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Gravitational Potential Energy - Lesson II.4.1


Key Terms:

gravitational potential energy | base level |ground level |total mechanical energy | IL, CCT, NUM

Gravitational Potential Energy
The barbell possesses gravitational potential energy.
Gravitational Potential Energy
The book possesses gravitational potential energy.
Gravitational Potential Energy
The hammer possesses gravitational potential energy.

Gravitational potential energy (Eg)

  • Is the energy stored as the result of the vertical position (height) of an object.
Relative to the position where the ball leaves the hand
  • The ball leaving the hand has 100% kinetic energy, Ek.
  • As the height of the ball increases, Ek is being reduced and Eg is gaining.
  • At maximum height, the ball has no kinetic energy and 100% potential energy.
  • When the ball is moving downward the potential energy is being converted to Ek.

This position may be relative to

  • ground level (the surface of the earth or the floor of any room) or

  • a base level (some arbitrary reference point).

For our juggler, the value of Ep will be larger if the position of the object was compared to the floor and not the base level of the hand.

  • It may be calculated using Eg = mgh where

    Eg = gravitational potential energy (J)
    m = mass of the object (kg)
    g = acceleration due to gravity = 9.80 m/s2
    h = change in height relative to the reference point (m)

Check Point

Sample Problem

A 25.0 kg box is lifted from the floor to a desk 1.87 m above the floor.

  1. What is the gravitational potential energy relative to the floor?
  2. What is the gravitational potential energy relative to a shelf 0.57 m high?
Solution:
m= 25.0 kg
g = 9.80 m/s2
Eg = mgh

  1. h = 1.87 m - 0 m = 1.87 m
    Eg = mgh
         = (25.0 kg)( 9.80 m/s2)(1.87 m)
         = 458 J

  2. h = 1.87 m - 0.57 m = 1.30 m
    Eg = mgh
         = (25.0 kg)( 9.80 m/s2)(1.30 m)
         = 319 J

    Check Point

  • The work done on an object results in an equivalent increase in gravitational potential energy.

  • Crane
    Crane lifting an object.
    Juggler
    A juggling juggler.

  • When an object is raised, kinetic energy and gravitational potential energy is constantly being interchanged.
  • The sum of kinetic and gravitational potential energy (total mechanical energy) remains constant in any system.

    ET = Eg + Ek

  • A moving golf ball possesses mechanical energy due to its speed (kinetic energy) and its vertical position above the ground (gravitational potential energy). Golf

Sample Problem 1. a) Determine the total mechanical energy of a 48 g golf ball if it has a velocity of 25 m/s when it leaves the golf club.

Solution

The total mechanical energy is 30 J.

b) If the golf ball goes in an arc and has a speed of 15 m/s at its maximum height, what will the maximum height be?

Solution

The maximum height of the golf ball will be 49 m.




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