0.14 Phy1110: force -- moments, torque, couple, and equilibrium  (Page 7/13)

Construction of my spring scale

My spring scale has:

• A handle on the top
• A hook on the bottom
• A very stiff spring on the inside, and
• A circular dial with a red hand and a black hand on the front. The dial is calibrated both in lb (pounds-force) andin kg (kilograms-force).

The red and black hands

The red hand is normally in rotational equilibrium pointing to zero on the dial. The black hand can be rotated 360 degrees using a knob on the front of thescale.

Weighing a piece of luggage

You begin the process of weighing a piece of luggage by turning the black hand to point to zero. Then you hook the scale onto the handle on the luggage andpull up on the scale, causing the luggage to be lifted off the floor.

The red and black hands move

When you do that, the spring extends very slightly allowing the hook to move relative to the body of the scale,which in turn causes the entire scale to become slightly longer from top to bottom. The change inthe state of the spring is proportional to the downward force (weight) exerted by the luggage on the hook.

The internal mechanism causes the red hand to rotate around the center of the dial. The position of the red hand indicates theweight of the luggage when compared to the printed calibrations on the face of the dial.

Equilibrium

When you are supporting the weight of the luggage with the spring scale, the luggage is being pulled down by the force of gravity and is being pulled up by the hook and your muscles. This causes thesystem to be in momentary equilibrium.

The black hand also moves

For convenience, the black hand moves along with the red hand, but unlike the red hand, the black hand doesn't return to zero when the luggage isallowed to settle back onto the floor. The position of the black hand, therefore,indicates the maximum angular excursion of the red hand, which indicates the weight of the luggage in either lb or kg.

Applying a force manually

When I hold the handle in one hand and pull on the hook with the other hand so that the overall length of the scale increases by about 1/4 inch, the redhand moves to a position indicating a force of approximately 20 lb or 9 kg.

When a spring balance is used in the following exercises, we will assume thatthe change in the overall length of the scale is negligible relative to the overall dimensions of the problem.

The difference between force and mass

The SI unit for mass is the kilogram with a symbol of kg.

An often-used non-SI unit for mass is the pound.

An area of potential confusion

Does the relationship between 20 lb and 9 kg as printed on the dial of my spring scale make sense? It only makes sense if you know what is meant by thoseabbreviations. (They do not indicate a 20-pound mass or a 9-kg mass as the abbreviations might lead you to believe.)

This is an area of physics that can be confusing -- the difference between force andmass.

Exercise relating pound-force to kilogram-force

Let's work through an exercise using the following abbreviations and see if we can justify the relationship between lb and kg indicated by the dial on my spring scale: