Unit 3.3: Potential Energy

Introduction

Potential energy is the stored energy in an object due to its position, configuration, or state. In this section, we focus on gravitational potential energy and elastic potential energy. Understanding potential energy is crucial for solving energy conservation problems in AP Physics.

Key Concepts

Gravitational Potential Energy (U_g): Energy stored by an object due to its height in a gravitational field.
It is given by: U_g = mgh, where m is mass, g is acceleration due to gravity, and h is height.
Elastic Potential Energy (U_s): Energy stored in a spring or elastic object when it is compressed or stretched.
It is given by: U_s = (1/2) k x², where k is the spring constant and x is the displacement from equilibrium.
Conservation of Energy: In an isolated system, the total energy (kinetic + potential) remains constant.

Tip: Always check that your units are consistent when calculating potential energy. For gravitational potential energy, ensure that mass is in kilograms, height in meters, and g in m/s².

Graphical Representations

Potential energy can be visualized with graphs:

A height vs. gravitational potential energy graph is linear if g is constant.
A force vs. displacement graph for a spring is linear, with the area under the curve representing the elastic potential energy.

Exam Strategy: When presented with a graph, look for the area under the curve or the slope to determine the energy stored.

Mathematical Routines

Solving potential energy problems typically involves:

Using U_g = mgh to calculate gravitational potential energy.
Using U_s = (1/2) k x² to calculate elastic potential energy.
Applying the conservation of energy principle to relate potential energy and kinetic energy.

Important: In conservation of energy problems, potential energy lost or gained is converted to kinetic energy or work done against friction.

Practice Activities

Activity 1: Gravitational Potential Energy

A 5 kg object is raised to a height of 10 m. Calculate its gravitational potential energy.

Activity 2: Elastic Potential Energy

A spring with a constant of 150 N/m is compressed by 0.2 m. Calculate the elastic potential energy stored in the spring.

Activity 3: Energy Conservation

A 2 kg ball is dropped from a height of 5 m. Assuming no air resistance, determine the ball’s kinetic energy just before it hits the ground.

Summary & Exam Preparation Tips

Potential energy is the stored energy of position or configuration. Key takeaways include:

Gravitational potential energy is calculated with U_g = mgh.
Elastic potential energy is calculated with U_s = (1/2) k x².
The principle of conservation of energy connects potential energy with kinetic energy.
Graphical representations, such as force vs. displacement graphs, help visualize energy relationships.

Regular practice with these equations and problem-solving techniques is essential for mastering energy concepts on the AP Physics exam.