Have you ever wondered how the astronauts weigh things while they are in a space shuttle? What instruments they use? Unfortunately, none of our scales or balances works where there is no gravity. You must have seen in a movie that the space station whose shape is like a donut is spinning around, creating centrifugal force so a person inside feels quasi gravity. In such an environment you are able to weigh by using such force created artificially. (There is another element in this that is called CoriolisÕ force, which is a force that pushes you in a direction opposite to the direction of the spin. This is the force that gives spin to a water tornado in a sink going down the drain).

We have to understand dynamic mechanics or physics to weigh or measure mass of a material where there is no gravity. One simple yet beautiful law in physics is the law of conservation of momentum. Momentum is a product of mass and its velocity. Unless there is a force exerted externally on a mass or a system that consists of a number of masses, the momentum of the mass or the sum of the momentum of masses inside the system stays the same forever. When two objects that are moving at certain velocities collide, the sum of the momentum of those two objects stays the same before and after the collision. In other words the momentum of the closed system or the system having no influence from the external world will stay the same regardless of the velocities of individual objects inside the system.

Suppose an object (M1) of 1kg is sitting still (or its velocity (V1) is zero) and a second object (M2) of 1kg is moving at the velocity V2 or 1 meter per second toward M1, and both are on the ice or a frictionless surface. When the moving object M2 collides with the object M1 (which is sitting still), then they stick together and travel as one piece after the collision. A quiz for a high school freshman would be, "at what velocity will M1 and M2 travel after the collision?"

Before the collision the object M1 has zero momentum as its velocity is zero, and the momentum of the object M2 is M2 times its velocity V2. Before the collision, the momentum of the system that is the sum of the momentum of M1 and M2 will be (M1 x V1) + (M2 x V2) = 1 kgm/sec. After the collision, the momentum of the system, since M1 and M2 travel as one unit, will be (M1 + M2) x Va, where Va is the velocity of M1 and M2 traveling together after the collision. Using the law of conservation of momentum, we know (M1 + M2) x Va = 1 kgm/sec, since the momentum after the collision is equal to the momentum before the collision. To solve the equation for Va, where Va = V/(M1 + M2). In this case Va = 1/(1+1), so Va = 0.5 m/sec or half of the initial velocity of M2 before the collision.

You can intuitively tell your speed slows down when you bump into someone on the ice and hang on. (Naturally both have be good enough skaters so both can keep standing after the collision).

What does this law have to do with measuring mass? Remember how we calculated the velocity of the M1 and M2 after they collided and started traveling as one piece? This velocity gets decreases as the mass of M2 gets bigger. In other words the velocity after the collision is inversely proportional to the mass after the collision. The law of conservation of momentum should help measure mass if we have a mechanism that gives a certain amount of momentum to an object to be measured and measures its velocity. Such a mechanism could be a gadget, like a pinball, where you pull the lever to push a ball. If the lever exerts the same force for the same period of time to an object (a product of force and time is defined as impulse), the lever can exert the same momentum or impulse to an object. Thus, by measuring the time an object takes to travel a fixed distance, we can calculate its velocity and figure out its mass. Mass of an object is proportional to the time of travel since mass is inversely proportional to its velocity; that is the distance divided by the time of travel.

Impulse = momentum = mass x velocity = mass x distance / time

Now another high school question. You are standing on the surface of the ice rink or a frictionless surface. That means you cannot kick the ice to get moving in any direction since the surface is so slippery that any kicking or jumping fails to give force to get you moving in any horizontal direction. You can jump but land on the same spot. In physics it means you are completely isolated from any external forces as if you are floating in space. How can you get away from the ice link?

The method described above is being utilized in mass spectroscopy. In a mass spectroscopy, instead of measuring time of travel, it measures deflection of an electrically charged particle traveling at a fixed velocity in a magnetic field.

From practical point of view I feel applying physics of simple oscillation is the easiest approach to allow a scale to be used in space. The frequency of a vibrating wire decreases as its mass of the wire increases. To be more precise its frequency is inversely proportional to the square root of its mass. Imagine the weighing pan is vibrating at a frequency, low enough so when you place or fasten a mass on the pan, the mass vibrates together with the pan, that is without rattling. Then its frequency decreases inversely proportional to the mass of the pan plus the mass on the pan, thus by measuring its change of frequency you can calculate the mass you fasten to the pan.

As the space age approaches, we may have to seriously consider designing scales or balances to be used in space. A simple kitchen scale or bathroom doesnÕt work where no gravity exists. It may pose a challenge, especially when we have to design and manufacture scales and balances at low prices similar to the present ones.

P.S. The answer to the quiz above: take off whatever you have with you; shoes, cap or wrist watch, and throw it away as hard as you can. Then you should start moving in the opposite direction of where your belongings are headed. I hope you understand why.

Note: Mass derived this way, or the law of mechanics, is defined as inertial mass, while mass defined by gravity is rest mass. It is a mystery why inertial mass turns out to be the same as rest mass or that mass derived by either way obeys the same universal laws. In other words the same physics can work for both masses. You may say, "so what?" But it was a challenge to Albert Einstein after he created his special theory of relativity. He tried to explain this mystery with his general theory of relativity.

You may address any comments concerning this editorial by email to Mr. Eto