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?
A) 4.0 m/s
B) 4.2 m/s
C) 4.4 m/s
D) 4.6 m/s
E) 9.8 m/s

Question

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? 
A) 4.0 m/s 
B) 4.2 m/s 
C) 4.4 m/s 
D) 4.6 m/s 
E) 9.8 m/s

Quizplus · Accepted Answer

Since the system is conservative, the total mechanical energy is conserved.
At the origin, the mechanical energy is:
$E_i = \frac{1}{2}mv^2 + U(0) = \frac{1}{2}(2.0	ext{ kg})(4.0	ext{ m/s})^2 + 2	ext{ J} = 18	ext{ J}$
At x = 7.0 m, the mechanical energy is:
$E_f = \frac{1}{2}mv^2 + U(7.0	ext{ m})$
Since the mechanical energy is conserved, $E_i = E_f$
$\frac{1}{2}(2.0	ext{ kg})(4.0	ext{ m/s})^2 + 2	ext{ J} = \frac{1}{2}(2.0	ext{ kg})v^2 + 8	ext{ J}$
Solving for v, we get $v\approx 4.2	ext{ m/s}$

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