Conservation of Energy, Kinetic Energy, and Potential Energy | MCAT Physics Prep

Need help preparing for the MCAT physics section? MedSchoolCoach expert, Ken Tao, will teach you what you need to know about Conservation of Energy, Kinetic Energy and Potential Energy. Watch this video to learn how to do well on the physics section of the MCAT exam!

The principle of conservation of energy states that energy cannot be created or destroyed. The first equation bellows tells us that in our universe, the total energy at any initial point in time is equal to the total energy at any later point in time. No energy could have been created or destroyed between those two points in time.

If you take a narrow view, you might think up situations where energy in a system seems to decrease. For example, a rolling car will eventually slow to a stop, seemingly losing energy. However, the net energy of the universe remains unchanged. This is because the system we were considering – a car – lost energy to its surroundings. For example, the friction force on the car’s tires produced heat that emanated into its surroundings. The car lost energy, but its surroundings gained an equivalent amount of energy, and so the net change in universal energy was zero. This is expressed by the equation below – note that if there was a positive change in energy in either a system or its surroundings, the other must have had an equal but negative change in energy in order to abide by the conservation of energy.

Types of Energies – Kinetic energy and Potential Energy

While the total energy of the universe cannot change, individual types of energy may increase or decrease. For instance, kinetic energy is the energy due to the motion of an object. There are various kinds of kinetic energy – rotational energy, for instance, is the kinetic energy of an object in rotation. On the other hand, translational energy is the kinetic energy of an object moving through space, which is our primary focus on the MCAT. In the equation for translational kinetic motion, below, m is the mass of an object moving through space and v is its velocity. As with other types of energy, the units of kinetic energy are joules, denoted with a capital J.

Potential energy is the energy stored in an object. Similar to kinetic energy, there's several types of potential energy. For instance, there are gravitational, elastic, and chemical potential energies. For simplicity, we will consider gravitational potential energy, which has the equation , where m is the mass of an object, g is the gravitational constant of an object on earth, and h is the height of an object above the surface of the earth.

Example

Let’s consider the change in potential and kinetic energy of an object undergoing projectile motion. Consider a 5 kg projectile fired with an initial velocity of 20 m/s at an angle of 45o off of a 25 m cliff. What is the speed of the projectile before hitting the ground?

The speed of a projectile is directly tied to its kinetic energy. The problem is asking us to find the final kinetic energy of the projectile, right before it hits the ground. Because the projectile is essentially touching the ground at the end of its motion, we can say that the projectile has zero potential energy right before touching its ground, and so all of the energy in the system will be in the form of kinetic energy. We can manipulate the conservation of energy equation to reflect the fact that all of the initial energy in the system (the initial kinetic and potential energy) will be converted into kinetic energy, with no loss of total energy.

We can determine the initial kinetic and potential energy of the projectile by substituting in the values given in the question stem. The initial kinetic energy can be found by plugging in the projectiles mass and velocity, while its potential energy can be found by plugging in its mass and height above the ground at launch. Before plugging in these values, we should note that every term for kinetic and potential energy features the objects mass. We can and should simplify the equation by eliminating the mass term on both sides of the equation. After doing so, we can substitute in our values and rearrange the equation to solve for vfinal.

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[victoria_zzz]

This is awesome!
How do you know when to apply this energy approach to solve problems and when to apply the kinematic formulas in order to save time? I understood you can do it either way, but I would like to spend little time solving problems. Thank you!

[muznahmirza]

i used vsin(theta) for velocity because I thought u just need to consider the y component and got the same answer. Im not sure why though or if that would make a difference?