Mechanical Work Sub Unit 2.1

TEKS 7 Objectives Define work done by a force or torque in a mechanical system. Explain the relationship between work, force applied, and the distance an object moves. Solve work problems, given force and distance information in English and SI units. Explain how efficiency relates to input work and output work for a mechanical system. Define radian measure of angles. Explain the relationship between work, torque applied, and the angle (in radians) through which and object moves. Solve work problems, given torque and angle information in English and SI units.

Work Linear When a force moves something a distance (like a pushing a car, moving a desk, lifting weights, etc.) Rotational When a torque causes rotational movement (like gears, pulleys, wheels, etc.)

Work done by a force Work (W) = Force (F) x Distance (d) Force Units English SI pounds newtons Distance Units English SI feet meters x = Work Units English foot pounds (ftlb) SI newton meters (Nm) 1 Newton meter (Nm) = 1 Joule (J)

Work Uses magnitude of force and displacement (both are vectors) Can be positive (if both force and displacement are in same direction) Can be negative (if force and displacement are in opposite direction)

Change in Potential / Kinetic Energy? Work equals change in energy Like when the barbell gains gravitational potential energy due to the work done to lift it. Or when braking, the kinetic energy of vehicle decreases due to the work done by the brakes.

Efficiency Machines convert work input to useful work output. Theoretically, “work in” equals “work out.” Realistically, “work in” is always greater than “work out.” Why? – Losses Efficiency output work input work = To get percentage, multiply by 100%

“Rotational Work” Work done by a torque Work (W) = torque (  ) x angle moved (  )  = F x l “  ” must be in radians  = Arc length r 1 rev = 360º = 2  rad

Summary Mechanical systems use force and torque to cause desired movement and do useful work. Work is done when a force or torque moves an object. Work is done only while the force or torque is applied in the direction of movement. Work equals force times displacement or torque times angle. Work is measured in ftlb or Nm (J= Nm). W=Fd; W=  The displacement used to calculate work is the distance the object moves while the force is applied. Efficiency describes how well a machine performs work. Efficiency is the ratio of output work to input work (Eff = W out / W in ). Actual efficiency always < 100% due to losses such as friction, air/water resistance, heating/cooling, etc. Angles can be measured in either radians or degrees. The radian is a dimensionless unit and is used in most calculations involving angles.