Basic Thermodynamics ~ J. Pohl © www.THERMOspokenhere.com () -  ()

Equator pseudo-Force

Mass, scale and scale reading
at the North Pole.
A large stone (possibly a meteorite) was found near the North Pole. At that location a beam balance (in conjunction with a set of standard masses) was used to determine its mass precisely: 1000 kiligrams. In addition, a linear spring scale was constucted. Figure North Pole shows the mass supported by the spring scale.

The stone was sold then shipped with the spring balance to its destination, Bonjol, Sumatra. The seller, having travelled with the stone, stepped onto the dock to meet the buyer. The scale had been erected and the stone place on it Figure Equator.



Mass, scale and scale reading
at the Equator.
that uses the extension of a mechanical spring to determine mass. Let the scale be calibrated at the North Pole.

Suppose Spring-Type scale we have a certified mass of 1,000 pounds. Demonstrate analytically that by measurement of a spring scale, the mass will weigh 1,000 pounds force at the North Pole but only 996 pounds force at the equator?

♦  Newton's Second Law will be applied. In each case the system is the thousand pound mass. The forces acting will be gravity and the support force (of the spring) of a scale. Our inertial reference has the center of Earth as the origin. This means we assume the center of Earth to move in a straight line at a constant speed. The vector triad, er(t), eθ(t) and K will be used. Imagine the mass to rest on a spring scale at the North Pole and later at the Equator.

Sketches depicting the two measurements of weight are combined in one drawing below:

A475_img1.png

Calculation: Scale Reading at the North Pole:  Newton's Second Law will tell us that number. The sketch (above center) shows the mass (on a scale position vector (center sketch) of the mass initiates at the center of Earth and extends the Earth radius, r, then a short distance further to arrive at bottom of the mass on the scale. Physically the mass contact with the scale as it (and the scale), rotate or pivot at that point on the Earth axis.

A super-precise answer is not needed; assume the radius of Earth as 3960 miles and the surface acceleration of gravity there to be 32.2 ft/s2. For this application, the forces of Newton's Second Law are gravity (at the Pole) and the supporting spring force of the scale. The equation is written as:

Polar Versus Equatorial Weight

Suppose we have a certified mass of 1,000 pounds. Demonstrate analytically that the mass will weigh 1,000 pounds force at the North Pole but only 996 pounds force at the equator?