Gravitational Potential Energy Equations and Examples
Learn how to rearrange the potential energy equation, calculate potential energy using the formula PE = mgh, and solve for mass and height in relation to gravitational potential energy. Explore examples of calculating potential energy for objects at different heights. Understand the concept of gravitational potential energy and its mathematical representation through practical scenarios.
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Presentation Transcript
Rearranging Potential Energy Equation
Learning Objectives I can mathematically rearrange the potential energy equation. I can calculate Potential Energy using the formula.
Gravitational Potential Energy (GPE) Potential Energy that depends upon an objects height above a reference point Formula: PE = mgh Potential energy is calculated by: The object s mass (m), multiplied by the earth s gravitational pull (g) (9.8 m/sec/sec), multiplied by the height (h) the object can fall.
Formula Representation Formula Represents PE = Potential Energy Joules (J) m = mass g = acceleration due to gravity h = height Units mass Kilogram (kg) m/s/s PE = mgh Meter (m)
Solve for Mass (m) Solve for Mass (m) Step 1 Divide both sides by gh PE = mgh gh __ __ gh m = P? ?
Solve Solve for Height for Height (h) (h) Step 1 Divide both sides by gm PE = mgh gm __ __ gm h = P? ??
Potential Energy Related Equations Potential Energy PE = mghm = ?? mass height ? h = ?? ??
Calculation Example #1 What is the gravitational potential energy of a 5kg object resting at a height of 3m off the ground? Given/ Unknown PE = m = g = h = 3m Work ? 5kg 9.8m/s/s PE = 147J PE = (5kg)(3m)(9.8m/s/s) PE = mgh
Calculation Example #2 What is the gravitational potential energy associated with a 75kg tourist at the top floor of the Sears Tower in Chicago, with respect to the street 436m below? Given/ Unknown PE = m = g = h = 436m Work ? 75kg 9.8m/s/s PE = 320,460J PE = (75kg)(436m)(9.8m/s/s) PE = mgh
Calculation Example #3 An automobile to be transported by ship is raised 7.0m above the dock. If its gravitational potential energy is 66,000J, what is the automobiles mass? Given/ Unknown PE = m = g = h = 7m Work 66,000J ? 9.8m/s/s 66,000? 68.6?2?/? 66,000? 9.8?/?/?(7?) m =?? ? = 962.1?? m = m = ?
Calculation Example #4 The gravitational potential energy of a 15kg object is 294J. What is the height of the object above the ground? Given/ Unknown PE = m = g = h = ? Work 294J 15kg 9.8m/s/s h =?? 294? 294? h = h = = 2? ?? 147???/?/? 9.8?/?/?(15??)
