Unit 3: Energy

Introduction

• Energy is an exciting unit with simple results explaining complex concepts.
• Allows manipulation of relationships with simple equations.
• Similar to forces in summarizing kinematics and connecting to the real world.

Section 5.1: Work

• Concept of Work in Physics:
  • Different from everyday use; in physics, work is force applied over a distance.
  • Formula: ( W = F \cdot \Delta D \cdot \cos(\theta) )
    • ( F ) is the force applied.
    • ( \Delta D ) is the displacement.
    • ( \theta ) is the angle between the force and displacement.
  • Unit: Joules (J).

Special Cases

• Theta Zero (( \theta = 0 )):
  • Force and displacement are in the same direction.
  • Simplified: ( W = F \cdot \Delta D ) as ( \cos(0) = 1 ).

Example Problems

• Example 1: Person pushing a shopping cart with 25 N force for 3.5 m:
  • ( W = 25 \cdot 3.5 = 88 ) Joules.
  • Special case: ( \theta = 0 ).
• Example 2: Curler accelerating a stone on frictionless ice:
  • Use ( \Delta D = \frac{V_i + V_f}{2} \cdot \Delta T ) to find displacement.
  • ( W = 15 \cdot 14 = 210 ) Joules (rounded).
  • ( \Delta D = 14 ) meters calculated from velocity and time.

Work with Force and Displacement in Different Directions

• Example: Custodian pulling a vacuum with a 50 N force at 30-degree angle:
  • ( W = 50 \cdot 3 \cdot \cos(30) = 130 ) Joules.

Special Cases with Zero Work

• Perpendicular Forces:
  • E.g., backpack force upward, movement horizontal (90-degree angle).
  • ( W = F \cdot \Delta D \cdot \cos(90) = 0 ) Joules.
• No Displacement:
  • E.g., student pushing car with 300 N force, but car doesn’t move.
  • ( \Delta D = 0 ) leads to ( W = 0 ) Joules.

Total Mechanical Work

• Example: Shopper pushing cart against friction:
  • Shopper's work: ( W_{shopper} = 41 \cdot 11 \cdot \cos(0) = 451 ) Joules.
  • Friction's work: ( W_{friction} = 35 \cdot 11 \cdot \cos(180) = -385 ) Joules.
  • Total work: ( W_{net} = 66 ) Joules.

Graphing Work Done

• Constant Force Graph:
  • Work is the area under the curve, ( W = F \cdot \Delta D ).
• Negative Work:
  • Work done against the movement direction results in negative work.
• Changing Force Graph:
  • Work is the area under the curve.
  • Can use average force for calculation: ( W = F_{average} \cdot \Delta D ).

Homework

• Apply the concepts learned in the lecture.
• Get comfortable with the idea of work as it will be used frequently.

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Enjoy the process of understanding and applying these fundamental concepts in physics!