In Example 10.5, the bottom left image in Figure 10.12 shows a block at rest against a compressed spring. At this moment, how much potential energy is stored in the spring?

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Let’s evaluate each option in turn, keeping in mind that the question asks for the potential energy stored in a compressed spring when a block is at rest against it, which is given by the formula U = 1/2 k x^2.
Option ".12 J": This value does not match the reported energy in the problem setup. Since the problem specifies the bottom left image in Figure 10.12 stores a certain amount of energy when compressed, 0.12 J would imply a very small product of k and x^2, which would require an unusually small displacement or spring constant compared to the scenario described. In short, this is not the energy depicted in the example.
Option "0.051 J": This is even smaller, about one tenth of 0.51 J, and far from the 0.78 J referenced by the problem’s answer. Unless the spring constant or displacement is drastically reduced, this value would not describe the energy stored in a compressed spring for the given figure. Therefore this option is inconsistent with the setup.
Option "6.1 J": This value is several times larger than 0.78 J, which would require a substantially larger displacement or a much stiffer spring than implied by the example. Without a correspondingly large kx^2/2, 6.1 J would not be the energy stored in the spring in the described configuration, making this option unlikely.
Option "0.78 J": This matches the energy stated in the problem’s answer key and aligns with the general relation U = 1/2 k x^2 for a compressed spring in the depicted setup. If the figure shows a particular compression and spring constant that yield 0.78 J, then this value correctly represents the potential energy stored at that moment. In summary, this option is consistent with the given reference and the physics of a spring’s potential energy.

PHYS 2305 Spring 25 Lin Quiz 07 - Chapter 9 (9.4-9.6) and Chapter 10 (10.1-10.8)

In Example 10.5, the bottom left image in Figure 10.12 shows a block at rest against a compressed spring. At this moment, how much potential energy is stored in the spring?

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