of a satellite in a circular orbit is determined by its mass and the radius of its orbit. For satellites A and B, the ratio of their masses is 3:1, and the radii of their orbits are r and 4r , respectively. The mechanical energy of a satellite in orbit is directly proportRead more
The total mechanical energy of a satellite in a circular orbit is determined by its mass and the radius of its orbit. For satellites A and B, the ratio of their masses is 3:1, and the radii of their orbits are r and 4r , respectively. The mechanical energy of a satellite in orbit is directly proportional to its mass and inversely proportional to the radius of the orbit.
Satellite A, having three times the mass of satellite B, has a greater gravitational interaction, leading to higher energy. However, its energy is also inversely related to the smaller orbital radius \( r \). Satellite B, with one-third the mass of A, moves in a larger orbit with a radius 4r . which further reduces its total mechanical energy.
Taking both the mass and orbital radius into account, the total mechanical energy of A is significantly larger than that of B. Specifically, the energy of A is 12 times that of B. This ratio arises because the increased mass of A amplifies its energy, while B’s larger orbital radius reduces its energy proportionally. Thus, the ratio of their total mechanical energies is 12:1, reflecting these combined effects.
To calculate the work required to move a particle away from a sphere, we consider the gravitational potential energy between the two. The particle has a mass of 10 g (0.01 kg), and the sphere has a mass of 100 kg with a radius of 10 cm (0.1 m). The work done is equivalent to the energy needed to oveRead more
To calculate the work required to move a particle away from a sphere, we consider the gravitational potential energy between the two. The particle has a mass of 10 g (0.01 kg), and the sphere has a mass of 100 kg with a radius of 10 cm (0.1 m). The work done is equivalent to the energy needed to overcome the gravitational attraction and take the particle far away, where gravitational potential energy becomes zero.
Gravitational potential energy is determined by the masses involved, the gravitational constant G = 6.67 x 10⁻¹¹ Nm² kg⁻², and the distance between the centers of mass. At the sphere’s surface, this distance is equal to the sphere’s radius (0.1 m).
Substituting the given values into the formula for gravitational potential energy, the calculation shows that the work required to take the particle far away is 6.67 x 10⁻¹⁰ J. This value represents the energy needed to overcome the gravitational pull between the sphere and the particle.
Hence, the work to be done is 6.67 x 10⁻¹⁰ J, reflecting the small but measurable gravitational interaction between the particle and the sphere due to their masses and proximity.
All the known planets move in elliptical orbits around the Sun. This motion is governed by gravitational forces and described by Kepler's laws of planetary motion, particularly the first law, which states that planets travel in elliptical paths with the Sun at one focus of the ellipse. Additionally,Read more
All the known planets move in elliptical orbits around the Sun. This motion is governed by gravitational forces and described by Kepler’s laws of planetary motion, particularly the first law, which states that planets travel in elliptical paths with the Sun at one focus of the ellipse.
Additionally, while the orbits are generally elliptical, they can appear nearly circular for some planets due to their low eccentricity. This elliptical movement accounts for variations in speed and distance from the Sun throughout their orbits, contributing to the dynamic nature of our solar system.
Gravitational shielding is not possible. While the gravitational force on a particle inside a spherical shell is zero, the shell does not block or shield the gravitational forces exerted by other bodies outside it on the particle inside. Therefore, gravitational shielding cannot occur.
Gravitational shielding is not possible. While the gravitational force on a particle inside a spherical shell is zero, the shell does not block or shield the gravitational forces exerted by other bodies outside it on the particle inside. Therefore, gravitational shielding cannot occur.
Give a comparison of inertial and gravitational masses.
Inertial mass and gravitational mass are two of the most basic concepts in physics, explaining properties of matter but different in their measurement phenomenon. Inertial mass is the definition of resistance that an object poses for changes in its motion once a force is applied on it. It quantifiesRead more
Inertial mass and gravitational mass are two of the most basic concepts in physics, explaining properties of matter but different in their measurement phenomenon.
Inertial mass is the definition of resistance that an object poses for changes in its motion once a force is applied on it. It quantifies the difficulty to accelerate an object. For instance, a more massive object with greater inertial mass will require much more force to achieve acceleration of equal magnitude to a less massive object. This concept was deeply placed in Newton’s second law of motion and measured in dynamic experiments involving motion and force.
On the contrary, the gravitational mass sets the intensity of interaction an object exhibits with the gravitational field. It expresses the degree to which an object experiences the force of gravitation by being at a given distance from some other heavy body such as Earth or the Sun. Gravitational mass is normally gauged by either gravitation between objects or its weight within a gravitational field of known strength.
Interestingly, inertial and gravitational masses are observed to be equal experimentally. It means they give the same numerical value for the same object. This is a principle of Einstein’s general theory of relativity, suggesting that gravitational force and acceleration can’t be distinguished in certain situations. Although they are conceptually different, the equality of these masses simplifies our understanding of motion and gravity in the universe.
See lessTwo satellites A and B have ratio of masses 3 : 1 in circular orbits of radii r and 4r. The ratio of total mechanical energy of A to B is
The total mechanical energy of a satellite in a circular orbit is determined by its mass and the radius of its orbit. For satellites A and B, the ratio of their masses is 3:1, and the radii of their orbits are r and 4r , respectively. The mechanical energy of a satellite in orbit is directly proportRead more
The total mechanical energy of a satellite in a circular orbit is determined by its mass and the radius of its orbit. For satellites A and B, the ratio of their masses is 3:1, and the radii of their orbits are r and 4r , respectively. The mechanical energy of a satellite in orbit is directly proportional to its mass and inversely proportional to the radius of the orbit.
Satellite A, having three times the mass of satellite B, has a greater gravitational interaction, leading to higher energy. However, its energy is also inversely related to the smaller orbital radius \( r \). Satellite B, with one-third the mass of A, moves in a larger orbit with a radius 4r . which further reduces its total mechanical energy.
Taking both the mass and orbital radius into account, the total mechanical energy of A is significantly larger than that of B. Specifically, the energy of A is 12 times that of B. This ratio arises because the increased mass of A amplifies its energy, while B’s larger orbital radius reduces its energy proportionally. Thus, the ratio of their total mechanical energies is 12:1, reflecting these combined effects.
See lessA particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. You may takr G = 6.67 x 10⁻¹¹ Nm² kg⁻²
To calculate the work required to move a particle away from a sphere, we consider the gravitational potential energy between the two. The particle has a mass of 10 g (0.01 kg), and the sphere has a mass of 100 kg with a radius of 10 cm (0.1 m). The work done is equivalent to the energy needed to oveRead more
To calculate the work required to move a particle away from a sphere, we consider the gravitational potential energy between the two. The particle has a mass of 10 g (0.01 kg), and the sphere has a mass of 100 kg with a radius of 10 cm (0.1 m). The work done is equivalent to the energy needed to overcome the gravitational attraction and take the particle far away, where gravitational potential energy becomes zero.
Gravitational potential energy is determined by the masses involved, the gravitational constant G = 6.67 x 10⁻¹¹ Nm² kg⁻², and the distance between the centers of mass. At the sphere’s surface, this distance is equal to the sphere’s radius (0.1 m).
Substituting the given values into the formula for gravitational potential energy, the calculation shows that the work required to take the particle far away is 6.67 x 10⁻¹⁰ J. This value represents the energy needed to overcome the gravitational pull between the sphere and the particle.
Hence, the work to be done is 6.67 x 10⁻¹⁰ J, reflecting the small but measurable gravitational interaction between the particle and the sphere due to their masses and proximity.
See lessAll the known planets move in
All the known planets move in elliptical orbits around the Sun. This motion is governed by gravitational forces and described by Kepler's laws of planetary motion, particularly the first law, which states that planets travel in elliptical paths with the Sun at one focus of the ellipse. Additionally,Read more
All the known planets move in elliptical orbits around the Sun. This motion is governed by gravitational forces and described by Kepler’s laws of planetary motion, particularly the first law, which states that planets travel in elliptical paths with the Sun at one focus of the ellipse.
See lessAdditionally, while the orbits are generally elliptical, they can appear nearly circular for some planets due to their low eccentricity. This elliptical movement accounts for variations in speed and distance from the Sun throughout their orbits, contributing to the dynamic nature of our solar system.
Is Gravitational shielding possible?
Gravitational shielding is not possible. While the gravitational force on a particle inside a spherical shell is zero, the shell does not block or shield the gravitational forces exerted by other bodies outside it on the particle inside. Therefore, gravitational shielding cannot occur.
Gravitational shielding is not possible. While the gravitational force on a particle inside a spherical shell is zero, the shell does not block or shield the gravitational forces exerted by other bodies outside it on the particle inside. Therefore, gravitational shielding cannot occur.
See less