Mechanics 4

• Mechanics is the study of motion, work, and energy

Work and Energy - Learning Goals

• Concepts of Work and Energy are explored
• Conservation of Energy is examined
• Kinetic Energy is defined and analyzed
• Potential Energy is investigated
• Gravitational Potential Energy is studied
• Power is calculated
• Efficiency is described

ENERGY

• It is a relatively recent concept, dating back to the 1800s
• Understanding energy is vital for analyzing processes like:
  • Water falling over a dam powering lights
  • Biological processes
  • Life cycle of stars
• Energy analysis proves more useful than Newton's laws when motion becomes complicated
• Energy is an abstract concept, not a tangible substance
• Energy can take various forms, including being stored in food, a moving body, combustion (thermal energy), and electrical energy
• In any process, energy transforms from one form to another
• Energy is always conserved

WORK

• Work has a specific definition in physics, differing from the general concept of effort
• Work specifically involves force and displacement
• When a force acts on a body causing it to move in the direction of the force, the work done is calculated by W = Fd
• The unit of work is the joule (J), equivalent to a newton multiplied by a meter
• A man applies a force of 300 N to a car
• The car moves 10 meters in the same direction as the force
• The work done by the man on the car is 3000 J (300 N * 10 m)
• This calculation holds true regardless of friction or acceleration

More Generally

• Work applies when force and displacement are not in the same direction
• Work involves the component of force in the direction of displacement
• The formula to calculate work is: Work = F * cos(θ) * d, where θ is the angle between the force and displacement

KINETIC ENERGY

• The kinetic energy is work that an object can perform because of its motion
• Examples: a moving fridge can exert work on a man, and a moving bat can exert work on a ball
• Kinetic energy depends on mass and velocity
• Increase in kinetic energy of a body equals the work done by the force on the body
• If a mass m starts from rest and force F applied over a time t across a distance d until a final velocity v is achieved the formula is
• The average velocity calculated as
• The Work equates to
• Therefore: W = KE = 1/2 mv^2

Potential Energy

• An object stores energy because of its position, such as a ball next to a compressed spring
• Potential energy exists at the microscopic level, arising from the position of electric charges, including chemical and nuclear potential energy

Gravitational Potential Energy

• Work raises a ram against the Earth's gravity in a pile driver
• The work done by a force F on an object is W = Fd = Fh = mgh, so the gain in Potential Energy = mgh

Example

• A force of 500 N overcomes the friction forces on a medium size car traveling at 65 km/hr
• Power required = 9000 W = 9 kW

Efficiency

• A machine is never ideal
• Not all input work becomes work which will output
• As this energy can be used, it dissipates as heat
• Efficiency = (Work output) / (Work in)
• Block and tackle has 40% efficiency
• A man provides 180 J of work and outputs 72 J

Mechanical efficiency of human body

• Efficiency is Work output / Energy used
• Cycling at 370 W has ~20% efficiency
• Swimming on the surface has <2% efficiency
• Swimming underwater has ~4% efficiency
• Shoveling has ~3% efficiency
• A typical petrol engine has ~40% efficiency