Potential Energy Transparency Master	Forms of Energy - Potential Energy: Activity 2: Key

Objects which are raised above the ground have gravitational potential energy (Ep). The potential energy can be calculated using Ep = mgh, where g has the value 9.8, m is the object's mass in kg., and h is its height in metres above the ground. This energy can be extracted to do useful work.

Transparency Master

A 1 kilogram brick is carried up the Eiffel Tower to the 275m platform. How much gravitational potential energy does the brick acquire? Answer: Ep = mgh = 1 x 9.8 x 275 = approximately 2700J (with respect to the ground) A balloon flying by drops a 1 kilogram brick from a height of 275m. How much gravitational potential energy does the brick have before it is dropped? Answer: Ep = mgh = 1 x 9.8 x 275 = approximately 2700J (with respect to the ground) How much kinetic energy does the brick (from question 2 above) have at the instant it reaches the ground? (Hint: What is the gravitational potential energy of the brick at the instant it reaches the ground?) Answer: approximately 2700J. Since the potential energy goes to zero (at zero height) the potential energy must have been converted to some other form of energy...in this case it appears as kinetic energy. How much energy is required for a 60kg person to climb 500m up the stairs of Toronto's CN Tower? Answer: Ep = mgh = 294 000K = 294kJ Students may notice that mg is actually weight .

5. How much gravitational potential energy is in 1m³ of water at the brink of Niagara Falls? 1m³ has a mass of 1000kg and Niagara Fall is approximately 50m high.
Answer: E_p = mgh
= 1000 x 9.8 x 50
= approximately 490kJ(with respect to the river at the bottom of Niagara Falls).

Notes

1. An object's gravitational potential energy is not a "fixed" quantity but rather a "relative" quantity. The gravitational potential energy of a body is always measured "relative" to some convenient baseline, such as the Earth's surface; however, all convenient reference levels are equally valid.

   For example, if you are standing with a 1 kilogram object one metre above the carpet on the ninth story of a tall building, and calculate its gravitational potential energy with respect to the floor and also calculate its gravitational potential energy with respect to the basement floor, you will get two very different values, both are equally valid.

2. The expression mgh, for the gravitational potential energy of an object, is nothing more than an expression of the work required to raise an object of mass m kilograms to a height of h metres.

   In other words,
   

   mg is the weight (force of gravity) on the object and h is the distance that it is moved;

   therefore the expression mgh (potential energy) is equivalent to Fd (work).