Motion in the Earth's Gravitational Field

A) Vertical Work and Potential Energy The work done in lifting a mass a vertical distance "d" or "h" is stored inside the body as increased potential energy (i.e. increased gravitational potential energy Ug or U)

Recall W = Fd Since F is equal and opposite to Fg = mg, and d = h, then W = Fd becomes U = mgh

B) Changes in Potential Energy and Kinetic Energy as an object moves in Earth's Gravitational Field. U = mgh U = 5 x 9.8 x 8 =392 J E k = 0E T = E k +U E T = E T = 392 J

U = mgh U = 5 x 9.8 x 8 =392 J E k = 0E T = E k +U E T = E T = 392 J U = mgh U = 5 x 9.8 x 3 = 147 J V f 2 = V i 2 +2ad V f 2 =0+2(9.8)(5) V f = 9.9 E k = mv 2 /2 E k = 5(9.9) 2 /2 E k = 245 J E T = E k +U E T = E T = 392 J

U = mgh U = 5 x 9.8 x 8 =392 J E k = 0E T = E k +U E T = E T = 392 J U = mgh U = 3 x 9.8 x 8 = 147 J V f 2 = V i 2 +2ad V f 2 =0+2(9.8)(5) V f = 9.9 E k = mv 2 /2 E k = 5(9.9) 2 /2 E k = 245 J E T = E k +U E T = E T = 392 J  U = U f – U i  U = 147 – 392  U = -245 J  E k = Ek f – Ek i  E k = 245 – 0  E k = +245 J

Note: 1) Total Energy is the same at all times - there is conservation of energy 2) As an object moves, the changes in U and Ek are equal and opposite

Sample Problems