Are kinetic energy and height inversely proportional to each other or directly proportional to each other? Why?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

At a height h, the gravitational potential energy P of an object with mass m is given by the relation P = m*g*h. If the object is considered to be a closed system, it is assumed that there is no frictional force and the mechanical energy M of the object consists of only the kinetic energy K of the object and its gravitational potential energy P, M = K + P. As the height increases, there is an increase in the gravitational potential energy P and a decrease in the kinetic energy K. The kinetic energy K is inversely proportional to the height of the object.

In real life this is demonstrated by the fact that if there is no addition of energy externally, as an object is pushed up a slope it is seen that its speed decreases. This shows that the kinetic energy of the object decreases and this is compensated by an increase in the gravitational potential energy.

deepakkumarkaran's profile pic

deepakkumarkaran | Student, Undergraduate | (Level 2) eNoter

Posted on

Look first of all K.E. is indepedent of the position. Rather it depends on the mass and velocity of the body. However it is not absolute. look at the following cases.

1. Consider two rest identical (assume mass to be the same) bodies, one at a height of 2m and other at a height of 5m from earth surface. Then their K.E. is zero in each case. Here it is independent of position.

2. In the above case if first body moves with a larger velocity than the second one then first one possess more K.E.. Same will be the reverse situation. Here it is independent of position.

3. If a body is moving upward direction, then its K.E. decreases and if ti moving downward then its K.E. increases. Here it depends on the position.

So you should be careful to understand the situation at first. Then proceed.

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