Description
Part 4: Conservation of Energy
So far in the course project, we applied what we have learned about forces to calculate quantities of motion. Motion is a change of position. Velocity and acceleration are used to describe motion. An analysis of motion helps introduce the real nature of physics—to understand the nature and behavior of the physical world. We will now use what we have learned about motion to demonstrate the transformation of energy. We have observed things that change but it is useful to consider things that do not change like the energy of a system. By keeping track of energy, as it is transformed from one kind to another, we can learn a great deal about the universe.
The total mechanical energyEof a system is defined as the sum of the kinetic energyKand potential energyU. In the absence of non-conservative forces, such as friction or air drag, the total mechanical energy remains constant and we say that mechanical energy is conserved.
Gravitational potential energy is the energy of an object due to its relative position in a gravitational field. If we define the lowest point, or reference point, to have zero potential energy, the gravitational potential energy of an object a distance ‘y’ above the reference can be written as follows where ‘m’ is the mass of the object in kg, ‘g’ is the acceleration due to gravity (9.8 m/s2), and ‘y’ is the height above the reference in meters. When the object reaches the lowest point y=0, the final gravitational potential energy is zero.
Kinetic energy is the energy of motion. For a projectile dropped from rest, the initial kinetic energy is zero. Once the object is released, it accelerates downward and the kinetic energy increases. Energy is transformed from gravitational potential energy into kinetic energy. Kinetic energy can be expressed mathematically as:
where ‘v’ is the speed of the object in m/s and ‘m’ is the mass in kg.
By conservation of energy, the initial energy of an object in freefall is equal to the final energy. Since (dropped from rest) and (at the reference point) the conservation of energy equation reduces to or
From the equation above, we can solve for the final velocity as
This equation can be used to validate the experimental data.
Objectives
- To represent the motion of an object through graphs of position and velocity versus time
- To observe the changes in potential energy, kinetic energy, and total mechanical energy of a freely-falling body
- To determine both theoretically and experimentally whether the total mechanical energy of a freely-falling body remains constant
Deliverables
- Complete the Course Project PowerPoint Deliverable
- Include a screenshot of your table and graph in Excel for one trial
- Conduct analysis of collected data
- Calculate theoretical values to validate experimental data
- Answer questions to draw valid conclusions from data
