A particle of mass m = 10 g moves in a dimension subjected to a force associated with a potential energy of the form Ep (x) = x2 (1-x/3) the magnitudes are given in SI a) Find the positions of particle balance and tell what type they are. b) Represent Ep (x). c) Give the expression of the force as a function of "x" and indicate the meaning of this force in each interval d) Analyze the possible movements of the particle for the different values of its mechanical energy e) Consider the case that the particle has a mechanical energy E = 1J and at t = 0 s its position is x = 1 m. i. What is the kinetic energy of it for time t = 0 and what type of movement does it perform? ii, At what point does this particle reach its maximum kinetic energy and what is its value? f) If the particle always moves near x = 0, that is, it always takes very small values of x (| x | «), the potential energy can be approximated as Ep (x) z x². Under these conditions i) What type of movement does the particle make? Ii) Obtain the oscillation frequency.
A particle of mass m = 10 g moves in a dimension subjected to a force associated with a potential energy of the form Ep (x) = x2 (1-x/3) the magnitudes are given in SI a) Find the positions of particle balance and tell what type they are. b) Represent Ep (x). c) Give the expression of the force as a function of "x" and indicate the meaning of this force in each interval d) Analyze the possible movements of the particle for the different values of its mechanical energy e) Consider the case that the particle has a mechanical energy E = 1J and at t = 0 s its position is x = 1 m. i. What is the kinetic energy of it for time t = 0 and what type of movement does it perform? ii, At what point does this particle reach its maximum kinetic energy and what is its value? f) If the particle always moves near x = 0, that is, it always takes very small values of x (| x | «), the potential energy can be approximated as Ep (x) z x². Under these conditions i) What type of movement does the particle make? Ii) Obtain the oscillation frequency.
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