Question

students built a computational simulation to model the conservation of energy in a closed system where a ball is dropped from a certain height. the system includes the balls gravitational potential energy at its initial height and its kinetic energy just before hitting the ground.
gravitational potential energy (gpe) is calculated as gpe = mgh, where m is the objects mass, g is gravity, and h is height.
kinetic energy (ke) is calculated using ke = \frac{1}{2}mv^{2} where m is mass and v is the velocity.
which steps should the students take to model the energy flow in the system accurately and verify the conservation of energy?
a calculate ke at multiple points and confirm that ke constantly increases as the ball falls to the ground.
b calculate gpe at multiple points and confirm that gpe constantly decreases as the ball falls to the ground.
c calculate gpe at the top and ke at the bottom and confirm that the values changed during the balls fall to the ground.
d calculate gpe and ke at multiple points and confirm that their sum remains constant during the balls fall to the ground.

Explanation:

Step1: Recall energy - conservation principle

In a closed - system, the total mechanical energy (sum of GPE and KE) is conserved.

Step2: Analyze each option

• Option A: Only calculating KE does not account for GPE and the total energy conservation.
• Option B: Only calculating GPE does not account for KE and the total energy conservation.
• Option C: Calculating GPE at the top and KE at the bottom only gives two - point values and does not verify conservation throughout the fall.
• Option D: Calculating GPE and KE at multiple points and confirming that their sum remains constant verifies the conservation of energy as the ball falls.

Answer:

D. Calculate GPE and KE at multiple points and confirm that their sum remains constant during the ball's fall to the ground