I.e., g.R 2 = GM, therefore we can rewrite equation number (iv) as follows: Getting the expressions of escape velocity now by equalizing E k and E p:Īs the expression of the acceleration due to gravity on the earth’s surface is g = GM/R 2 Gravitational Potential Energy = E p= (GMm/R) …………. Work Done to send the object from the surface of the earth to an infinite distance or Gravitational Potential Energy: Now if the escape velocity of earth is V, then the initial kinetic energy(KE) of the object would be: Kinetic Energy = E k = (½) m V 2 ………………. In other words, the kinetic energy (E k) of the object due to its velocity (v) must exceed or at least equal its gravitational potential energy (E p). We will derive the equations using the following condition: The initial kinetic energy of the object would at least equalize the amount of work done to send the same object from the surface of the earth to an infinite distance. As we derive the formula of this escape velocity, this point will get clearer.Įscape velocity Derivation – derive formula as √(2gR) But the value of this velocity would be different for them. This is to be noted that this concept of escape velocity is not only applicable to the earth but also it is equally applicable to all other planets and satellites. Sir Isaac Newton is considered to have been the first to think about such a situation, launching a projectile horizontally from a very high tower.įigure 1: An object with different projection speeds This velocity is referred to as the escape velocity of the Earth. Eventually, with even greater horizontal speed, it will escape the Earth’s gravitational pull and never come back (see Fig. If the velocity is increased further, an elliptical path will follow. It has been seen that when the initial horizontal velocity of a projectile increases sufficiently, the object will not fall back to the Earth following a parabolic pathway, but will describe a circular path around the Earth (see Figure 1). Escape velocity is the velocity at which an object is able to escape from the gravitational field of a planet.Ĭoncepts of Escape Velocity – explanation with diagram Why, unlike Earth, Mercury does not have an atmosphere? | Escape Velocity for MercuryĮscape velocity is defined as the minimum velocity with which if an object is thrown from the surface of the earth or any other planet or satellite then the object defeats the gravitational attraction working on it and can go beyond this attraction.Escape Velocity is √2 times of Orbital velocity for nearby orbits.What factors affect the value of the escape velocity?.Escape velocity Derivation – derive formula as √(2gR).Concepts of Escape Velocity – explanation with diagram.Using integral calculus, we can work backward and calculate the velocity function from the acceleration function, and the position function from the velocity function.Ī motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. By taking the derivative of the position function we found the velocity function, and likewise by taking the derivative of the velocity function we found the acceleration function. In Instantaneous Velocity and Speed and Average and Instantaneous Acceleration we introduced the kinematic functions of velocity and acceleration using the derivative. This section assumes you have enough background in calculus to be familiar with integration. Find the functional form of position versus time given the velocity function.Find the functional form of velocity versus time given the acceleration function.Use the integral formulation of the kinematic equations in analyzing motion.Derive the kinematic equations for constant acceleration using integral calculus.By the end of this section, you will be able to:
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