Problem 11 - Chemistry: The Central Science

Question

In what two ways can an object possess energy? How do these two ways differ from one another?

Step-by-Step Solution

Answer

An object can possess energy in two ways: kinetic energy and potential energy. Kinetic energy is the energy of motion and is represented by the formula \(KE = \frac{1}{2}mv^2\), where \(m\) is the mass and \(v\) is the velocity of the object. Potential energy is the energy based on an object's position or state, such as gravitational potential energy represented by the formula \(PE_{grav} = mgh\), where \(m\) is the mass, \(g\) is gravity, and \(h\) is the height from a reference point. The main differences between them are that kinetic energy depends on motion while potential energy depends on position or state, and kinetic energy changes only when speed changes, while potential energy changes whenever position or state changes.

Step 1: Identify the two ways an object can possess energy

An object can possess energy in two ways: kinetic energy and potential energy.

Step 2: Define kinetic energy

Kinetic energy is the energy an object has due to its motion. It is represented by the formula: \[KE = \frac{1}{2}mv^2\], where \(KE\) is the kinetic energy, \(m\) is the object's mass, and \(v\) is its velocity. The faster the object moves or the more massive it is, the more kinetic energy it possesses.

Step 3: Define potential energy

Potential energy is the energy an object has due to its position in a force field (such as the gravitational force field on Earth). There are different forms of potential energy, such as gravitational potential energy, elastic potential energy, and chemical potential energy. For gravitational potential energy, it can be represented by the formula: \[PE_{grav} = mgh\], where \(PE_{grav}\) is the gravitational potential energy, \(m\) is the object's mass, \(g\) is the acceleration due to gravity, and \(h\) is the height of the object from a reference point. The higher the object is placed or the more massive it is, the more potential energy it possesses.

Step 4: Explain the differences between kinetic and potential energy

Kinetic and potential energy are different in several ways: 1. Kinetic energy is the energy of motion, while potential energy is the energy based on an object's position or state. 2. Kinetic energy depends on an object's mass and velocity, while potential energy depends on its mass and position (or height in the case of gravitational potential energy) or the state of the system (e.g. compression or tension for the elastic potential energy). 3. While an object's kinetic energy changes only when its speed changes, potential energy changes whenever its position or state changes. 4. Additionally, kinetic energy is a scalar quantity, while the potential energy is also scalar, but can be related to the vector force field, such as the gravitational force acting on the object.