Engineering Expert Witness Blog

      Last time we saw how Henry Cavendish built upon the work of scientists before him to calculate Earth’s mass and its acceleration of gravity factor, as well as the universal gravitational constant.   These values, together with the force of gravity value, F_g, which we’ll introduce today, moved scientists one step further towards being able to discover the mass and gravity of any heavenly body in the universe.

      According to Newton’s Second Law of Motion, the force of gravity, F_g, acting upon any object is equal to the object’s mass, m, times the acceleration of gravity factor, g, or,

F_g = m × g

      So what is F_g?  It’s a force at play way up there, in the outer reaches of the galaxy, as well as back home.   It keeps the moon in orbit around the Earth and the Earth orbiting around the sun.   In the same way, F_g keeps us anchored to Earth, and if we were to calculate it, it would be calculated as the force of our body’s mass under the influence of Earth’s gravity.   It’s common to refer to this force as weight, but it’s not quite so simple.

      Using the metric system, the unit of measurement most often used for scientific analyses, weight is determined by multiplying our body’s mass in kilograms by the Earth’s acceleration of gravity factor of 9.8 meters per second per second, or 9.8 meters per second squared.

      For example, suppose your mass is 100 kilograms.   Your weight on Earth would be:

Weight = F_g = m × g = (100 kg) × (9.8 m/sec²) = 980 kg · m/sec² = 980 Newtons

     Newtons?   That’s right.   It’s easier than saying kilogram · meter per second per second.   It’s also a way to pay homage to the man himself.

      In the English system of measurement things are perhaps even more confusing.   Your weight is found by multiplying the mass of your body measured in slugs by the Earth’s acceleration of gravity factor of 32 feet per second per second.   Slugs is British English speak for pounds · second squared per foot.   We normally refer to weight in units of  pounds, and in engineering circles it’s pounds force.

      For example, suppose your mass is 6 slugs, or 6 pounds · second squared per foot.   Your weight on Earth would be:

Weight = F_g = m × g = (6 Lbs · sec²/ft) × (32.2 ft/sec²)= 193.2 Lbs

      To avoid any confusion, you could just step on the bathroom scale.

      Next time we’ll see how the force of gravity is influenced by an inverse proportionality phenomenon.

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