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 7.0 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 7.0 m along the +x-axis?

Quizplus · Accepted Answer

From conservation of energy, we have:
1/2mv1^2 + PE(0) = 1/2mv2^2 + PE(7)
where v1 = 4 m/s, m = 2 kg, and PE(0) = 8 J (corresponding to x=0)
At x=7 m, the potential energy is PE(7) = 12 J
Solving for v2, we get:
v2 = sqrt((v1^2 + 2(PE(0) - PE(7))/m) = 4.1 m/s.

FIGURE 8-11 a 2