Kinetic and Potential Energy: Ball in Free Fall
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MATH1052-edX
① This GeoGebra example dynamically visualizes a ball in free fall, showing how its kinetic energy and gravitational potential energy interconvert over time, illustrating the conservation of mechanical energy. ② Core mathematical concepts include quadratic functions (displacement vs. time), linear functions (velocity vs. time), energy formulas (E_k=½mv², E_p=mgy), and derivatives/slopes (velocity as the derivative of displacement). ③ Construction highlights: using GeoGebra commands Circle, Line, and Segment to draw the ball and reference lines; sliders (button1, button2, button3) control initial velocity v0, initial height y0, and mass m; functions f, f', s, s', s'' define kinematic quantities; points P, Q, Q' and energy curves kin, pot, TotalEnergy are constructed for dynamic updates. ④ Suitable for high school physics or mathematics classes to teach energy conservation, function graphs, and derivatives, or as an inquiry-based learning resource.
GeoGebra Commands & Parameters
Circle(P, 0.4) → cLine((0, (-d) - 0.4), (1, (-d) - 0.4)) → s''Segment((-2, -0.4), (-2, (-d) - 0.4)) → sSegment((-2, -0.4), (0, -0.4)) → s'
AI Drawing Prompt Reference
Create a free-fall energy demonstration figure on a coordinate plane. Use a circle to represent the falling ball, placing its center at x = 0. Draw a horizontal reference line parallel to the x-axis to serve as a baseline for comparing height or energy levels. Add a vertical segment beneath that baseline to indicate the drop region/boundary. Include a horizontal segment from the left reference position up to the ball’s baseline level so the diagram visually supports the idea of displacement relative to the reference. Arrange these geometric elements so they fit a dynamic, parameter-controlled setup.
The prompt above was compiled from the original drawing commands and is for reference only.