Énergie et travail d'une force

Energy is one of the most important and yet ambiguous concepts in physics; fortunately, the relationship between energy and work can aid in the understanding of many physics problems.

Energy – particularly mechanical energy – is often defined as the ability to do work, that is, to exert a net force on an object causing it to move a certain distance. Mechanical energy can come in the form of position-dependent energy, referred to as potential energy, and motion-dependent energy, called kinetic energy. While the potential and kinetic energy of an object can be converted to one another, the law of energy conservation dictates that the total energy of an isolated system remain constant.

This video will introduce the work-energy principle, discuss the concepts of kinetic and potential energies, and use the law of energy conservation to relate these energies in an experiment involving gliders sliding down a track.

While there are numerous types of energy, mechanical energy most clearly illustrates the idea that energy is the ability to do work. One such example is when a cannonball flies into a brick wall.

In this case, a body, the cannonball, does work on an object, the wall, by exerting a net force and causing the object to move a certain distance. Work is defined as the dot product of the applied force and the distance moved. This applied force must be in the direction of the displacement in order for work to be done, that is, only the component of force parallel to the displacement can do work.

Now, we can relate work to mechanical energy, which is made up of kinetic energy and potential energy. A body in motion from one location to another, such as the cannonball, has translational kinetic energy and the ability to do work.

Suppose we accelerate the cannonball from an initial velocity of vi to a final velocity of vf – a process governed by an equation from kinematics. This event requires a constant net force, driven by Newton’s second law, to be applied over a certain distance. By combining the two equations, and noting that translational kinetic energy is defined as ½mv2, it is clear that the work done on the cannonball, which is Fnet times D, is equal to the difference in the final and initial kinetic energies. This is the work-energy principle.

When it comes to potential energy, a boulder at the edge of a cliff has large gravitational potential energy. Upon release, it has the potential to do work on the ground. This potential work depends on the mass of the boulder, acceleration due to gravity, and height of the fall. And this work is equal to the potential energy before the fall, or Pi.

As per the law of conversation, energy can be converted during an event, but the total energy of the system must remain the same. Therefore, the sum of the initial potential and kinetic energies must equal the sum of the final energies. The boulder’s initial velocity and kinetic energy are zero while its final height and potential energy are also zero. Therefore, the initial gravitational potential energy is equal to the final translational kinetic energy. By using our previous equations, a number of relationships can be drawn between the velocity, height, mass and energy.

Now that you’ve learned the principle of work-energy and law of energy conservation, let’s see how these concepts can be applied to an experiment involving mechanical energy.

This experiment consists of a velocity sensor, an air track, a few identical aluminum blocks, a glider, a few weights that can be added to the glider, a scale, air supply and a ruler.

Place the glider on the scale and record its mass. Connect the air supply to the air track and turn it on Measure the height of one of the aluminum blocks and record it in the lab notebook. Place the aluminum block under the foot of the air track that lies closest to the air supply. This will be the lowest height configuration.

Place the glider at its initial position and release it from rest. Using the velocity sensor, record the glider velocity as it passes the final position on the track. Repeat this procedure five times and calculate average velocity.

Place an additional aluminum block under the air track raising the height configuration. Measure the difference between hi and hf as before and verify this is twice the height of an aluminum block. Repeat the set of velocity measurements for this height configuration.

Place a final aluminum block under the air track, assuming the height difference is now three times the block height and repeat velocity measurements. Next, place some weights to increase the glider’s mass, and then repeat the experiment to measure velocities at the three different heights.

Using the equations derived from the work-energy principle, the potential and kinetic energies for each run can be calculated being cognizant of the units for each of the variables. The potential energy differences for the various heights are listed in the PE column of the table. As expected, the potential energy of the system increases with increased height and heavier mass, indicating a greater potential to do work.

The values for the translational kinetic energy are also found in the table in the KE column. Similar to the potential energy, the kinetic energy is greater for the heavier glider and yet the final velocities of the heavier glider are the same as the lighter glider. This is clear from the equation relating the energies where the velocity is only a function of the height. Furthermore, the velocity increases at a rate proportional to the square root of the height as expected.

According to the law of energy conservation, the KE and PE columns in the table should be equal, and they nearly are. The discrepancies in the two sets of values come from errors in the measurements taken which are estimated to be around 10% for this type of experiment.

The applications involving the work-energy principle are ubiquitous and involve all different forms of energy.

Roller coasters are a perfect example of mechanical energy conversion. The massive coaster is initially pulled up to a large height in front of a steep incline. The substantial potential energy gained at the top of the incline is then converted to kinetic energy for the rest of the ride. During the ride the coaster experiences a constant exchange of potential and kinetic energy.

Chemical reactions also exhibit energy conversion with the energy typically being exchanged between chemical potential energy and thermal energy. If the reaction is exothermic, the potential energy is given off as heat to the environment, while the opposite is true for endothermic reactions. Some exothermic reactions can be explosive thereby generating kinetic energy which does work on its surroundings.

You’ve just watched JoVE’s introduction to Energy and Work by Force. You should now understand both the concept and importance of the work-energy principle and how the law of energy conservation can relate potential and kinetic energies. Thanks for watching!