In Example 10.3, if the origin of the system was displaced 10 m in the upwards direction (5 m above the top of the hill), how would the change in Christine’s potential energy be affected when she travels from the top of the hill to the bottom of the hill?

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To analyze what happens to Christine’s potential energy change when the origin is displaced, we must separate absolute potential energy from the change in potential energy between two points.
Option A: 'Her change in potential energy would increase' would be incorrect because the change in potential energy between the top and bottom of the hill depends on the vertical height difference, not on an absolute energy value or where we call zero.
Option B: 'Her change in potential energy would stay the same' is the correct line of reasoning: the change in gravitational potential energy between two elevations is ΔPE = m g Δh, where Δh is the vertical drop from top to bottom. Shifting the reference origin by +10 m adds a constant to both h_top and h_bottom, but their difference Δh remains unchanged, so ΔPE does not change.
Option C: 'Her change in potential energy would decrease' would only be true if the height difference decreased, which it does not; the physical geometry of the hill remains the same, so Δh is unchanged, and thus ΔPE is unchanged.
Option D: 'It is not possible to decide without knowing Christine's mass' is not accurate here: while the absolute potential energy depends on mass, the change ΔPE between two points depends on m and Δh, and since Δh is fixed by the hill, we can determine the nature of the change without needing the exact mass value; we only need to know that the height difference is the same.
In summary, because the origin shift adds a constant to both reference heights but does not alter the vertical separation between top and bottom, the change in potential energy remains the same.

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

In Example 10.3, if the origin of the system was displaced 10 m in the upwards direction (5 m above the top of the hill), how would the change in Christine’s potential energy be affected when she travels from the top of the hill to the bottom of the hill?

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