Work, Energy, and Power

Work, Energy & Power

Horsepower

  • Horsepower is mentioned, humorously contrasted with "cowpower."

Work

  • Work is defined as the distance moved multiplied by the component of the force in the same direction as displacement.

  • Formula: W = F \cdot d \cdot cos(\theta), where:

    • W is work.

    • F is the force.

    • d is the displacement.

    • \theta is the angle between the force and displacement vectors.

  • If a person carries a bag of groceries without lifting or lowering it, they are doing no work on the bag because the force they exert has no component in the direction of motion.

Work (Continued)

  • Work done by forces opposing motion (e.g., friction) is negative.

  • Centripetal forces do no work because they are perpendicular to the direction of motion.

Joule

  • The SI unit of work is the joule (J).

  • Named after James Prescott Joule (1818–1889).

Work & Energy

  • Mechanical energy is the ability to do work.

  • Two types of mechanical energy:

    • Kinetic energy (energy of movement).

    • Potential energy.

  • If an object is not moving, it has no kinetic energy.

Work & Energy (Kinetic Energy)

  • Work done equals the change in kinetic energy: W = \Delta KE

  • If net work is positive, kinetic energy increases.

  • If net work is negative, kinetic energy decreases.

Work & Energy (Kinetic Energy Example)

  • Kinetic energy of a 625-kg roller coaster car moving at 18.3 m/s:

    • KE = (0.5) (625 \text{ kg}) (18.3 \text{ m/s})^2

    • KE = 104653 \text{ J} = 1.05 \times 10^5 \text{ Joules}

Work & Energy (Units)

  • Work and kinetic energy have the same units: Joules.

  • 1 Joule = 1 Newton-meter (Nm).

Potential Energy

  • Potential energy is the potential to release energy and become kinetic energy.

  • Often related to object's height above the ground.

  • Formula: PE = mgh, where:

    • m is mass.

    • g is the acceleration due to gravity.

    • h is the height in the y-direction.

  • Potential energy can also be stored in springs.

Potential Energy (Springs)

  • Potential energy stored in a compressed spring can be converted to kinetic energy.

Problem Solving While Conserving Energy

  • Total mechanical energy is the sum of kinetic and potential energy.

  • Energy moves between potential and kinetic forms.

Law of Conservation of Energy

  • Energy cannot be created nor destroyed.

  • The sum of all energies in a system is constant.

  • If there's a non-conservative force like friction, kinetic and potential energies dissipate as heat (thermal energy).

  • Total energy is conserved, but not all usable for work.

Conservation of Energy in Collisions

  • Elastic Collision:

    • Kinetic energy is conserved.

    • Example: Newton’s Cradle.

  • Inelastic Collision:

    • Kinetic energy is not conserved.

    • Some KE lost to surroundings as heat.

    • Some KE converted to PE.

    • Example: Ballistic Pendulum.

Energy Types

  • Mechanical

  • Thermal

  • Electrical

  • Radiant (Light)

  • Chemical

Solving Work Problems

  1. Draw a free-body diagram.

  2. Apply Newton’s laws to determine unknown forces.

  3. Find the work done by a specific force.

  4. To find the net work, either find the net force and then the work it does, or find the work done by each force and add.

Mechanical Advantage

  • Work{in} = Work{out}

  • Mechanical advantage (MA) is the ratio of output force to input force.

  • MA = \frac{Force{out}}{Force{in}}

  • MA = \frac{Distance \, of \, which \, effort \, is \, applied}{Distance \, which \, load \, is \, moved}

Mechanical Advantage Example

  • Examples of force and distance for varying forces. In the slide: Forces of 100N, 50N, 33%N, and 25 N are applied over distances of 10 cm, 20cm, 30 cm, 40cm.

Mechanical Advantage (Pulley Example)

  • Kevin pulls a rope 4 m through a pulley system to raise a box 2 m.

  • What is the MA of the pulley system?

    • MA = \frac{D{applied}}{D{moved}} = \frac{4 \text{ m}}{2 \text{ m}} = 2\n

Mechanical Efficiency

  • Expressed as a percentage:

    • Efficiency = (\frac{Work{out}}{Work{in}}) \times 100

  • Never greater than 100%.

Power

  • Power is the rate at which work is done.

  • The difference between walking and running up stairs is power; the change in gravitational potential energy is the same.

  • SI unit of power is the watt (W).

Power Example

  • Will N. Andable lifts a 100-pound barbell 10 times in 1 minute.

  • Ben Pumpiniron (same height) lifts the same barbell 10 times in 10 seconds.

  • Both do the same amount of work.

  • Ben is more "powerful" because he does the same work in less time.

Summary of Energy and Work

  • Work: W = F \cdot d \cdot cos(\theta)

  • Kinetic energy is energy of motion: KE = \frac{1}{2}mv^2

  • Potential energy is energy associated with forces that depend on the position or configuration of objects: PE = mgh

  • The net work done on an object equals the change in its kinetic energy: W_{net} = \Delta KE

  • If only conservative forces are acting, mechanical energy is conserved.

  • Power is the rate at which work is done: P = \frac{W}{t}