FIGURE 8-12 A 2-kg mass is moving along the x axis. The potential energy curve as a function of position is shown in Figure 8-12. The system is conservative. There is no friction.
-Refer to Figure 8-12. If the object is at rest at the origin, what will be its speed at 9.0 m along the +x-axis?

Question

FIGURE 8-12  A 2-kg mass is moving along the x axis. The potential energy curve as a function of position is shown in Figure 8-12. The system is conservative. There is no friction.
-Refer to Figure 8-12. If the object is at rest at the origin, what will be its speed at 9.0 m along the +x-axis?

Quizplus · Accepted Answer

At the origin, the object has only potential energy, not kinetic energy, so its total mechanical energy is 0. As the object moves to the right, its initial potential energy is converted into kinetic energy. When the object has moved 9.0 m to the right, its potential energy has decreased by about 20 J, which means its kinetic energy has increased by the same amount. Using conservation of energy, we have:
initial potential energy = final potential energy + final kinetic energy
0 J = -20 J + 1/2 mv^2
Solving for v, we get:
v = sqrt(40/2) = 3.16 m/s ≈ 3.5 m/s.

FIGURE 8-12 a 2-Kg Mass Is Moving Along the X