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### Course: High school physics (DEPRECATED) > Unit 5

Lesson 5: Gravitational potential energy and conservative forces# Gravitational potential energy and conservative forces review

Review the key concepts and equations for gravitational potential energy, conservative forces, and nonconservative forces.

## Key terms

Term (symbol) | Meaning |
---|---|

Gravitational potential energy ( | Energy due to position of an object in a gravitational field. SI unit is joule ( |

Conservative force | A force for which the work done by the force only depends on the initial and final positions and is independent of path taken. The net work is zero when the starting and ending positions are the same. An example is the force of gravity. |

Nonconservative force | A force for which the work done depends on path taken. An example is the friction force. |

Potential energy ( | Energy stored due to the position of an object. |

## Equations

Equation | Symbol breakdown | Meaning in words |
---|---|---|

The change in gravitational potential energy is directly proportional to mass, gravitational field strength, and change in height. |

## Common mistakes and misconceptions

**1) Sometimes people are confused about how to measure height for a change in gravitational potential energy.**Since the change in gravitational potential energy only depends on the change in height, the definition of where

## Learn more

For deeper explanations of conservative and nonconservative forces, see our video about
conservative and nonconservative forces.

To check your understanding and work toward mastering these concepts, check out our exercise on calculating change in gravitational potential energy.

## Want to join the conversation?

- Does anyone know why the value of gravity in the exercises is sometimes used as positive 9.8 and others are -9.8? Isn't gravity's constant, always -9.8.(8 votes)
- we've learned that we must always use positive 9.81 while doing exercises but the change can normally occur while doing force changes as in the change of height h2 can be shorter than h1 and it leads to a negative gravity value(5 votes)

- How is the work done by the force independent when there has to be some type of force exerted on an object?(1 vote)
- Its a late reply, but I think I understand what you are asking. A conservative force (like gravity) only cares about the objects starting position and its ending position. So when they say its independent they mean that it does not rely on -how- you arrive at your final location.

Displacement is your final minus your initial. (X - Xo) for example. If Fgrav = mg, and W = F*d, then you can see that how you arrive at your location doesn't matter. If you start at 0 then go 30m east, then 20m west then 40m east, and finally 30m west. 30-20+40-30 = 20m So your displacement from 0 is 20m. (20-0) = (X - Xo).

Notice that if you plug this information into W = F*d, the path had no affect on the d value, and if you had just gone from 0 to 20m without going back and forth, you would arrive at the same Work done. Thus, conservative forces are independent of the path you take.(6 votes)

- When is g -9.8m/s^2, and when is it +?(1 vote)
- It depends on how we choose to define the positive and negative directions when working on a problem. We can arbitrarily say that g is positive or negative as long as we are consistent with our signs throughout the problem. Note that if a problem is given to you, it may already define which directions are positive and negative.(4 votes)

- I don't really understand the formula. How do you find the change in gravitational potential energy?(1 vote)
- You do final potential energy - initial potential energy. For example:

Lets say you had a ball with a mass of 1 kg that you move from ground level to 5 meters above the ground. What is the change in potential energy?

Well the change in potential energy would be equal to:

Final potential energy - initial potential energy

= gm(5 m) - gm (0 m)

= (9.8 m/s^2)(1 kg)(5 m)

= 49 Joules

This means that in the process of lifting the ball, the ball gained 49 J of gravitational potential energy. Hope this helps!(1 vote)

- Does anyone know why the value of gravity in the exercises is sometimes used as positive 9.8 and others are -9.8? Isn't gravity's constant, always -9.8.(0 votes)
- So I was confused about this too. The positive value of 9.81 m/s^2 is used to calculate the magnitude of the change.

The direction (upward or downward) is determined by the sign of the height difference (∆y).

Gravity itself is always positive in the context of acceleration due to gravity, but the change in potential energy can be positive or negative depending on the direction of movement.

Hope this helps!(1 vote)