Energy as a function of work

Kinetic and potential energy are a function of work. It is defined as the product of the force applied on a body and the displacement of the body caused by this force. Mathematically, it is expressed as:

W = F × d

where W represents work, F is force, and d is displacement. Work occurs when a force causes a body to move. In fact, work is done by the force acting on the body.

This image demonstrates the concept of work: it shows how work is the product of the force and the displacement of the body from the initial point A to the final point B.

It is interesting to note that if d is zero, then the work done is also zero. This means that when a force is applied but there is no displacement, no work is done, regardless of the force’s magnitude.

So, if you push a wall but cannot move it, even if you feel tired, you haven’t done any work—according to physics!

When Hercules stopped a moving boulder with his shoulder, did he do work? Yes, he did negative work. In this case, the direction of the force he applied was opposite to the direction of the boulder’s displacement, resulting in negative work.

Work is always measured in joules (J), which is a product of Newtons and meters.

Now, the question is, can a moving body do work? By virtue of its motion, the answer is yes. A moving body can do work because it can use its kinetic energy.

What is kinetic energy?

Energy is stored work. In other words, it is the energy within a body that can be used to perform work. So, when a body is moving, it possesses kinetic energy, which it can use to do work. Kinetic energy exists because of the motion of the body. As long as the body is moving, it has kinetic energy.

Kinetic Energy (KE) = 1/2 mv²

where KE represents kinetic energy, m is the mass of the object, and v is its velocity.

Hence, velocity is a measure of kinetic energy, or it contributes to kinetic energy. The work-energy theorem relates the concepts of kinetic energy to work. Work is done when the kinetic energy of a body changes. In other words, the difference between the initial and final kinetic energy equals the work done.

For example, when you push a rolling ball up a slope, it loses kinetic energy as its speed decreases and eventually reaches zero. During this process, the ball does work, and kinetic energy transforms into work done.

Can kinetic energy be negative?

From the equation above, we can see that kinetic energy depends on the mass of the body and the square of its velocity. Since mass can never be negative and is always finite, and the square of velocity is always positive, kinetic energy is always a positive quantity, regardless of the direction of motion. Therefore, kinetic energy depends on the speed of the body, not its velocity.

Is kinetic energy the only form of energy a body can possess? What about stationary bodies—can they not possess energy to do work? Of course, they can. Stationary bodies can possess various forms of energy, such as heat energy, chemical energy, or muscular energy.

What is potential energy?

In this discussion, we will focus on a type of energy known as potential energy, which is an umbrella term that includes all these other forms. Potential energy is stored in a body due to its position, often by virtue of its height. Among these forms, the one we will demonstrate is gravitational potential energy, which is especially important in understanding stored energy in a body.

Gravitational Potential Energy (PE) = m × g × h 

Where:

m is the mass of the object,

g is the acceleration due to gravity (typically 9.8 m/s² on Earth),

h is the height of the object above a reference point.

Can potential energy be negative?

A good example of negative potential energy is electrons orbiting around the nucleus and planets orbiting the Sun. Attractive forces, like gravity or electromagnetism, hold these toward a central point, requiring energy for them to escape their orbits. This binding energy is called negative potential energy.

Transformation of potential energy into kinetic energy

We have learned that kinetic energy is capable of doing work. So, kinetic energy can be used to achieve work. For example, when you push a moving ball to roll up a slope, it uses its speed to move upward and effectively does work. But what about a body raised to a height—can it also achieve work? Can it move up a slope using its speed or convert its gravitational potential energy into work?

While this isn’t directly possible, gravitational potential energy (or simply potential energy) first converts into kinetic energy, which can then be used to do work. How does potential energy convert into kinetic energy? When you release a ball from a certain height, it falls and gains speed. This increase in speed boosts its kinetic energy, allowing it to do work.

For example, a ball raised to a certain height can roll down a slope, then use the speed gained on the downward slope to climb an upward slope. In this way, potential energy can ultimately be used to achieve work.

The formula showing the conversion of potential energy to kinetic energy is as follows:

m × g × h = 1/2 × m × v²

where:

m is the mass of the object,

g is the acceleration due to gravity,

h is the height (initial potential energy),

v is the final velocity (related to the kinetic energy gained).

Thus, as potential energy converts into kinetic energy, it increases the speed of the body. This speed then enables it to do work, as demonstrated by the Kinetic-Potential energy model by Labkafe here.

Example of how potential energy affects kinetic energy

In the above model, the straight slope gives the ball a certain amount of potential energy, which converts into kinetic energy as the ball descends, giving it speed.

Conversely, on the curved slope, fascinating energy transformations take place (follow stages 1,2 and 3). In the first half, as the ball descends, it gains velocity due to the conversion of potential energy into kinetic energy. This speed enables the ball to climb the upward slope that follows.

Balls are released at the same instant from starting point.

Balls in motion along the two paths.

Ball following the curved path reaches the end point first.

However, when the ball begins its descent again, it no longer has an uphill slope to slow it down. Instead, it moves onto a downhill section, which allows it to gain even more speed. This added boost, combined with the increased height of the second slope, enables the ball on the curved path to reach the endpoint faster than the ball on the straight slope.

This scenario demonstrates how the transformation of potential energy into kinetic energy gives the ball on the curved slope an advantage. The curved slope allows the ball to maintain and build upon its speed, helping it reach the endpoint before the ball on the straight slope.

How does experimental demonstration help?

This apparatus from Labkafe demonstrates how visualizing kinetic and potential energy is essential to truly understand these core energy concepts. With this model, students gain a hands-on understanding, and teachers have an effective tool to explain the critical role of energy transformations.

Incorporate this demonstration kit into your curriculum to give students a clearer grasp of how work, kinetic energy, and potential energy interconnect. This is a must-have resource for secondary schools aiming to deepen students’ understanding of energy dynamics in a tangible way.

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