2025.03.06prelim

Work and Energy

• Work Calculation: [ W = F \cdot d ]

  • Units: N × m ≡ J (Joule)

  • Example: Pushing a cart with F = 100 N over 5.00 m results in work done.

• James Joule's Contribution:

  • Proved that the same amount of work results in the same amount of heat.

Work and Direction

1. Only the component of force in the direction of displacement contributes to work done.

2. If there is no displacement, no work is done.

Units for Acceleration and Weight

• Units for g:A. mB. NC. m/sD. m/s²E. kg/m/s

• Units for Weight:A. mB. NC. m/sD. m/s²E. kg/m/s

• Newton Definition:A. m/sB. m/s²C. kgD. kg/m/sE. kg/m/s²

Practical Application of Work

• A box weighing 2.0 N lifted 1.0 m requires:

  • Work: [ W = F \cdot d = 2.0 ext{N} \cdot 1.0 ext{m} = 2.0 J ] - Correct option: C.

Horizontal Movement

• Pushing a box with a weight of 2.0 N sideways on a frictionless surface also results in work:

  • Needed energy (work) is 0.0 J since displacement is not vertical.

• If friction of F = 20.0 N acts against a cart that performs 100 J of work:

  • Distance it could pull = 100 J / 20.0 N = 5.00 m (Correct option: D)

Understanding Work Through Examples

• For a 210 N weight held at 1.0 m, the work done is 0 J since there is no displacement.

• Comparative Work Example:

  • A. 400 N to drag a 75 kg log 5.0 m on dirt

  • B. 400 N to pull a 1200 kg cart on concrete

  • Compare: Both scenarios require the same amount of work, if friction is negligible.

Work Equation and Power

• General Form: [ W \equiv F \cdot d \cdot \cos(\theta) ]

  • Where ( \theta ) is the angle between force and displacement.

  • Special Cases: ( \cos(0º) = 1 ) means complete work is done when force is in the same direction as displacement.

Introduction to Power

• Power is the rate of work or energy use: [ P \equiv \frac{W}{t} ] or [ P \equiv \frac{E}{t} ]

• Power Units:

  • [ P = \frac{W}{t} = \text{Joules}/ ext{second} = Watts ]

  • 1 hp = 746 W

Energy vs Power

• Power and energy are distinct:

  • Power = Rate of energy use

  • Energy Units: Joules (J)

  • Power Units: Watts (W) = J/s

Key Concepts in Energy

• Mechanical Energy Types:

  • Linear kinetic energy, gravitational potential energy, spring potential energy, rotational kinetic energy

  • Not thermal energy or chemical potential energy

Conservation of Energy

• Newton's Third Law of Motion applies:

  • [ Work_{action} = - Work_{reaction} ]

• Energy types can change forms but cannot be created or destroyed.

Kinetic Energy Principles

• If no friction, kinetic energy formula: [ E_k = \frac{1}{2} mv^2 ]

• Kinetic energy is influenced by mass and velocity:

  • If you double velocity, kinetic energy quadruples.

Examples of Kinetic Energy Calculations

• A 1.0 kg mass at 1.0 m/s: Calculate its kinetic energy.

• A watermelon with 4500 J of kinetic energy, find its speed.

• Energy conversion can reveal mass: if 1000 J of heat is released from sliding to stop, find mass if it started at 65 m/s.

Gravitational Potential Energy

• Gravitational force work equation: [ W = F imes d ]

• Potential energy equation: [ E_p = mgh ]

• When measuring height, reference point matters.

Example Scenarios

• Determine potential energy of a 1.0 kg object at 1.0 m.

• Analyze a dropped bowling ball or sliding gourd to compare initial motion and final velocity using energy principles.

Conservation of Energy in Vertical Motion

• Energy maintains constant in certain conditions throughout height shift and free-fall scenarios.