FIGURE 8-11 A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in Figure 8-11. The system is conservative. There is no friction.
-Refer to Figure 8-11. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 4.0 m along the +x-axis?

Question

FIGURE 8-11  A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in Figure 8-11. The system is conservative. There is no friction.
-Refer to Figure 8-11. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 4.0 m along the +x-axis?

Quizplus · Accepted Answer

From conservation of mechanical energy, the total mechanical energy is constant. At the origin, the total mechanical energy is $E = \frac{1}{2}mv_0^2 + U_0 = \frac{1}{2}(2	ext{ kg})(4.0	ext{ m/s})^2 + 0 = 32	ext{ J}$. At a position 4.0 m along the +x-axis, the total mechanical energy is $E = \frac{1}{2}mv^2 + U(x)$. Setting these equal and solving for $v$ gives $v = \sqrt{\frac{2}{m}(E - U(x))} = \sqrt{\frac{2}{2	ext{ kg}}(32	ext{ J} - 6	ext{ J})} \approx 4.4	ext{ m/s}$. Therefore, the correct answer is (C).

FIGURE 8-11 a 2