The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocityRead more
The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocity along any desired trajectory. It tends toward center of the earth through its own acceleration, with gravitational pull due to earth acting over it.
When an object is dropped from rest and allowed to fall freely, it accelerates toward the Earth at a rate constant near the surface. The rate is determined by the mass of the Earth and the distance from its center. The gravitational field intensity at that point can be thought of as the gravitational force exerted on the object divided by its mass. Since the force causing the acceleration is the weight of the object, the gravitational field intensity directly relates to how quickly the object accelerates as it falls.
The intensity of gravitational field at any point in Earth is given by acceleration experienced by any freely falling body. In this context, it proves that this strength of gravitational field is indeed what causes an object to fall with acceleration so as to bring out the relation between intensity of gravitational field and the motion of falling bodies directly.
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at wRead more
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at which it is located, and the strength of the gravitational field acting upon it. For instance, when an object is taken to a greater height, it is endowed with gravitational potential energy that can easily be changed into kinetic energy should the object fall.
Gravitational potential energy also relates to setting up a “zero level” of potential energy. A zero level of potential energy is established arbitrarily; most often, at ground level or infinity. When the zero level is set to be at ground level, the gravitational potential energy of an object at that height is zero. The gravitational potential energy will increase as the object moves above this level. In the case where the zero level is set at infinity, the potential energy of an object will approach zero as it moves infinitely far away from any massive body. This zero level provides for uniform calculations of potential energy in different settings and makes the analysis of gravitational interactions easier.
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field. When an object iRead more
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field.
When an object is at a distance r from the center of the Earth, it feels a gravitational force due to the mass of the Earth. To determine the gravitational potential energy we consider the work done against this gravitational force in moving an object from a reference point, which is often considered to be infinity, at which the potential energy is zero, to the distance r.
The gravitational force acting on the mass is given by Newton’s law of gravitation as is proportional to the product of the masses and inversely proportional to the square of the distance between them. In order to obtain the expression for potential energy, it is necessary to integrate that force over the distance from infinity to. This results in an expression for gravitational potential energy that tells the amount of energy stored for being at a certain location within the gravitational field.
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which notRead more
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which nothing can escape.
The condition for a uniform spherical body of mass M to be a black hole is that the radius must be less than or equal to the Schwarzschild radius. Now, the Schwarzschild radius, or rₛ, is directly proportional to the mass of the body and can be easily expressed in terms of its mass. A body, when its radius is equal to its Schwarzschild radius, is a black hole.
If we take a black hole of mass nine times the Earth’s mass, we can calculate its Schwarzschild radius. Earth’s mass is about 5.97 x 10²⁴ kilograms. Therefore, the mass of the black hole would be 9 x 5.97 x 10²⁴ kg. Using the formula for the Schwarzschild radius, we can calculate the particular radius for this black hole. This radius will set the point at which the speed of escape equals the speed of light and thus form a black hole.
When a satellite orbits the Earth, its total energy is a combination of kinetic energy and gravitational potential energy. The satellite remains in orbit because its total energy is negative, meaning it is bound to Earth’s gravitational field. Doubling the satellite's kinetic energy significantly inRead more
When a satellite orbits the Earth, its total energy is a combination of kinetic energy and gravitational potential energy. The satellite remains in orbit because its total energy is negative, meaning it is bound to Earth’s gravitational field. Doubling the satellite’s kinetic energy significantly increases its total energy. If this increase is sufficient to make the total energy positive, the satellite escapes Earth’s gravitational influence.
In this situation, the additional kinetic energy allows the satellite to exceed the escape velocity required to leave Earth’s gravitational pull. The escape velocity is the minimum speed a body needs to break free from the gravitational field without further propulsion. By doubling the kinetic energy, the satellite surpasses this threshold, no longer constrained by Earth’s gravity.
This event would cause the satellite to transition from a stable orbit to a trajectory that takes it away from Earth indefinitely. It would no longer maintain its orbit or fall back to Earth because the increased energy breaks the balance between its gravitational attraction and the centrifugal force from its motion. Instead, it follows an open trajectory, leaving Earth’s gravitational field and venturing into space, no longer bound by Earth’s pull.
Show that the gravitational field intensity of the earth at any point is equal to the acceleration produced in the freely falling body at that point
The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocityRead more
The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocity along any desired trajectory. It tends toward center of the earth through its own acceleration, with gravitational pull due to earth acting over it.
When an object is dropped from rest and allowed to fall freely, it accelerates toward the Earth at a rate constant near the surface. The rate is determined by the mass of the Earth and the distance from its center. The gravitational field intensity at that point can be thought of as the gravitational force exerted on the object divided by its mass. Since the force causing the acceleration is the weight of the object, the gravitational field intensity directly relates to how quickly the object accelerates as it falls.
The intensity of gravitational field at any point in Earth is given by acceleration experienced by any freely falling body. In this context, it proves that this strength of gravitational field is indeed what causes an object to fall with acceleration so as to bring out the relation between intensity of gravitational field and the motion of falling bodies directly.
See lessWhat is meany by gravitational potential energy of a body? What is the zero level of potential energy?
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at wRead more
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at which it is located, and the strength of the gravitational field acting upon it. For instance, when an object is taken to a greater height, it is endowed with gravitational potential energy that can easily be changed into kinetic energy should the object fall.
Gravitational potential energy also relates to setting up a “zero level” of potential energy. A zero level of potential energy is established arbitrarily; most often, at ground level or infinity. When the zero level is set to be at ground level, the gravitational potential energy of an object at that height is zero. The gravitational potential energy will increase as the object moves above this level. In the case where the zero level is set at infinity, the potential energy of an object will approach zero as it moves infinitely far away from any massive body. This zero level provides for uniform calculations of potential energy in different settings and makes the analysis of gravitational interactions easier.
See lessDerive an expression for the gravitational potential energy of a body of m located at distance r from the centre of the earth.
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field. When an object iRead more
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field.
When an object is at a distance r from the center of the Earth, it feels a gravitational force due to the mass of the Earth. To determine the gravitational potential energy we consider the work done against this gravitational force in moving an object from a reference point, which is often considered to be infinity, at which the potential energy is zero, to the distance r.
The gravitational force acting on the mass is given by Newton’s law of gravitation as is proportional to the product of the masses and inversely proportional to the square of the distance between them. In order to obtain the expression for potential energy, it is necessary to integrate that force over the distance from infinity to. This results in an expression for gravitational potential energy that tells the amount of energy stored for being at a certain location within the gravitational field.
See lessA Black hole is a body from whose surface nothing may evan escape. What is the condition for an uniform spherical body of amss M to be a black hole? What should be the radius of such a black hole if its mass is nine times the mass of the earth?
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which notRead more
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which nothing can escape.
The condition for a uniform spherical body of mass M to be a black hole is that the radius must be less than or equal to the Schwarzschild radius. Now, the Schwarzschild radius, or rₛ, is directly proportional to the mass of the body and can be easily expressed in terms of its mass. A body, when its radius is equal to its Schwarzschild radius, is a black hole.
If we take a black hole of mass nine times the Earth’s mass, we can calculate its Schwarzschild radius. Earth’s mass is about 5.97 x 10²⁴ kilograms. Therefore, the mass of the black hole would be 9 x 5.97 x 10²⁴ kg. Using the formula for the Schwarzschild radius, we can calculate the particular radius for this black hole. This radius will set the point at which the speed of escape equals the speed of light and thus form a black hole.
See lessA Satellite is in an orbit around the earth. If its kinetic energy is doubled, then
When a satellite orbits the Earth, its total energy is a combination of kinetic energy and gravitational potential energy. The satellite remains in orbit because its total energy is negative, meaning it is bound to Earth’s gravitational field. Doubling the satellite's kinetic energy significantly inRead more
When a satellite orbits the Earth, its total energy is a combination of kinetic energy and gravitational potential energy. The satellite remains in orbit because its total energy is negative, meaning it is bound to Earth’s gravitational field. Doubling the satellite’s kinetic energy significantly increases its total energy. If this increase is sufficient to make the total energy positive, the satellite escapes Earth’s gravitational influence.
In this situation, the additional kinetic energy allows the satellite to exceed the escape velocity required to leave Earth’s gravitational pull. The escape velocity is the minimum speed a body needs to break free from the gravitational field without further propulsion. By doubling the kinetic energy, the satellite surpasses this threshold, no longer constrained by Earth’s gravity.
This event would cause the satellite to transition from a stable orbit to a trajectory that takes it away from Earth indefinitely. It would no longer maintain its orbit or fall back to Earth because the increased energy breaks the balance between its gravitational attraction and the centrifugal force from its motion. Instead, it follows an open trajectory, leaving Earth’s gravitational field and venturing into space, no longer bound by Earth’s pull.
See less