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Conservative Forces: Examples & Effects

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  • 0:05 What Is a Conservative Force?
  • 1:27 Force Due to Gravity
  • 2:59 Elastic Spring Force
  • 4:33 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Learn how to tell if a force is conservative and what exactly is being conserved. Then look at a couple of specific examples of forces to see how they are conservative.

What Is a Conservative Force?

Every once in a while you'll hear the topic of conservation come up. You might be watching a movie where an injured person is told to conserve their energy, or you might hear on the news that people need to conserve water due to a drought. No matter how it comes up, the basic concept of conservation is that you are maintaining a supply of something instead of using it all up.

Conservation is also a concept that comes up in physics, such as with conservative forces. Despite the name, what's being conserved with conservative forces is energy. Here, force and energy are related through work. Work is a force multiplied by a displacement, and the result comes in the form of energy. Often, conserving this energy is accomplished by transferring potential energy to kinetic energy and vice versa within a system instead of giving off the energy in some other form.

We can tell whether or not a force is conservative by looking at something called path independence. A force is path independent and, therefore, conservative when the work done by the force does not depend on the route the object travels. Say we have a particle moving from point A to point B. In this image, we see a few examples of different paths a particle could take to move between the points. However, no matter which path is chosen, the work done by the force moving the particle will be the same as long as it is conservative. To help further understand path independence, we'll look at a couple examples of forces and show that they are path independent and therefore conservative.

Example Paths for Moving a Particle from Point A to Point B
path independence diagram

Force Due to Gravity

Force due to gravity is the attractive force between all objects with mass. On Earth, we feel this force as weight. This is one of the most common conservative forces we can look at. For this example, the work being done on an object is the force due to gravity multiplied by height. The work done turns out to be the change in potential energy, which can be written as follows.

Delta PE = m * g * (h{f} - h{i})

m = mass

g = acceleration due to gravity

h{f} = final height

h{i} = initial height

If we think of someone dropping a ball while standing still, this equation makes sense. The ball will drop straight down, so the change in height, (h{f} - h{i}), will be the exact distance it travels. Now, imagine a ball being dropped out of a moving car instead. It doesn't drop straight down. It now travels horizontally in the direction the car was moving while falling to the ground. The change in height is no longer necessarily the exact distance the ball travels since it's moving in two dimensions.

However, the equation for change in potential energy doesn't adjust to show the horizontal travel. The only distances given are still the final and initial heights. So for the work done by the force due to gravity, it doesn't matter what path the ball takes to travel from the initial height to the final height. This lets us see that force due to gravity is path independent and a conservative force.

(Left) Ball being Dropped Straight Down, (Right) Ball being Dropped from a Moving Car
ball dropped from car diagram

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