Potential Energy and Conservative Forces

An energy associated with the position of bodies in a system. Changes in this energy may accompany opposite changes in kinetic energy in such a way that the total energy remains constant, or is conserved. Energy associated with position is called potential energy, and forces that can be associated with a potential energy are called conservative forces. A system in which the total mechanical energy, kinetic and potential, is constant, is called a conservative system


Example 1.

When we throw a 0.150-kg baseball straight up in the air, The initial upward velocity is 20.0 m/s. Use conservation of energy to find how high it goes, ignoring air resistance.


Solution

the only force doing work on the ball after it leaves your hand is its weight. Let's take the origin at starting point(point1), where the ball leaves your hand; then y1 =0. At this point, v1= 20.0 m/s. We want to find the height at point 2, where it stops and begins to fall back to earth. At this point, v2=0 and y2 is unknown.

Then K1+U1 = K2+U2, or

1/2 mv1^2+ mgy1=1/2 mv2^2+ mgy2,

1/2(0.150kg)(20.0 m/s)^2 + (0.150 kg)(9.80 m/s^2)(0)
= 1/2(0.150kg)(0)^2 + (0.150 kg)(9.80 m/s^2)y2,

y2 = 20.4 m


Answer