Question

a rock falls off a high cliff to the ground below. ignoring friction, which statement correctly compares the energy of the rock at different points of its fall? *hint: this is similar to the penny problem we did in class.

a) the total energy just before it falls is less than its total energy half - way down.
b) the total energy just before it hits the ground is less than its total energy just before it falls.
c) the total energy just before it hits the ground is greater than its total energy half - way down.
d) the total energy just before it falls is equal to its total energy just before it hits the ground.

Explanation:

According to the law of conservation of energy, in the absence of non - conservative forces (like friction, which is ignored here), the total mechanical energy (sum of kinetic and potential energy) of a system remains constant. For the falling rock, at any point during its fall (just before falling, half - way down, just before hitting the ground), the total energy (kinetic + potential) is the same.

• Option A: Incorrect. By conservation of energy, total energy just before falling is equal to total energy half - way down.
• Option B: Incorrect. Total energy just before hitting the ground is equal to total energy just before falling.
• Option C: Incorrect. Total energy just before hitting the ground is equal to total energy half - way down.
• Option D: Correct. Since there is no non - conservative force (friction is ignored), total energy is conserved.

Answer:

D. The total energy just before it falls is equal to its total energy just before it hits the ground.