Useful Energy/Work Output: the energy or work
that a machine does in performing a task
◦ useful energy or work is less than the total energy or
work since some energy is always lost as heat according
to the laws of thermodynamics
Efficiency: a measurement of how effectively a
machine converts energy/work input into useful
energy/work output; may be expressed as a ratio
(or fraction), or as a percent
To calculate efficiency, as a percent:
percent efficiency =
usefulworkoutputW × 100
totalworkinputW This is a general formula that can be used to
calculate the percent efficiency for any work or
energy conversion.
Example Problem B3.1:
A crane lifts a load of construction materials from the ground to
the second floor of a building. In the process, the crane does 2.30
× 104 J of work or mechanical energy input, while doing 8.00 × 103
J of useful work or mechanical energy output in lifting the load.
What is the mechanical percent efficiency of the crane?
WO × 100
WI
Formula:
PE =
Substitute:
8.00103 J
PE =
× 100
4
2.3010 J
Calculate:
Units/Sig Digs
PE = 34.7826%
= 34.8%
Statement:
The crane is 34.8% efficient.
Example Problem B3.2:
An internal combustion engine with an efficiency of 15.0% is
used to do 3.20 × 104 J of useful work, or mechanical energy
output. Calculate the mechanical energy input that had to
be supplied by the combustion of fuel in the engine.
Formula:
PE =
EOenergyout
EIenergyin
× 100
EO
× 100
EI =
PE
3.20104 J
EI =
× 100
15.0
Substitute:
Substitute:
Calculate:
Calculate:
Units/Sig Digs:
EI = 213 333.3 J
= 2.13 105 J
Statement:
The mechanical energy input was 2.13 105 J.
Read pages 215 – 217 & 220.
Complete Practice Problems #1
# – 3 on pages
216 – 217.
Complete Check and Reflect questions #1, 3,
5, 7, 8, 9 on page 220.