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) = x2 + x3 , with = 2.00 J/m2 and = 0.300 J/m3 . 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 +ˆx 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)
When conservative forces only do work on a ssystem the total mechanical energy of the system is conserved.

Apply conservation of mechanical energy

K2 + U2 = K1 + U1

K2 + U2 = 0 + U1

K2 = U1 - U2

= (-alfa*x^2 + beta*x^3) - (-alfa*x^2 + beta*x^3)

= 0 - (-2*4^2 + 0.3*4^3)

= 12.8 J <<<<<<<<-----------------------Answer

b) Workdone by conservative force = change in kinetic energy

= 12.8 J <<<<<<<<-----------------------Answer

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