Download 17.7 Measuring mechanical energy and power

17.7 MEASURING MECHANICAL ENERGY AND POWER
Before you continue, review Modules 14.1 to 14.4 and 16.2 which provide information about
energy. Energy is defined by scientists as the capacity to do ‘work’. Anything that does work can
be called a machine and a machine either transfers energy from one place to another, or
converts energy from one form to another (for example, from mechanical energy to electrical or
heat energy). In this module we will focus on mechanical energy.
Mechanical energy is the energy associated with the
position or movement of anything that has mass. The
mechanical energy transferred doing a job, depends on both
the force used and the distance moved by the force. Energy
is measured in SI units called joules (J), after the English
physicist James Prescott Joule (1818 – 1889) who studied
mechanical energy and heat. A joule is the energy transferred
when a force of 1 newton (N) moves a distance of 1 metre (m):
energy transferred (J) = force (N) × distance moved (m)
A medium sized tomato weighs about 100 g and gravity pulls
down on that with a force about 1N. 1J is therefore the energy
required to lift a tomato, against the force of gravity, a vertical
distance of 1 metre. For most purposes, the joule is rather a
small unit so we often measure energy in kilojoules (kJ); 1
kilojoule = 1000 joules. The Russian weight-lifter on the right
has lifted about 150 kg to a height of about 2 m. We can use
the equation above to calculate how much energy he has
transferred from his muscles to the bar. The force needed to lift
150 kg is 1500 N and the distance moved is 2 m, so:
energy transferred = 1500 × 2 = 3000 J (or 3 kJ).
Kinetic energy is the energy associated with
any moving mass. This energy is transferred to
the mass when a force accelerates it from rest to
its present velocity. When the mass is slowed
down or stopped, for example if it hits something, some or all of its kinetic energy will be
transferred to other masses or converted into
other forms of energy such as heat and sound.
The kinetic energy Ek joules, of an object with
mass m kg travelling at a velocity of v metres
per second, is given by the formula:
Potential energy is the stored energy that an
object may have because of its position, usually
its height above the ground (see Module 14.2).
Because of gravity, energy is transferred to any
mass when it is lifted above the ground. If the
object falls, its potential energy will be converted
into kinetic energy as it accelerates downwards.
The potential energy Ep joules, of an object with
a mass of m kg, at a height of h metres, where
the acceleration due to gravity is g m/s2, is given
by the formula:
Ek = ½ mv2
Ep = mgh
Power is energy delivered fast! When we say that an electric saw is more powerful than a hand saw
we mean that it cuts wood faster. A powerful car will climb a hill faster than
a less powerful one. Scientists define power as the amount of energy
transferred or converted in a given time. Power is measured in SI units
called watts (W) after Scottish engineer James Watt (1736 – 1819) who
developed the first efficient steam engine. A watt is the power delivered
when 1 joule of energy is transferred or converted in one second:
power (W) = energy (J) ÷ time (s)
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1. What are energy and power? How are they calculated and what are their SI units?

2. An athlete with a mass of 48 kg runs up a long flight of steps in 15 seconds. The top
of the steps is 16 m above the ground. (i) What is the main energy conversion involved
in climbing the stairs? (ii) How much energy is converted? (iii) What is the potential
energy of the athlete at the top of the steps? (iv) What is the power of the athlete?
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