MEASUREMENT OF MASS, WEIGHT AND TIME

The mass of a body is the quantity of matter or material which the body contains. It is a scalar quantity and it is constant. The SI unit of mass is the kilogram (kg) In order to help us understand the working of some of the instruments which will be discussed here; we must first say something about weight.

Weight is the force which the earth exerts on a body. The body is attracted towards the centre of the earth by the force of gravity which varies from place to place.

Therefore, weight also varies from place to place according to the force of gravity at that place. The following instruments are used for measuring the mass of a substance.

The lever balance
This balance has a scale pan, a pointer and a circular scale graduated in grams. It measures mass by raising a fixed mass over a scale; the distance the fixed mass is raised depends on the mass of the object placed in the scale pan (see fig below). Weighing with a lever balance is direct and much faster than with a beam balance, although the reading accuracy is much lower. A reading accuracy of 0.1 g can be obtained with a lever balance and this is usually sufficiently accurate for most secondary school experiments.

The beam balance
The beam balance is a more delicate instrument than the lever balance. It measures mass by balancing two equal masses, one of which is known. Figure below shows the parts of a beam balance. The object whose mass is to be found is placed in the left hand scale pan ad standard masses are placed in the sight hand scale pan. When the two masses are equal, the pointer will swing through an equal number of divisions on either side of the central mark where it will finally come to rest.

The working of the beam balance uses the principle of moments. The two scale pans X and Y are equidistant from the pivot 0. When balance is achieved, the moments about 0 are equal. That is

l x m = l x s

Where s is the known mass in Y, m is the unknown mass in X, and l is the distance of each scale pan from the pivot. From the above equation we can see that m = s.

The reading accuracy of the balance can be as high as 0.001 g. Some beam balances have chain attachments which enable them to measure masses to accuracy of a fraction of a gram.

To use a beam balance, we follow the procedure given below:
(a) lift the front of the balance case and make suit that it is securely locked in the raised position.

(b) Adjust the levelling screws at the base of the balance until the plumb-line hangs vertically over the fixed point P.

(c) Raise the beam, and check to see if the pointer swings through an equal number of divisions on either side of the central mark. If it does not do so, then first make sure that the stirrups have not been displaced. Adjust the balancing (or adjusting) screws slightly if this is still necessary.

(d) Place the object to be weighed in the left hand scale pan.

(e) Using forceps, try to balance this object with standard masses (normally made of brass) placed in the right band scale pan.

(f) Having found a known whole number mass which is slightly less than the mass of the object, add extra fractional masses, in decreasing order of magnitude; until the pointer swings through an equal number of divisions on either side of the central mark.

(g) Always remember to lower the beam every lime masses are to be added to or removed from the pan.

(h) Note the total sum of the standard masses while they are still in the pan. Check this total when returning them to their box.

(i) Remove the object whose mass has now been found from the scale pan and lower the front of the balance case.

The following precautions should always be taken when using the beam balance
(i) Always use forceps to pick up the known masses.
(ii) Do not weigh hot objects.
(iii) Do not place wet objects on the scale pans.
(iv) Do not add or remove known masses while the beam is in the raised position.

The metre rule as a weighing balance

Given a metre rule, a known mass of say 100.0g, and a knife edge, it is possible to determine an unknown mass. The metre rule is balanced at its centre of gravity (the 50.0 cm mark for a uniform rule) on a knife edge and the known mass is placed on the right hand side at a distance x cm from the fulcrum. The position of the unknown mass M is then adjusted on the left hand side until the rule is in equilibrium, at a distance y from the fulcrum. Then, by the principle of moments,

My = 100x
M = 100x/y

The unknown mass can then be calculated from this equation.

Measurement of weight

As was said earlier, the weight of a body is the force with which it is attracted inwards the centre of the earth. It varies according to the distance of the body from the centre of the earth. Therefore, since the earth is not a perfect sphere, the weight of a body will vary slightly from place to place over the surface of the earth.

The scientific unit of weight is the Newton (N) and in general, on earth, a mass of 1 kg has a weight of 9.8 N. For practical purposes, a weight of 1 N can be taken as being equivalent to a mass of 100 g (on earth).

The spring balance
The spring balance consists principally of a spiral spring, it works, on the principle stated in Hooke’s Law that, provided the elastic limit is not exceeded, the extension of a spring is directly proportional to the applied force (i.e. the applied weight).

This principle is made use of in calibrating a spring balance, by hanging known weights on the spring, masking the extension they produce, and writing their value on the scale next to the mark (see fig below). The spring balance is used for measuring the weight of an object. The object is suspended from the hook of the spring balance. Some spring balances have a scale pan attached to the hook. In this case, the object is placed in the scale pan. The weight of the object, which is a force, causes the spring to stretch, thus moving a pointer over the graduations on the scale, and in this way gives a direct reading of the weight of the object.

The following precautions should always be taken when using a spring balance.
(i) Use the spring balance in a vertical position, if possible.
(ii) Hold the balance still while taking the reading.

(iii) Place your eye along the level of the pointer while taken the reading to avoid parallax errors.
(iv) Before taking a reading, lightly tap the spring balance a few times.
(v) Always use an appropriate spring balance which will use the full range of the scale for the weights being measured.

How to obtain the mass of an object using the spring balance

If the weight of an object is known to be W, then the mass (m) can be obtained indirectly by applying the relation:

Weight (W) = mass (m) x acceleration due to gravity (g)

That is mass (m) = w/g  Measurement of Time.
The unit of time is the second. The stop watch or stop clock is the instrument used in the laboratory for measuring time intervals. It can be started or stopped by pressing a knob or lever.

The stop watch enables very accurate measurement of small intervals of time in seconds and fractions of a second. In one type of stop watch, the second hand makes one revolution in one minute and the scale is graduated in 0.2 s intervals. In the other type, the second hand makes one revolution in 30.0 s and the scale graduated in intervals of 0.1 s (see figures below). As can be seen from the illustrations above, in both types there are two dials, a larger one reading the seconds and a smaller one for reading the minutes.

Reading the time interval from the stop watch shown in Fig. (a) above is straight forward. The reading of the minute hand is noted, and that of the second hand also read and added to it (3.0 minutes and 13.4 seconds in Fig. (a)).

But reading time intervals from the stop watch shown in Fig. (b) we must pay special attention to the position of the minute hand in order to know whether the second hand has travelled through more than 30.0 seconds.

In such cases the minute hand will have moved through more than half of the minute interval (e.g. 5.0 minutes 38.7 seconds in Fig. (b)). So, before reading the second hand, the position of the minute hand must be noted and read to the nearest half minute.

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