A 2-kg mass is moving along the x axis. The potential energy curve as a function

Question

A 2-kg mass is moving along the x axis. The potential energy curve as a function of
position is shown in the Figure. The system is conservative. There is no friction.
A> Refer to figure. If the kinetic energy of the object at the origin is 12 J, what will be kinetic energy at 2.0 m along the +x-axis?
B>Refer to Figure. If the kinetic energy of the object at the origin is 12 J, what will be the speed of object at 6.0 m along the +x-axis?
C>Refer to figure. If the object is at rest at the origin, what will be its speed at 9.0 m?
D>Refer to figure. If the object is at rest at the origin, what will be its kinetic energy at 10 m?

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Explanation / Answer

For a conservative system remains conserved i.e. remains the same. E = K.E. + P.E. at origin E0 = 12 + 22 = 34 J a. Energy at x = 2, K2 = E - U2 = 34 - 10 = 24 Jnext step b. Energy at x = 6, K6 = E - U6 = 34 - 30 = 4 J K6 = (1/2) * m * v62 = 4 J (1/2) * 2 * v62 = 4 speed at 6 m v6 = v4 = 2 m/snext step c.Energy at x = 9, K9 = E - U9 = 34 - 10 = 24 J K9 = (1/2) * m * v92 = 24 J (1/2) * 2 * v92 = 24 speed at 9 m, v9 = v24 = 4.899 m/snext step d. Energy at origin E0 = (1/2) * m * v02 + U0 = 0.5 * 2 * 02 + 22 = 22 J K.E. at 10 m K10 = E0 - U10 = 22 - 15 = 7 J

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