Mechanical Work

Sub Unit 2.1http://www.uhigh.ilstu.edu/tech/

PT/

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 UnitsEnglish foot • pounds (ft•lb)

SInewton • meters (N•m)

1 Newton meter (N•m) = 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 workinput 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 ft•lb or N•m (J= N•m). 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 = Wout / Win). 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.