Work and Power

Work

• Force causes displacement in direction of force
• W = Fd
• Unit is newton x meter = joule (J)
• If force is at angle to displacement must find component of force in that direction
• On graph of force vs. distance, work equals area under curve
• Work can be done against gravity, friction, spring, etc.

Machines<

• Six types of Simple Machines
  • Lever
  • Inclined plane
  • Pulley
  • Screw
  • Wedge
  • Wheel & axle
• Device to multiply force or change its direction
• Can't increase work
• Can increase output force by increasing input distance
• Also can increase output distance by increasing input force

Efficiency

• Work output divided by work input
• A measure of losses due to friction
• Often expressed as a percentage.

Power

• Rate of doing work
• P = W/t = F(d/t) = Fv
• Unit is watt (W) = J/s
• Often expressed as kilowatts (kW)
• English unit is horsepower (hp)
• 1hp = 746 W

Energy

• The ability to do work
• Two types of mechanical energy
• Potential energy
• Kinetic energy

Gravitational Potential Energy

• Stored energy due to position in gravitational field
• Equals work done to reach elevated position
• Must be referenced to some zero point
• E_P = mgh

Elastic Potential Energy

• Equals work done to stretch or compress spring or other elastic material
• Energy stored depends on stiffness of spring and distance stretched or compressed
• Spring constant, k (N/m) describes stiffness
• Force from spring: F = kd
• Energy stored or work done:
• E_P = W = ½Fd = ½kd²

Other types of Potential Energy

• Electrical and magnetic potential energy are due to position in electrical or magnetic field
• Chemical potential energy due to chemical composition of material

Kinetic Energy

• Energy due to motion
• E_K=½(mv²)
• Since velocity is squared, kinetic energy is always positive.
• To double speed, energy must be quadrupled
• Work done on object to change speed equals change in kinetic energy

Conservation of Energy

• In a closed system with no dissipative forces, total energy remains constant
• Energy can change forms but is not gained or lost.
• Dissipative forces cause energy loss as heat (friction)
• Conservative forces have no energy losses
• In a closed system, total energy remains constant
• Energy can change forms but can't be created or destroyed
• Potential energy converts to kinetic when object falls, converts back to potential if it rises again: roller coaster or pendulum
• Energy stored in spring can convert to kineitc energy if used to launch object: mousetrap car
• Work input to system increases total energy by amount of work done
• Work done by system decreases energy by amount of work done

Conservative Forces

• Work done by conservative forces does not depend on the path taken: gravitation
• For conservative forces, total work done on closed path is zero.
• Example: lifting object from floor to table involves same amount of work no matter what route is taken. When returned to floor, same amount of work can be extracted.

Dissipative Forces

• Total work around closed path is not zero.
• Work done depends on length of path
• Main dissipative force is friction
• Work done against friction = F_f d = energy lost to heat

Work in Rotary Motion

• Work done by torque:W = Tq = Frq
• where qis the angular displacement in radians, F is the force, and r is the torque arm of the force, usually the radius of the rotating body.
• Assumes force is perpendicular to radius

Power in Rotary Motion

• Power is rate of doing work
• Average power equals work done divided by elapsed time in this case the rotary work
• P = Tq/t but q/t = w, so P = Twwhere T equals the torque and w is the angular velocity

Kinetic Energy in Rotary Motion

• E_K= ½Iw²
• Rolling objects have both linear and rotational kinetic energy.
• When objects roll downhill, potential energy is converted to both linear and rotational kinetic energy
• The amount of each depends on rotational inertia of object.
• High rotational inertia means more energy bound up in making object roll, less left for linear speed.

Vocabulary

• elastic potential energy
• gravitational potential energy
• kinetic energy
• law of conservation of energy
• power

Summary

• Work = displacement times force in that direction; unit is joule
• Work = area under force vs. displacement graph
• Power is rate of doing work
• Machines help us do work by using less force over greater distance
• Efficiency = work out / work in
• Gravitational potential energy is due to elevated position and equals work done lifting object.
• Kinetic energy is due to motion
• Elastic potential energy depends on force constant and distance spring is stretched.
• Conservation of energy means sum of all types of energy in closed system is constant.