The acceleration due to gravity is denoted by g , which on Earth comes out to be about 9.8 m/s². It indicates the strength of the pulling force that the Earth exerted upon the objects resting on it due to mass and radius. It pulls all these objects towards the center due to gravitational force, wherRead more
The acceleration due to gravity is denoted by g , which on Earth comes out to be about 9.8 m/s². It indicates the strength of the pulling force that the Earth exerted upon the objects resting on it due to mass and radius. It pulls all these objects towards the center due to gravitational force, where this gravitational force is said to provide weight to them.
When we think of the Moon, the gravitational acceleration is much lower than that of Earth. This is what is called g’ . The Moon’s mass is approximately 1/80th that of Earth, and its radius is about half that of Earth. Thus, the gravitational force felt on the Moon is much weaker.
From calculations of gravitational acceleration on the Moon, it was determined that this acceleration is around 0.49 m/s². This smaller gravitational pull impacts the behavior of objects on the Moon’s surface greatly. For instance, if a person weighed 100 kg on Earth, then he or she would weigh about 6.1 kg on the Moon. This is because the movements are easier, and it is possible to jump higher because the gravitational force is less. This difference in gravity serves to play a crucial role in many scientific and engineering applications pertinent to lunar exploration and habitation.
For earth,
g = GM/R² = 9.8 ms⁻²
For moon,
g’ = (G(M/80))/(R/2)² = 1 GM/20 R²
= 1/20 x 9.8 = 0.49 ms⁻²
The escape velocity of a projectile from Earth is approximately 11.2 kilometers per second. This is the minimum speed that has to be achieved for an object so that it may leave the gravitational influence of Earth and enter into space without further propulsion. At this speed, the projectile can breRead more
The escape velocity of a projectile from Earth is approximately 11.2 kilometers per second. This is the minimum speed that has to be achieved for an object so that it may leave the gravitational influence of Earth and enter into space without further propulsion. At this speed, the projectile can break free from the gravitational influence of the planet.
The relevance of this concept is crucial especially in the fields of astronomy and space exploration. Therefore, it determines whether there can be a launch satellite and spacecraft. For example, a rocket must obtain such escape velocity to gain orbit or travel beyond the atmosphere of Earth. Unless this speed is achieved, it will eventually fall on the Earth due to gravity attraction.
Its actual influencing factors are the mass of the Earth and the planet’s radius. Although this escape velocity is constant in a range of about 11.2 kilometers per second, it varies when it comes to other celestial bodies. For example, the escape velocity from the Moon is much lower simply because of its smaller size and radius. Escape velocity understanding is very imperative to plan a mission from the Earth to space with some given velocity and compute energy requirements for launching satellites.
The escape velocity is the minimum speed needed for an object to break free from Earth's gravitational field without any additional propulsion. Importantly, this velocity does not depend on the mass of the projectile being launched. This characteristic stems from the principle that all objects, regaRead more
The escape velocity is the minimum speed needed for an object to break free from Earth’s gravitational field without any additional propulsion. Importantly, this velocity does not depend on the mass of the projectile being launched. This characteristic stems from the principle that all objects, regardless of their mass, experience the same acceleration due to gravity when in free fall.
As a result, whether the projectile is a feather or a heavy rocket, the required escape velocity remains constant at approximately 11.2 kilometers per second. The escape velocity is influenced primarily by the mass of the Earth and its radius, along with the universal gravitational constant. This means that if a projectile is launched with the correct speed, it will have enough energy to overcome the gravitational pull of the Earth and continue into space, regardless of its own mass.
This concept is crucial for space exploration, as it allows scientists and engineers to calculate the necessary launch speeds for spacecraft, ensuring they can achieve the desired trajectory and reach their intended destinations. Understanding that escape velocity is independent of the projectile’s mass simplifies the design and planning of space missions, making it a fundamental aspect of orbital mechanics.
When a thin, uniform rod of mass m and length l , is hung at the lower end and allowed to fall vertically, it turns about this hinge. Gravity acting down on the thin rod has caused it to turn. Potential energy is transforming into kinetic energy. Initially, when the rod is vertical, its center of maRead more
When a thin, uniform rod of mass m and length l , is hung at the lower end and allowed to fall vertically, it turns about this hinge. Gravity acting down on the thin rod has caused it to turn. Potential energy is transforming into kinetic energy.
Initially, when the rod is vertical, its center of mass is at a height of l/2 from the hinge. As it falls, this height has decreased. Right before the top end hits the floor, all the gravitational potential energy has been converted to kinetic energy, and velocity will have increased significantly at the top of the rod.
The velocity of the upper end of the rod upon striking the floor can be found by analyzing the motion and energy transformations involved. The distance between the center of mass and the upper end of the rod will play a crucial role in determining the final velocity when the rod is rotating. By the time the top end hits the ground, it has gained a particular velocity, which depends on the length of the rod and the effects of gravity. This is a great example of rotational dynamics and energy conservation in practice.
When three equal masses, each of mass m , are placed at the corners of an equilateral triangle with a side length l , the gravitational field at the center of the triangle is zero because of the symmetrical arrangement of the masses. Each mass generates a gravitational field that points toward itselRead more
When three equal masses, each of mass m , are placed at the corners of an equilateral triangle with a side length l , the gravitational field at the center of the triangle is zero because of the symmetrical arrangement of the masses. Each mass generates a gravitational field that points toward itself.
At the centroid, equidistant from every corner of the triangle, the gravitational fields created from each mass can be weighed. Since the masses were equal and symmetrically placed, the magnitudes of the gravitational fields which they created were identical in magnitude. However, their directions were such as to point toward each corresponding mass.
At the centroid, when the vector sums of gravitational fields of three masses are taken, then these cancel out each other completely. This happens as the angles between lines drawn connecting each mass and the centroid are all the same so that vectors pointing out of each pair of masses would add to point in opposite directions.
Thus, the net gravitational field at the center of the triangle becomes zero. This result shows an important concept in physics: symmetry can cause cancellation effects, leading to a balanced state in gravitational interactions.
If the mass of earth is 80 times of that of moon and its diameter is double that of moon and g on earth is 9.8 m / sec², then the value of g on moon is
The acceleration due to gravity is denoted by g , which on Earth comes out to be about 9.8 m/s². It indicates the strength of the pulling force that the Earth exerted upon the objects resting on it due to mass and radius. It pulls all these objects towards the center due to gravitational force, wherRead more
The acceleration due to gravity is denoted by g , which on Earth comes out to be about 9.8 m/s². It indicates the strength of the pulling force that the Earth exerted upon the objects resting on it due to mass and radius. It pulls all these objects towards the center due to gravitational force, where this gravitational force is said to provide weight to them.
When we think of the Moon, the gravitational acceleration is much lower than that of Earth. This is what is called g’ . The Moon’s mass is approximately 1/80th that of Earth, and its radius is about half that of Earth. Thus, the gravitational force felt on the Moon is much weaker.
From calculations of gravitational acceleration on the Moon, it was determined that this acceleration is around 0.49 m/s². This smaller gravitational pull impacts the behavior of objects on the Moon’s surface greatly. For instance, if a person weighed 100 kg on Earth, then he or she would weigh about 6.1 kg on the Moon. This is because the movements are easier, and it is possible to jump higher because the gravitational force is less. This difference in gravity serves to play a crucial role in many scientific and engineering applications pertinent to lunar exploration and habitation.
For earth,
g = GM/R² = 9.8 ms⁻²
For moon,
See lessg’ = (G(M/80))/(R/2)² = 1 GM/20 R²
= 1/20 x 9.8 = 0.49 ms⁻²
The escape velocity of a projectile, from the earth is approximately
The escape velocity of a projectile from Earth is approximately 11.2 kilometers per second. This is the minimum speed that has to be achieved for an object so that it may leave the gravitational influence of Earth and enter into space without further propulsion. At this speed, the projectile can breRead more
The escape velocity of a projectile from Earth is approximately 11.2 kilometers per second. This is the minimum speed that has to be achieved for an object so that it may leave the gravitational influence of Earth and enter into space without further propulsion. At this speed, the projectile can break free from the gravitational influence of the planet.
The relevance of this concept is crucial especially in the fields of astronomy and space exploration. Therefore, it determines whether there can be a launch satellite and spacecraft. For example, a rocket must obtain such escape velocity to gain orbit or travel beyond the atmosphere of Earth. Unless this speed is achieved, it will eventually fall on the Earth due to gravity attraction.
Its actual influencing factors are the mass of the Earth and the planet’s radius. Although this escape velocity is constant in a range of about 11.2 kilometers per second, it varies when it comes to other celestial bodies. For example, the escape velocity from the Moon is much lower simply because of its smaller size and radius. Escape velocity understanding is very imperative to plan a mission from the Earth to space with some given velocity and compute energy requirements for launching satellites.
See lessThe velocity with which a projectile must be fired so that it escape earth’s gravitational field (escape velocity) doesn’t depend on
The escape velocity is the minimum speed needed for an object to break free from Earth's gravitational field without any additional propulsion. Importantly, this velocity does not depend on the mass of the projectile being launched. This characteristic stems from the principle that all objects, regaRead more
The escape velocity is the minimum speed needed for an object to break free from Earth’s gravitational field without any additional propulsion. Importantly, this velocity does not depend on the mass of the projectile being launched. This characteristic stems from the principle that all objects, regardless of their mass, experience the same acceleration due to gravity when in free fall.
As a result, whether the projectile is a feather or a heavy rocket, the required escape velocity remains constant at approximately 11.2 kilometers per second. The escape velocity is influenced primarily by the mass of the Earth and its radius, along with the universal gravitational constant. This means that if a projectile is launched with the correct speed, it will have enough energy to overcome the gravitational pull of the Earth and continue into space, regardless of its own mass.
This concept is crucial for space exploration, as it allows scientists and engineers to calculate the necessary launch speeds for spacecraft, ensuring they can achieve the desired trajectory and reach their intended destinations. Understanding that escape velocity is independent of the projectile’s mass simplifies the design and planning of space missions, making it a fundamental aspect of orbital mechanics.
See lessA thin uniform rod of mass m and length l is hinged at the lower end to a level floor and stands vertically. It is now allowed to fall, then its upper end will strike the floor with the velocity
When a thin, uniform rod of mass m and length l , is hung at the lower end and allowed to fall vertically, it turns about this hinge. Gravity acting down on the thin rod has caused it to turn. Potential energy is transforming into kinetic energy. Initially, when the rod is vertical, its center of maRead more
When a thin, uniform rod of mass m and length l , is hung at the lower end and allowed to fall vertically, it turns about this hinge. Gravity acting down on the thin rod has caused it to turn. Potential energy is transforming into kinetic energy.
Initially, when the rod is vertical, its center of mass is at a height of l/2 from the hinge. As it falls, this height has decreased. Right before the top end hits the floor, all the gravitational potential energy has been converted to kinetic energy, and velocity will have increased significantly at the top of the rod.
The velocity of the upper end of the rod upon striking the floor can be found by analyzing the motion and energy transformations involved. The distance between the center of mass and the upper end of the rod will play a crucial role in determining the final velocity when the rod is rotating. By the time the top end hits the ground, it has gained a particular velocity, which depends on the length of the rod and the effects of gravity. This is a great example of rotational dynamics and energy conservation in practice.
See lessThree equal masses, m each are placed at the three corners of an equilateral triangle of side length l. The gravitational field at centre of triangle is
When three equal masses, each of mass m , are placed at the corners of an equilateral triangle with a side length l , the gravitational field at the center of the triangle is zero because of the symmetrical arrangement of the masses. Each mass generates a gravitational field that points toward itselRead more
When three equal masses, each of mass m , are placed at the corners of an equilateral triangle with a side length l , the gravitational field at the center of the triangle is zero because of the symmetrical arrangement of the masses. Each mass generates a gravitational field that points toward itself.
At the centroid, equidistant from every corner of the triangle, the gravitational fields created from each mass can be weighed. Since the masses were equal and symmetrically placed, the magnitudes of the gravitational fields which they created were identical in magnitude. However, their directions were such as to point toward each corresponding mass.
At the centroid, when the vector sums of gravitational fields of three masses are taken, then these cancel out each other completely. This happens as the angles between lines drawn connecting each mass and the centroid are all the same so that vectors pointing out of each pair of masses would add to point in opposite directions.
Thus, the net gravitational field at the center of the triangle becomes zero. This result shows an important concept in physics: symmetry can cause cancellation effects, leading to a balanced state in gravitational interactions.
See less