Student Handout-AP Physics 1-Energy

#Physics

AP Physics 1: Energy Unit - Student Handout

Key Topics Covered

1. Work and Energy

Definition of work ( $W = F d \cos θ$ )
Work done by a constant force
Work-Kinetic Energy Theorem

Work and Energy Diagram

2. Kinetic Energy ( $K E$ )

Definition: $K E = \frac{1}{2} m v^{2}$
Relationship between work and kinetic energy

Kinetic Energy Graph

3. Potential Energy ( $P E$ )

Gravitational Potential Energy: $P E_{g} = m g h$
Elastic Potential Energy: $P E_{s} = \frac{1}{2} k x^{2}$

Potential Energy Diagram

4. Conservation of Energy

Law of Conservation of Mechanical Energy: $K E_{i} + P E_{i} = K E_{f} + P E_{f}$
Energy transformations in different systems

Energy Conservation Example

5. Power

Definition: $P = \frac{W}{t}$
Power in terms of force and velocity: $P = F v$

Power Formula

6. Work Done by Non-Conservative Forces

Effects of friction and air resistance
Energy dissipation and thermal energy

Friction Energy Loss

Essential Equations

$W = F d \cos θ$
$K E = \frac{1}{2} m v^{2}$
$P E_{g} = m g h$
$P E_{s} = \frac{1}{2} k x^{2}$
$K E_{i} + P E_{i} = K E_{f} + P E_{f}$
$P = \frac{W}{t}$
$P = F v$

Key Concepts & Applications

Energy Conservation: Understanding how energy is transferred and conserved in closed and open systems.
Work-Energy Theorem: Relating work done on an object to its change in kinetic energy.
Power: How quickly work is done or energy is transferred.
Real-World Applications: Roller coasters, pendulums, springs, and energy efficiency in machines.

Example Problems

1. Kinetic Energy Calculation

A 2 kg object moves at 5 m/s. What is its kinetic energy?
Solution:
$K E = \frac{1}{2} m v^{2} = \frac{1}{2} (2) (5)^{2} = 25 J$

2. Potential Energy Calculation

A 3 kg object is lifted to a height of 4 m. What is its gravitational potential energy?
Solution:
$P E_{g} = m g h = (3) (9.8) (4) = 117.6 J$

3. Energy Conservation

A 1 kg ball is dropped from a height of 10 m. Find its velocity just before it hits the ground.
Solution:
Using energy conservation:
$m g h = \frac{1}{2} m v^{2}$
$(1) (9.8) (10) = \frac{1}{2} (1) v^{2}$
$98 = \frac{1}{2} v^{2}$
$v = \sqrt{196} = 14$ m/s

Summary

Energy exists in different forms (kinetic, potential, thermal, etc.).
The total mechanical energy in a system is conserved unless external forces do work.
Work is the transfer of energy, and power is the rate at which work is done.
Understanding energy principles helps explain motion, forces, and real-world applications.