is the stored energy objects possess due to their position in a gravitational field. It's crucial for understanding how energy transforms as objects move vertically, like in or .
Calculating gravitational involves mass, height, and . This concept ties into the broader principle of energy conservation, helping us analyze various physical systems and predict object behavior in Earth's gravity.
Gravitational Potential Energy Fundamentals
Gravitational potential energy concept
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Gravitational potential energy () represents stored energy in objects due to their position within gravitational fields measured relative to a reference point (Earth's surface)
done by gravity equals negative change in gravitational potential energy W=−ΔUg demonstrating inverse relationship
GPE decreases when gravity performs positive work (object falls) while GPE increases with negative work (object rises)
Derivation of potential energy expression
states work done by a force equals change in energy
near Earth's surface expressed as [F_g = mg](https://www.fiveableKeyTerm:f_g_=_mg) where m is mass and g is gravitational acceleration (9.8 m/s²)
Work done by gravity calculated as W=Fg⋅d=mgd where d is
Change in gravitational potential energy derived as ΔUg=−W=−mgd
Final expression for GPE near Earth's surface [U_g = mgh](https://www.fiveableKeyTerm:u_g_=_mgh) where h represents height above reference point
Applications and Problem Solving
Near-Earth potential energy calculations
Key variables for GPE problems include mass (m), gravitational acceleration (g), and height (h)
Common problem types involve calculating GPE at different heights, finding GPE changes for vertical displacements, and determining heights from given GPE values
Ensure unit consistency using SI units (kg for mass, m for height, J for energy)
Mechanical energy conservation in gravity
combines kinetic and potential energies Emech=KE+PE
states total mechanical energy remains constant without
occur between GPE and during motion (free fall, pendulum swings)
Applications include analyzing pendulum motion, , and
Non-conservative forces (friction, air resistance) cause gradual decrease in mechanical energy over time