Question 1
One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0, as shown in Figure 1 . When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0, as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring's equilibrium position, as shown in Figure 3 , where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible.
When the object is located at the position shown in Figure 3, which of the following equations correctly indicates the total mechanical energy of the object-spring-Earth system?
1/2m₀v₀² + 1/2k₀x₀²
1/2k₀x₀²
1/2k₀x₀² + mgx₀
1/2k₀x₀² - mgx₀