Expalin why the escape velocity of an object does not depend on the objects mass . What does escape velocity d

Question

What is Newtons concept of escape velocity?

Answer 1

To escape the Earth's gravity, an object must have kinetic energy that is equal to or greater than the gravitational potential energy keeping it in place.

Both of these depend linearly on the mass of the object, and hence this cancels. So the escape velocity does not depend on the mass of the object, only on the mass and radius of the Earth.

Answer 2

Any object is pulled toward earth with a force.

When an object is thrown up with a speed v, it has initially a kinetic energy given by ½ m v v.

As the object separates from the earth’s center, its speed and hence its kinetic energy decreases where as the distance from the earth’s center increases.

When the kinetic energy becomes zero, the object stops momentarily there and returns toward the center of the earth because the earth pulls it with a force

Suppose that an object of mass m is at a distance of h from the center of earth.

This is pulled down by a gravitational force F = G M m / h^2. m is the mass of the object.

Because of this force it moves through a distance S, and the work done by this force is F x s. This work is converted into the kinetic energy of the body given by
1/2 mv^2.

Thus at any height h,

(1/2) m v v = (G M m / h^2) x S .

‘m’ in both sides gets cancelled and hence we have only

(1/2) v v = G M / h^2.

Thus for any object the velocity is given by the above equation and is independent of the mass of the object.

Now suppose an object is at infinite distance from the earth. Then there is no force that will pull the object toward earth and it will not come to earth.

Suppose by some means we bring the object to a distance little less than infinity, then the object will be pulled toward the earth initially by a very little force and the force becomes greater and greater as it approaches the earth.

Finally it will have a definite speed when it reaches the earth’s surface. As already stated this speed is independent of the mass of the object and is the same for all masses.

Now imagine this situation. A body is thrown with a speed (from the earth’s surface) that is little more than the speed that was attained by the object mentioned in the previous example.

The object will move to infinite height and will never return to earth.

This speed is the escape speed and is called escape velocity.

Answer 3

Despite what it says above, two objects with the same speed but different mass DO NOT possess the same kinetic energy. (I see you changed your post after I commented on this)

Kinetic energy = 1/2m(v^2)

The energy well of a body's gravitational force on you can be found through the relation

GMm/r,

where G is the gravitational constant, M is the mass of the body, m is your mass (or at least the same mass as in the kinetic energy equation), and r is the mean distance between your centers. Obviously then, you must possess at least enough kinetic energy to escape this well. So by equating the two

0.5m(v^2) = GMm/r

m can be divided out from BOTH SIDES, thus it is independent of your (or the escaping body's) mass, but not of the body you (or the object) is escaping from.

0.5(v^2) = GM/r
v = sqrt(2GM/r)

Answer 4

Escape velocity doesn't depend on mass for the same reason that the speed of a falling object (absent air resistance) doesn't depend on mass. The gravitational force is proportional to the mass; the acceleration and resulting speed is constant.

Answer 5

Escape velocity is that velocity required to slip the surly bonds of Earth's gravity. It is approximately 18,000 miles an hour. Any object, regardless of size or mass, will escape at that velocity.

Answer 6

The same reason that Galileo's big and small cannon balls hit the ground at the same time when he dropped them from the Leaning Tower of Pisa. If I weigh twice as much as you it will take twice as much energy to get me into space. If we both reach escape velocity, 11.3 km/second, I'll have twice as much kinetic energy as you and we'll both just escape Earth's gravity.

Answer 7

Physics which i wasnt good in.

Answer 8

http://en.wikipedia.org/wiki/Escape_velocity