A spring scale is a weighing scale used to measure pulling force. Experiments for which such a scale can be used include leverage using pulleys, determining the volume of irregular objects and exploring questions of engineering load safety.

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## Measuring an Irregular Volume

An irregularly shaped object can be weighed in air and submerged in water. The difference in weight is the buoyancy force by the displaced water, that is the force of water trying to push the object up. Knowing the density of water, one can then find the volume of the displaced water, and therefore the volume of the object. Knowing the weight in air, the object's density can be found. This is useful for example to determine whether an object is solid gold or just gold-plated. The principle behind this experiment is called Archimedes' principle, which states that buoyancy force equals the displaced water's weight. (This can be proven by noting that water of the same shape and volume as the object, filling the same void the object fills, itself neither spontaneously sinks nor is forced up out of the water by the buoyancy force. Its only force against the buoyancy force is its own weight.)

## Block and Tackle

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, used to gain mechanical advantage in lifting. The mechanical advantage can be determined by how far the rope must be pulled to raise the weight a unit distance. For example, if the rope must be pulled four meters to lift the weight one meter, then the mechanical advantage (the ratio of force output to the force applied) is 4:1. A 100 N mass could be lifted with the force of only 25 N. A spring balance can enter into the experiment by weighing the mass and the measuring the tension of the rope (or string) being pulled to determine the mechanical advantage.

## Trick Question

Suppose two weights of equal mass hang off opposite sides of a table. They are connected by a string that goes across the top of the table. One can insert a spring scale to measure the tension. Divide the string and attach one mass's string to the bottom hook of the scale, and the other mass's string to the top hook. What is the force that the scale reads? Is it equal to the weight of one mass, or to the sum of both?

One weight acts no different from a ceiling holding the other weight up, so the scale measures just the weight of a single mass.

This is a good demonstration of Newton's third law of motion, that each action has an equal and opposite reaction. The forces exerted by the two masses on each other are equal and opposite.

## Another Trick Question

A mass hangs from the two ends of a rope that is looped over a pulley above. The mass weighs 100 N. What would a spring pulley attached between one rope end and the mass read?

50 N, since the force is divided up so each rope gets half. That the rope is attached at the top is immaterial, since the 50 N force merely needs to cancel out between opposing directions for the rope to keep from moving. Each rope end pulls up 50 N. The rope at the pulley pulls 50 N in both directions. This is all that's needed to hold up the 100 N mass.

## Another Trick Question

Suppose one end of the rope in the last problem is nailed to a nearby wall. Suppose also that the rope is rated to 60 N. The mass is then holding onto one rope end. What will the spring scale register?

100 N, if the rope keeps from breaking long enough for the scale to be read.

## Hyatt Regency Walkway Collapse

In 1981, a walkway in the Kansas City Hyatt Regency collapsed because of a change of design between the architect's drawings and their implementation; 114 people were killed. The error can be simulated in a spring scale demonstration. Hang four spring scales from a solid horizontal rod. Hang string of varying lengths from each. Then tie equal masses to each. Record the scale readings. Now attach each mass to its respective scale. Each scale will still read the same as before. Now hang the top hook of each scale onto the bottom hook of a scale above it. Hang the top scale on the horizontal rod. Now take readings again. This design difference is the difference between the architectural blueprints and the implementation of the walkway design. It is the difference between four men holding onto a rope, and one man holding onto a rope while each man below hangs onto the feet of the man above him. The man at the top can't hold the weight of four men so he lets go and everyone falls off the rope.