Section 4.8: Energy Bar Charts & Graphs
Energy bar charts visually represent energy transformations and conservation in a system. Each bar shows the amount of kinetic, potential, and other forms of energy at a given moment.
Purpose:
- Track energy conversion between forms (e.g., potential → kinetic).
- Verify energy conservation.
- Compare energy magnitudes at different instances.
Bar Chart Construction:
- Height of each bar proportional to energy quantity.
- Use color or pattern to distinguish energy types.
- Time progression from left to right or along axis.
Example 1
A 2 kg block slides down a frictionless ramp from height 5 m. Draw energy bar charts at the top, midpoint, and bottom.
Top: PE = mgh = 2*9.8*5 = 98 J, KE = 0
Midpoint: PE = 49 J, KE = 49 J
Bottom: PE = 0, KE = 98 J
Example 2
A pendulum of mass 1 kg swings from 0.8 m height. Draw energy bar chart at highest, halfway, and lowest points.
Highest: PE = 1*9.8*0.8 = 7.84 J, KE = 0
Halfway: PE = 3.92 J, KE = 3.92 J
Lowest: PE = 0, KE = 7.84 J
Practice Problems
- Mass 3 kg slides down 6 m ramp, frictionless. Draw bar chart at top, middle, bottom.
- Spring with k = 200 N/m compressed 0.2 m. Show energy distribution at compressed, half, and relaxed positions.
- Roller coaster car, mass 500 kg, height 20 m. Sketch bar chart at start, midpoint, and bottom.
- Block oscillates on spring. Draw bar chart for maximum compression, equilibrium, and maximum extension.
- Ball dropped from 10 m. Show bar charts at release, 5 m, and impact.