Question

gravitational potential energy derivation?

Answer 1

the energy possessed by the body of its virtue of its position then it is potential energy
si unit is joule
PE=MGH

Answer 2

As very little, we were told that earth has gravity, and we are not flying away from the earth because the gravitational force holds us from flying away. The gravitational force is defined as Fg= GMm/(r^2). You might have learned this formula in a non-calculus based general physics class. Also, you might have learned the other formula relating to gravitational potential energy. The gravitational potential energy is given as U=-GMm/r. How exactly is the gravitational potential energy related to the gravitational force formula. The following is the mathematical derivation for gravitational potential energy from gravitational force.   Assumption: we move an object away from the center of earth, and we define the U=0 when r=infinity  dU=-dW=-Fdr*cos(theta)  du= -Fgdr*cos(theta)   since we are simply moving the object away from the earth's center theta=180 degrees, the angle between gravitational force and the dr   du=Fgds Uf-Ui=Int(ri to rf)Fgdr Lets take rf=infinity and Uf=0 -Ui=Int(ri to infinity)Fgdr Ui=-Int(ri to infinity)Fgdr Ui= -Int(ri to infinity)GMm/(r^2)dr    =GMm/r (ri to infinity)    = 0-GMm/ri    =-GMm/ri   Now, we have derived the gravitational potential energy. The formula means at ri, we have the potential energy Ui. We can use this formula to find out the change of potential energy when moving from one point to the other (Uf-Ui). Change in potential energy is more of an interest to physicist.