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  • Whether you are a student who wants to be fitter, a netballer who wants a faster more powerful throw, a sprinter who wants to win that race or a weightlifter who wants to lift heavier weights, you are trying to make your muscles work better.

    There are three major factors that affect how well your muscles perform – strength, power and endurance.


    Muscle strength is also a result of the combination of three factors:

    • Physiological strength, which depends on factors such as muscle size, the cross-sectional area of the muscle and responses to training.
    • Neurological strength, which looks at how weak or how strong the signal is that tells the muscle to contract.
    • Mechanical strength, which refers to a muscle’s pulling force and the way those forces can be changed using bones and joints as levers.

    When we talk about the strength or muscles, we are describing the maximum force a muscle can exert. Muscle strength is directly dependant upon the size of the cross-sectional area of muscle, so if after a period of training, you increase your muscle size by 50%, you will also increase the force the muscle can develop by 50%.

    For every 1 square centimetre of cross sectional area, muscle fibres can exert a maximum force of approximately 30–40 newtons (the weight of a 3–4 kg mass).

    Example: Emily can lift 21 kg (210 newtons force) using muscles that have a cross-sectional area of 6 cm2. Use this formula to work out how many newtons per square centimetre her muscles can pull with:

    \frac{\textup{force}}{\textup{area}} = \frac{210}{6}

    \; \; \; \; \; \; \; = 35 \; \textup{N}/\textup{cm}^{2}

    Emily’s friend Alisha has larger muscles that have a cross-sectional area of 8 cm2. Use this formula to work out what weight Alisha should be able to lift if her muscle tissue is similar to Emily’s:

    \textup{force}= \frac{\textup{force}}{\textup{area}} \times \textup{area}

    \; \; \; \; \; \; \; = 35 \times 8

    = 280\; \textup{N}\; (28\; \textup{kg} \; \textup{mass})


    When muscles contract or stretch in moving a load they do work, and energy is transferred from one form to another. The power of muscles refers to how quickly the muscles can do this work and transfer the energy.

    Example: A weightlifter lifts 100 kg up a distance of 1.5 m. 100 kg has a weight force of 1000 newtons. Use this formula to calculate the work done (energy transferred) by the weightlifter:

    \textup{work} = \textup{force}\;\times\;\textup{distance\;moved\;by\;the\;force}

    = 1000\; \textup{N}\; \times \; 1.5\; \textup{m}

    \; \; \; \; \; \; \; = 1500 \; \textup{joules\;of\;energy}

    If the weightlifter lifts the 100 kg explosively and takes only 0.5 seconds to make the lift, use this formula to calculate the power their muscles produce:

    \textup{power } = \frac{\textup{work}}{\textup{time}}

    \textup{power } = \frac{\textup{1500\; J}}{\textup{0.5 s}}

    = \textup{3000 joules of energy per second}

    = \textup{3000 watts of power (3000\;W)}

    Where does the energy come from and where does it go?

    The energy for muscle contraction comes from glucose transported by the blood and deposited in muscle tissues. In the weightlifter example, the energy has been transformed to gravitational potential energy. Also, heat energy will be generated in the muscle tissues themselves. This means that the muscles will have transferred even more energy than the amount calculated above.

    Putting the relationships together

    There are three different equations that can be simplified to make an even more useful equation:

    \textup{power} = \frac{\textup{change\; in\; energy}}{\textup{time}}

    \textup{power} = \frac{\textup{work\; done}}{\textup{time}}

    = \frac{\textup{force}\; \times \; \textup{distance}}{\textup{time}}


    \textup{velocity} = \frac{\textup{distance}}{\textup{time}}

    the formula can be rewritten: power = force × velocity

    Sports scientists use this formula to measure the power profiles of particular sets of muscles by measuring both the force of the muscles and the speed with which they are contracting or lengthening. They have found that the greatest power is produced when the load is much less than the maximum load on the muscles.


    Muscle endurance refers to how well the muscles can exert and hold maximum force over and over and over again.

    Activity idea

    Measuring grip strength gathers and examines data about wrist strength at different angles.

    Measuring the power output of elite athletes analyses bench press force, velocity and load data.

      Published 21 June 2007 Referencing Hub articles
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