While kinetic energy is energy that is associated with motion, potential energy<\/em> is associated with an object\u2019s position. It can be thought of as stored energy that has the potential to gain kinetic energy. We will focus on two ways of storing energy: lifting an object up to some height, and stretching or compressing a spring.<\/p>\n\n\n\n If you lift an object into the air, it will gain kinetic energy when you let go and it begins to fall. This kinetic energy was converted from gravitational potential energy<\/em>. Gravitational potential energy is given by<\/p>\n\n\n\n UG<\/sub><\/em> = m<\/em>g<\/em>h<\/em> <\/p>\n\n\n\n where m<\/em> is the mass of the object, h<\/em> is the height it has been lifted up to, and g = 9.81 m\/s2<\/sup><\/em> is the strength of Earth’s gravitational field (when you are close to the surface). We’ll see in chapter 12 <\/a>that this is also the acceleration of an object in free fall.<\/p>\n\n\n\n As far back as the 1600s, precise measurements were made which determined that the strength of gravity is different in different locations, with a large factor being elevation above sea level. Isaac Newton derived a precise mathematical relationship between the strength of a gravitational field, Earth’s mass, and the distance from the center of the Earth:<\/p>\n\n\n\n g<\/em> = G<\/em> (M<\/em><\/sup>⁄d2<\/sup><\/sub>)<\/em> <\/p>\n\n\n\n where M<\/em> is the mass of Earth, d<\/em> is the distance from your location to the center of Earth, and G<\/em> is a fundamental constant of the universe known as the gravitational constant. Newton did not know the precise value for G<\/em>: he derived the general relationship between g<\/em>, M<\/em>, and d<\/em>, and the values (in any system of units) were experimentally determined later.<\/p>\n\n\n\n In SI units, M = 5.972\u00d71024<\/sup><\/em> kg and G = 6.67\u00d710-11<\/sup> m3<\/sup>\u2044kg\u00b7s2<\/sup><\/em>. On average, at sea level, d = 6.371\u00d7106<\/sup> m<\/em>; substituting these values gives us g = 9.81 m\u2044s2<\/sup> \u2248 10 m\u2044s2<\/sup><\/em>. <\/p>\n\n\n\n The energy stored in a compressed or stretched spring is given by<\/p>\n\n\n\n Usp<\/sub><\/em> = 1<\/sup>\u20442<\/sub><\/em> k<\/em>x2<\/sup><\/em> <\/p>\n\n\n\n The spring constant k<\/em> depends on the particular spring you are using, and has units of J\/m2<\/sup>. The distance x<\/em> is measured relative to the equilibrium position<\/em> of the spring.<\/p>\n\n\n\n6.4.1 Gravitational potential energy<\/h3>\n\n\n\n
Universal gravitation<\/h4>\n\n\n\n
6.4.2 Spring potential energy<\/h3>\n\n\n\n
Practice<\/h4>\n\n\n\n\n