Energy conservation with conservative forces: A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?

Question

Quizplus · Accepted Answer

Conservation of energy states that the initial potential energy plus the initial kinetic energy of the system is equal to the final potential energy plus the final kinetic energy of the system. At the origin, the object has only kinetic energy, and at 7.0 m, the object has only potential energy. Therefore, we can set the initial kinetic energy equal to the final potential energy:

(1/2)mv^2 = mg(5.5)

where m is the mass of the object, v is its final speed, and 5.5 is the difference in potential energy between the origin and 7.0 m. Solving for v, we get v = sqrt(2g(5.5)) = 4.2 m/s, which is choice B.

Energy Conservation with Conservative Forces: a 2