A hiker lifts a backpack from the ground to a ledge 2 meters above the ground. Which situation would result in the greatest increase in the backpack's gravitational potential energy?
Lifting a heavier backpack to the same 2-meter ledge
Gravitational potential energy is given by \(PE = mgh\), where m is mass, g is the acceleration due to gravity and h is the height gained.
Since g is constant, the gain in PE depends on the product of mass and vertical height. To maximise it, either the mass or the height must be as large as possible.
Keeping the height fixed at 2 metres and increasing the mass (a heavier backpack) directly increases m, so \(mgh\) rises.
Lifting to only 1 metre halves h, and carrying horizontally gives no vertical rise (\(h=0\)), so neither increases PE more.
Hence, the answer is lifting a heavier backpack to the same 2-meter ledge.
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