Question

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

Short answer

An object can possess energy in two ways: kinetic energy and potential energy. Kinetic energy is the energy of motion, given by the formula $KE=\frac{1}{2}m{v}^2$, and depends on the object's mass and velocity. Potential energy is the stored energy due to the object's position in a force field, such as gravitational (formula $U_g=mgh$) or elastic (formula $U_e=\frac{1}{2}k{x}^2$). The main difference between kinetic and potential energy is that kinetic energy is related to motion, while potential energy is related to an object's position or configuration within a force field.

Step-by-step solution

1. Define Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It depends on the object's mass and velocity. The formula for calculating kinetic energy is given by: $$KE=\frac{1}{2}m{v}^2$$ where $KE$ is the kinetic energy, $m$ is the mass of the object, and $v$ is its velocity.

2. Define Potential Energy

Potential energy is the stored energy an object has because of its position in a force field, typically a gravitational or elastic force field. It depends on the object's mass, height, and the force acting on it. Two common types of potential energy are gravitational potential energy and elastic potential energy. The formula for gravitational potential energy is: $$U_g=mgh$$ where $U_g$ is the gravitational potential energy, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height of the object above a reference point. The formula for elastic potential energy, when dealing with a spring, is: $$U_e=\frac{1}{2}k{x}^2$$ where $U_e$ is the elastic potential energy, $k$ is the spring constant, and $x$ is the deformation of the spring from its equilibrium position.

3. Comparing Kinetic and Potential Energy

Kinetic and potential energy differ in several ways: 1. Kinetic energy is related to the motion of an object, whereas potential energy is related to an object's position or configuration within a force field. 2. Kinetic energy depends on an object's mass and velocity, while potential energy depends on factors such as mass, height, and the force acting on it (gravitational or elastic). 3. Kinetic energy represents energy in action, while potential energy represents stored energy that has the potential to be converted into other forms, including kinetic energy. 4. The main type of potential energy discussed in the context of everyday objects is gravitational potential energy, while kinetic energy applies to any object in motion, regardless of the forces involved.

Example

Consider a ball at the top of a hill. The ball has potential energy due to its height above the ground and the force of gravity acting on it. If the ball rolls down the hill and gains speed, it loses potential energy and gains kinetic energy. At the top of the hill, the ball has only potential energy, and at the bottom, it has only kinetic energy (ignoring air resistance). During its descent, the ball possesses a mixture of both potential and kinetic energy.