Mechanical Work

1
Mechanical Work

• Sub Unit 2.1

2
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.

3
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.)

4
Work done by a force

• Work (W) Force (F) x Distance (d)

Work UnitsEnglish foot
pounds (ftlb) SInewton meters (Nm)
Force Units English SI
pounds newtons
Distance Units English SI
feet meters

x
1 Newton meter (Nm) 1 Joule (J)
5
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)

6
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.

7
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

To get percentage, multiply by 100
8
Rotational Work

• Work done by a torque

? must be in radians
Work (W) torque (?) x angle moved (?)
? F x l
1 rev 360º 2? rad
9
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). WFd 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 ration of output work to
  input work (Eff Wout / Win)
• Angles can be measured in either radians or
  degrees. The radian is a dimensionless unit and
  is used in most calculations involving angles.