A particle of mass m = 3.0 kg moves along the x axis withoutfriction through a r

Question

A particle of mass m = 3.0 kg moves along the x axis withoutfriction through a region in which its potential energy U(x) variesas shown in the Figure. When the particle is at x = 7.5 m, itsvelocity is 1.225 m/s. What is the magnitude of the force that actson the particle at this position? The particle will move back and forth in a limited region along thex axis. What is the smallest value of x which the particle everhas? Hint: What is the total energy of the particle?Like a roller coaster in a valley, if E_tot is not large enough,the coaster can't make it over the hills on either side. Thecoaster will oscillate back and forth between an xmin and anxmax.

Explanation / Answer

at x = 7.5    kinetic energy = (1/2) m v2 = (1/2) * 3.0 *1.2252   = 2.251 Joules . So total energy is    kinetic + potential = 2.251 +   -4 =   -1.749 Joules . If the total energy was all potential, the object would be alittle to the left of x = 7.5. If we look on the graph forthe x coordinate that relates to U = -1.75   weget... .        x =7.0    is the smallest possible position for theobject

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