Gravitational potential energy :
- The energy stored in an object because of its position or state is called potential energy.
- This energy is relative.
- It increases as we go to greater heights from the surface of the earth.
- P.E. [at a height h] = mgh.
- P.E. [on the ground ] = zero.
- But for large values of h, the value of g decreases with increase in h.
- For an object at infinite distance, value of potential energy to be zero there.
- Thus, for smaller distances, i.e. heights, the potential energy is less than zero, i.e. it is negative.
- When an object is at a height h from the surface of the earth, P.E. = -GMm/R+h
Escape velocity :
- Value of g keeps decreasing as we go higher above the surface o f the earth.
- Thus, the force pulling any object downward, decreases as the ball goes up.
- Its maximum height depends on its initial velocity.
- Higher the initial velocity u, the larger is the height reached by the ball.
- The minimum velocity that is required for an object to free itself from the gravitational force exerted by an earth is called Escape Velocity.
- Above a particular value of initial velocity of the ball, Any object is able to overcome the downward pull by the earth and can escape the earth forever and will not fall back on the earth. This velocity is called escape velocity.
- If u = escape velocity, Body escapes the gravitational force of the earth.
- The force of gravity becomes zero only at in-finite distance from the earth.
- For the object to be free from the gravity of the earth, it has to reach infinite distance from the earth. i.e. the object will come to rest at in-finite distance and will stay there.
- The spacecrafts which are sent to the moon or other planets have to have their initial velocity larger than the escape velocity
- They can overcome earth’s gravitational attraction.
Why Space travellers as well as objects in the spacecraft appear to be floating ?
- Value of g is only 11% less than its value on the surface of the earth.
- Height of a spacecraft is not the reason for their weightlessness.
- Weightlessness is caused by their being in the state of free fall.
- As the velocity of free fall does not depend on the properties of an object, the velocity of free fall is the same for the spacecraft, the travelers and the objects in the craft.
- Thus, if a traveller releases an object from her hand, it will remain stationary with respect to her and will appear to be weightless.