Question

a ball is rolling down a hill. four positions are marked on its path as shown in the image, and the amount of energy the ball contains at each position is shown in the table. which graph most accurately represents the data?
(table: position 1: kinetic energy (j) 0, potential energy (j) 10; position 2: kinetic energy (j) 5, potential energy (j) 5; position 3: kinetic energy (j) 5, potential energy (j) 5; position 4: kinetic energy (j) 10, potential energy (j) 0. image shows the hill with four positions marked.)

Explanation:

To determine the correct graph, we analyze the energy data for each position:

Step 1: Understand Energy Trends

• Kinetic Energy (KE): At Position 1, KE = 0 J; Positions 2 & 3, KE = 5 J; Position 4, KE = 10 J.
• Potential Energy (PE): At Position 1, PE = 10 J; Positions 2 & 3, PE = 5 J; Position 4, PE = 0 J.
• KE and PE are inversely related (total mechanical energy is conserved, assuming no friction: \( \text{Total Energy} = \text{KE} + \text{PE} \), which is \( 10 \, \text{J} \) at all positions).

Step 2: Analyze Graph Requirements

A correct graph will show:

• KE increasing from Position 1 to 4 (0 → 5 → 5 → 10).
• PE decreasing from Position 1 to 4 (10 → 5 → 5 → 0).
• The sum of KE and PE is constant (10 J) at each position.

Step 3: Match to Graph Features

The graph should have two lines (or bars) for KE and PE:

• KE: Starts at 0, stays at 5 for Positions 2–3, then rises to 10.
• PE: Starts at 10, stays at 5 for Positions 2–3, then falls to 0.

(Note: Since the specific graph options are not fully visible, the key is to identify the graph where KE and PE follow these trends. For example, a graph with KE as a line increasing in steps and PE as a line decreasing in steps, with their sum constant.)

Answer:

The graph where Kinetic Energy increases (0 → 5 → 5 → 10) and Potential Energy decreases (10 → 5 → 5 → 0) (exact graph depends on the options, but the trend is as above).