By Benjamin Crowell

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**Sample text**

The y component of the velocity can be connected to the height via the constant acceleration equation [3] vf2 = vi2 + 2a∆y , d / As the skater free-falls, his PE is converted into KE. ) and Newton’s second law provides the acceleration, [4] a = F/m , in terms of the gravitational force. 2 Potential Energy: Energy of Distance or Closeness 39 The algebra is simple because both equation [2] and equation [3] have velocity to the second power. Equation [2] can be solved for v 2 to give v 2 = 2KE/m, and substituting this into equation [3], we find KEf KEi 2 =2 + 2a∆y .

Rather than depending on yourself to avoid any mistakes with signs, it is better to check whether the final result make sense physically. If it doesn’t, just reverse the sign. Although the equation for gravitational potential energy was derived by imagining a situation where it was transformed into kinetic energy, the equation can be used in any context, because all the types of energy are freely convertible into each other. Gravitational PE converted directly into heat example 2 A 50-kg firefighter slides down a 5-m pole at constant velocity.

Net/∼shawn. gravitational potential energy: The skateboarder in the photo has risen from the bottom of the pool, converting kinetic energy into gravitational potential energy. After being at rest for an instant, he will go back down, converting PE back into KE. magnetic potential energy: When a magnetic compass needle is allowed to rotate, the poles of the compass change their distances from the earth’s north and south magnetic poles, converting magnetic potential energy into kinetic energy. ) electrical potential energy: Socks coming out of the dryer cling together because of attractive electrical forces.