Question

based on this graph, which chart represents the energy for point a?
height (m) vs. time (s)
graph of height (m) on y - axis (0 - 8) and time (s) on x - axis (0 - 4), with a blue line starting at (0,6), peaking at (0.5,8), then going to (1,6) point a, (2,0), (3,0), (4,6)
three bar charts: first: $e_p$ bar height 6, $e_k$ bar height 2; second: $e_p$ bar height 2, $e_k$ bar height 0; third: $e_p$ bar height 2, $e_k$ bar height 6

Explanation:

To solve this, we analyze the energy at point A using the principles of mechanical energy (potential \( E_p \) and kinetic \( E_k \)):

Step 1: Analyze the height at point A

From the height - time graph, point A has a height (\( h \)) of 6 m. Potential energy \( E_p = mgh \) (where \( m \) is mass, \( g \) is gravity). A higher height means more \( E_p \).

Step 2: Analyze the motion at point A

The object is moving (since the height is changing, not at rest), so it has kinetic energy \( E_k \). But at the peak (height = 8 m), \( E_k = 0 \) (momentarily at rest). At point A (height = 6 m, between peak and the lowest point at \( t = 2 \) s), the object is descending, so \( E_p \) is decreasing and \( E_k \) is increasing. However, \( E_p \) is still larger than \( E_k \) here (since height is 6 m, not near 0).

Step 3: Match with the bar charts

• First chart: \( E_p = 6 \), \( E_k = 2 \) ( \( E_p > E_k \), consistent with height = 6 m and moving).
• Second chart: \( E_k = 0 \) (incorrect, as the object is moving at A).
• Third chart: \( E_k > E_p \) (incorrect, since height is 6 m, \( E_p \) should be larger).

Answer:

The first chart (with \( E_p = 6 \) and \( E_k = 2 \))