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Measurement of Forces in Physics By Comparison to an Arbitrary Agreed-Upon Unit
The effect of the weight hanged on a coil spring on the extension of the spring
A coil spring is hanged with a weight hanger and pointer attached to its end. Different known weights with equal increments (in this case 500g, 1000g, 1500g, 2000g – according to the coil's flexibility) are hanged and the readings of the pointer with the respective weights are marked on a sheet of paper.
The results show that equal weight increments stretch the spring equally (linear relationship) what we call Hooke's law.
Take in account that this linear relationship between weight and length displacement of the spring is limited to the working range of the spring (too small weights will not stretch the spring at all whereas too big weights will compromise its flexibility).
The measurement of the weight of different objects with a calibrated spring
Basically, we have built here a simple weight spring balance with a scale calibrated to 500g increments. It's possible to refine the scale by using weights with smaller increments like 250g, 100g or less and mark the readings on the scale. But because we have already discovered the principle of the linearity of the spring's operation mode and it's clear that the higher the weight applied on the spring the longer the spring is stretched in a continuous way, we can refine the readings by dividing farther the scale by calculation alone.
We can also use springs with different flexibilities in order to weigh different ranges of weights.
Now we can use the apparatus we have built in the 1st experiment to measure unknown weights (between the limits of the working range of the spring). We hang the objects on the hanging hook and mark the respective pointer readings on the ready calibrated paper scale we created in the former experiment. By this we compare the unknown weight to the calibrated scale in order to get the unknown object's weight. Take in account that we are able to determine the weight of the objects approximately since the scale is not refined enough. We can compare the readings obtained by our trials to those of a commercial spring scale or to a digital one and check the accuracy of our experimental instrument.
The measurement of the Earth gravity force applied on an object
We are able to measure the weight of an object with a calibrated spring because the object is pulled down by the force of Earth gravity and as a result the spring is stretched and the pointer points to the weight marked on the scale. In other words, the weight property of an object is the force applied by gravity on the object. But how can we measure this force?
A force stretches the spring - higher the force, longer the spring. A certain spring extension means a certain weight and a certain weight means a certain force. From this we can conclude that a certain spring extension means also that a certain force is applied. But how can we measure this force?
Say the unknown gravity force applied on a weight of 1kg stretches the spring a certain length. The same unknown force is applied by gravity on any other object that stretches the spring the same length as the 1kg weight does. But how can we quantify this force?
Force units do not exist in nature and we can't pick them up. So we have to define or invent units arbitrarily in a convenient way. In order to do this, the force applied by gravity on a mass (weight in a simplistic way) of 1kg is defined as 1 kilogram-force. So 1 kilogram-force is our basic force unit.
Now we can use our spring scale, we have built in the 1st experiment, to measure not only weights but also forces. Say, an object hanged on the spring stretches it twice than a weight of 1kg and points to 2kg of weight. The meaning is that the object weighs 2 kg and the force applied by gravity is also twice namely 2 kilogram-force. And if another object weighs 1.5 kg the meaning is that the force applied is 1.5 kilogram-force or 1500 gram-force. It's clear that the numerical values of the force in kilogram-force units and the weight in Kg are the same by definition. The meaning is that on one side of the scale are marked weights in kg units and on the opposite identical side of the scale we can mark forces in kg-force units with the same numerical values.
But today we use mainly a more modern and practical force unit called newton (symbol: N) (1 kilogram-force equals 9.81 N).
It's clear that we can translate our scale's weight readings to force readings like kilogram-force (same numerical value) or N (multiplying by 9.81), and so our spring weight balance is also a force meter in the same time.
Measuring other forces than Earth's gravity.
Till now we have measured only gravitational forces which account for the weight property of bodies. But can we also measure non-gravitational forces as well?
We can place our force meter in a horizontal position and stretch the spring by hand for example. The pointer will point now to the force exerted by our hand on the spring and not by gravity.
It's clear that we can use our force meter to measure not only weight (gravitational forces) but also other forces as well.
- Any physical measurement is achieved by comparison to an agreed-upon arbitrary unit - in the case of force to the kilogram-force or more commonly to the newton.
- The same applies when we measure weights. We did it by comparing to a standard weight of 1kg found everywhere but take in account that this unit of 1kg is an agreed-upon arbitrary unit also.
- The weight property of an object is the force applied by gravity on the object.
- Because the higher the force or weight applied on a spring the longer the spring stretches in a continuous way, it's convenient and possible to measure forces and weights by using a calibrated spring.
- The "kilogram-force" unit is equal to the magnitude of the force exerted by Earth's gravitational field on one kilogram of mass. This unit is less in use today.
- The more common force unit in use today is the newton (N, named after Isaac Newton) that is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared. 1kilogram-force equals to 9.81 newtons.
- Note that there is a difference between mass and weight, but from a practical point of view, on Earth, they are the same. In order not to confuse physics beginners to whom this video is intended we avoided the use of the more correct term "mass" in some cases (only in the video) and replaced it by weight. We suggest that also teachers adopt this practice and defer some issues like mass vs. weight and units in general to a later stage.