Work, Power, and Machines

• Work, power, and machines are interrelated concepts

Work

• Work occurs when a force acts on an object, causing it to move in the direction of the force.
• Work requires a force acting on an object in the direction of movement.
• Work is calculated by multiplying the force applied by the distance the object moves: Work = Force x Distance or W = F x d.
• The unit of work is the Joule (J), which is equal to Newton * meters (N * m).
• No work is done, if there is no motion or if the force acts in the wrong direction.

Calculating Work examples

• Lifting a 1000N barbell 2m overhead requires 2000 J of work.
• Applying a force of 26.67 N to a 40 kg box to move it 15 m requires 400 J of work.
• A man who weighs 686N and does 3,340,000 J of work runs 4,869,971 m.

Power

• Power is the rate at which work is done.
• The formula for power is Power = Work / Time or P = W / t.
• The unit of power is Joules per second (J/s).

Calulating Power examples

• A horse that exerts 14,920 J of work in 20 seconds exerts 746 W of power.
• Lifting a box using 300 W of power in 1.5 seconds results in 450 J of work.
• Using 72 N of force to lift a box 1.0 m over 2.0 seconds requires 36 W of power.
• Applying 42 W of power to an object and completing 7 J of work means it took 0.167 seconds to move the object.

Machines

• A machine is a device that changes a force, making work easier.
• Machines cannot reduce the amount of work needed, but can change the force or distance required.
• If a machine applies a larger force, the distance decreases, and vice versa, work remains the same.

Input and Output

• Input force refers to the force exerted on the machine.
• Input distance is how far the input force acts.
• Input work refers to the work done by the input force over the input distance.
• Output force refers to the force exerted by the machine.
• Output distance is how far the output force acts.
• Output work refers to the work done by the output force over the output distance.

Mechanical Advantage

• Mechanical advantage compares the input force to the output force.
• Mechanical advantage indicates how effective and helpful the machine is.
• Mechanical advantage is either MA or IMA.

Simple Machines

• There are six simple machines:
  • Inclined Plane
  • Lever
  • Pulley
  • Wheel and Axle
  • Screw
  • Wedge

Inclined Plane

• An inclined plane is a slanted surface along which a force moves an object to a different elevation.
• It is also known as a ramp.
• IMA = distance along the plane / Δ in height

Lever

• A lever is a rigid bar that moves around a fixed point (fulcrum).
• Levers have two arms:
  • Input arm is where work is applied.
  • Output arm is where the work is done.
• IMA = length of input arm / length of output arm
• There are 3 Classes of Levers:
  • First-Class Lever: the fulcrum is in the middle (e.g. see-saw).
  • Second-Class Lever: the load is in the middle (e.g. wheelbarrow).
  • Third-Class Lever: the effort is in the middle (e.g. broom).

Pulley

• A pulley is a wheel with a groove for a rope.
• Pulleys can change the size, direction, or both of the input force.
• IMA = the number of ropes supporting the load.
• There are different pulley types:
  • Fixed pulley: the wheel is attached to a fixed location.
  • Movable pulley: attached to the load.
  • Pulley system: combines fixed and movable pulleys, creating a large mechanical advantage.

Wheel and Axle

• A wheel and axle are two disks or cylinders with different radii.
• One disk or cylinder has a larger diameter than the other.
• IMA = radius of the input "wheel" / radius of the output "axle".

Screw

• A screw is a cylinder with an inclined plane wrapped around it.
• The closer the threads, the greater the mechanical advantage.

Wedge

• A wedge is two inclined planes back to back.
• It is a V-shaped object with two inclined planes sloped toward each other.
• The thinner the wedge, the greater the mechanical advantage.

Compound Machines

• Compound machines are a combination of two or more simple machines that operate together.