Question

A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function of position r. Express your answer in terms of some or all of the following: x, a, and U. (c) Find the speed at the origin z = 0 such that when the particle reaches ta, it stops momentarily and reverses the direction of its motion. Express you answer in terms of some or all of the following: x, a, m and you

Answer 1

The graph of the botential energy! U= -loe as -x2 70 x Let total mechanical energy be +E --V. ap -UcE <o at x= I a potential energy U= No e a = - 4 potential energy at azia - and total energy = -00 Total mechanical energy TE = KE+PE Vo = KE 7ų) KE - -Uo + uc = Uo (& ²) b) The relation bemn force and potential energy iba given ap =-do (a tok (use 2 = Uo e a2 *c-20 F- -2020 2 ds ae -22 az 2Uoxe -22 a 2

-200 22 which means at a=ta speed of particle is or @ Kinectic energy meamp total energy will be in the form of only potential energy at a=ta; Total mechanical energy! Ez-Voeren -vo at x=0;PE -U. By energy conservation! TE @2-19,= TE@X=0 KE + PE @2209 = KEPPE @2-0 o+ (-00) = L muz-Uo & muz o=J20 C1-ye) Ano' Uo-logo VOC Hve)