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Potential Energy

The potential energy of an object is generally defined as the energy an object has because of its position relative to other objects that it interacts with. There are different kinds of potential energy such as gravitional potential energy, chemical potential energy, electrical potential energy, to name a few. In this section we will be looking at gravitational potential energy.

Definition 1: Potential energy

Potential energy is the energy an object has due to its position or state.

Gravitational potential energy is the energy of an object due to its position above the surface of the Earth. The symbol PEPE is used to refer to gravitational potential energy. You will often find that the words potential energy are used where gravitational potential energy is meant. We can define potential energy (or gravitational potential energy, if you like) as:

P E = m g h P E = m g h
(1)

where PE = potential energy measured in joules (J)

m = mass of the object (measured in kg)

g = gravitational acceleration (9,8 m·s-29,8m·s-2)

h = perpendicular height from the reference point (measured in m)

A suitcase, with a mass of 1kg1kg, is placed at the top of a 2m2m high cupboard. By lifting the suitcase against the force of gravity, we give the suitcase potential energy. This potential energy can be calculated using Equation 1.

If the suitcase falls off the cupboard, it will lose its potential energy. Halfway down the cupboard, the suitcase will have lost half its potential energy and will have only 9,8J9,8J left. At the bottom of the cupboard the suitcase will have lost all it's potential energy and it's potential energy will be equal to zero.

Objects have maximum potential energy at a maximum height and will lose their potential energy as they fall.

Figure 1
Figure 1 (PG10C3_007.png)

Exercise 1: Gravitational potential energy

A brick with a mass of 1kg1kg is lifted to the top of a 4m4m high roof. It slips off the roof and falls to the ground. Calculate the potential energy of the brick at the top of the roof and on the ground once it has fallen.

Solution

  1. Step 1. Analyse the question to determine what information is provided :
    • The mass of the brick is m=1kgm=1kg
    • The height lifted is h=4mh=4m

    All quantities are in SI units.

  2. Step 2. Analyse the question to determine what is being asked :
    • We are asked to find the gain in potential energy of the brick as it is lifted onto the roof.
    • We also need to calculate the potential energy once the brick is on the ground again.
  3. Step 3. Identify the type of potential energy involved :

    Since the block is being lifted we are dealing with gravitational potential energy. To work out PEPE, we need to know the mass of the object and the height lifted. As both of these are given, we just substitute them into the equation for PEPE.

  4. Step 4. Substitute and calculate :
    P E = m g h = ( 1 ) ( 9 , 8 ) ( 4 ) = 39 , 2 J P E = m g h = ( 1 ) ( 9 , 8 ) ( 4 ) = 39 , 2 J
    (2)

Gravitational Potential Energy

  1. Describe the relationship between an object's gravitational potential energy and its:
    1. mass and
    2. height above a reference point.
    Click here for the solution
  2. A boy, of mass 30kg30kg, climbs onto the roof of a garage. The roof is 2,5m2,5m from the ground. He now jumps off the roof and lands on the ground.
    1. How much potential energy has the boy gained by climbing on the roof?
    2. The boy now jumps down. What is the potential energy of the boy when he is 1m1m from the ground?
    3. What is the potential energy of the boy when he lands on the ground?
    Click here for the solution
  3. A hiker walks up a mountain, 800m800m above sea level, to spend the night at the top in the first overnight hut. The second day he walks to the second overnight hut, 500m500m above sea level. The third day he returns to his starting point, 200m200m above sea level.
    1. What is the potential energy of the hiker at the first hut (relative to sea level)?
    2. How much potential energy has the hiker lost during the second day?
    3. How much potential energy did the hiker have when he started his journey (relative to sea level)?
    4. How much potential energy did the hiker have at the end of his journey?
    Click here for the solution

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