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Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е....
Derive an expression for the energy needed to launch an object from the surface of Earth...
Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of some or all of the variables h, mass of the object m, mass of Earth mE, its radius RE, and gravitational constant G.
Derive an expression for the energy needed to launch an object from the surface of Earth...
Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of some or all of the variables h, mass of the object m, mass of Earth mE, its radius RE, and gravitational constant G.
The gravitational potential energy of a small satellite with mass m orbiting the Earth, mass M,...
The gravitational potential energy of a small satellite with mass m orbiting the Earth, mass M, is U(r) = −(GMm)/r, where r is the radial distance from the center of Earth to the satellite. Derive the gravitational force F(r) acting on the satellite by evaluating the gradient of the potential energy.
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical...
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical masses (e g. Earth and Sun) s u--GMm, where r distance between their centers. If the masses are not spherical, this expression is not valid. However, we can still find the total potential energy by dividing the non-spherical mass into bits, treating each tiny bit as a point mass (which gravitates like a sphere), and adding their effects. That is, U-J -GMdm. This integral...
An astronaut with a mass of 70 kg is standing on the surface of a spherical...
An astronaut with a mass of 70 kg is standing on the surface of a spherical asteroid that is 10 km in diameter and has a mass of 1x1015 kg. He knows he can jump straight up 0.2 meters on Earth with his spacesuit on. Can he generate enough energy by jumping to propel himself high enough off of the surface of the asteroid to grab a spacecraft that is orbiting 1 km above? (G=6.67x10-11Nm2/kg2 , g=9.8m/s2)
Given the formula of the kinetic energy of a particle m with speed v: KE =...
Given the formula of the kinetic energy of a particle m
with
speed v:
KE = 1⁄2mv2 ,
and the formula of the gravitational potential energy:
PE = -GMEm/R,
where G is gravitational constant and ME and R=6378 km are the
mass and the radius of Earth. Now the particle is shot from Earth
surface to space. Find the minimum required initial speed for this
particle to completely escape the influence of Earth gravity (i.e.
PE=0). Notice that the gravitational...
the formula for potential energy is p= mgh, where Pis potential energy, m is mass, g is gravity, and h is height
the formula for potential energy is p= mgh, where Pis potential energy, m is mass, g is gravity, and h is height. which expression can be used to represent g?1 p-m-h2 p-mh3 p/m0-h4 p/(mh)
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of...
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of radius R is found to be V(r, 9) = -E, cose (--) where E, is a constant and r and 0 are the spherical radial and polar angle coordinates, respectively. This electric potential is due to the charges on the conductor and charges outside of the conductor 1. Find an expression for the electric field inside the spherical conductor. 2. Find an expression for...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the...
The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However,...
The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from the Earth's surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, 9h. Express the equation in terms of the radius R of the Earth, g, and h. 9A Suppose a 74.35 kg...
3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical masses (e g. Earth and Sun) s u--GMm, where r distance between their centers. If the masses are not spherical, this expression is not valid. However, we can still find the total potential energy by dividing the non-spherical mass into bits, treating each tiny bit as a point mass (which gravitates like a sphere), and adding their effects. That is, U-J -GMdm. This integral...
Given the formula of the kinetic energy of a particle m
with
speed v:
KE = 1⁄2mv2 ,
and the formula of the gravitational potential energy:
PE = -GMEm/R,
where G is gravitational constant and ME and R=6378 km are the
mass and the radius of Earth. Now the particle is shot from Earth
surface to space. Find the minimum required initial speed for this
particle to completely escape the influence of Earth gravity (i.e.
PE=0). Notice that the gravitational...
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of radius R is found to be V(r, 9) = -E, cose (--) where E, is a constant and r and 0 are the spherical radial and polar angle coordinates, respectively. This electric potential is due to the charges on the conductor and charges outside of the conductor 1. Find an expression for the electric field inside the spherical conductor. 2. Find an expression for...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the...
The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from the Earth's surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, 9h. Express the equation in terms of the radius R of the Earth, g, and h. 9A Suppose a 74.35 kg...
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