A point mass, m = 0.0900 kg, moves along the x-axis where the only force acting

Question

A point mass, m = 0.0900 kg, moves along the x-axis where the only force acting on it is a conservative force with a potential energy function given by U (x) = - alpha x^2 + beta x^3, with alpha = 2.00 J/m^2 and beta = 0.300 J/m^3. The object is initially at rest near x = 0. To get it moving from this point of unstable equilibrium, a negligibly small force is applied in the + x direction (i.e. just enough to get it moving, not enough to warrant inclusion in answering the question). (a) When the object reaches the point of x = 4.00 m what is its speed? (b) How much work was done by this force as the object moved this 4.00 m distance?

Explanation / Answer

a) u(4) = -2*16+0.3*64 = -12.8 J

at x = 0

u(0) = 0

kinetic energy = potential energy

1/2mv^2 = 12.8 J

v = 16.86 m/s

b) work done = change in kinetic energy = k2-k1 = u1-u2 = 12.8 J

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