MEASUREMENT OF TIME AND MASS

MEASUREMENT OF MASS AND WEIGHT                                                        GO BACK

MASS

The mass of a substance is a measure of the quantity of matter it contains.

To measure mass it is usually compared with standard Masses

Principle of Mass Measurement

see FIG1

In FIG 1 above M1 is a known mass or standard mass, while M2 is the unknown mass.

At equilibrium when the beam is in perfect horizontal position, this equation is applicable

M1 x L = M2 x A

Therefore  M2 =(M1 x L)/A

This is the Principle of measurement for most mass measuring instruments, beam balance or chemical beam balance

Another means of measuring mass is by measuring the weight of the item.

Weight =Mass x g  where g  is the gravitational constant, g=9.8m/s^2

Therefore,  Mass = weight/g

This is how to measure Mass from weight and this is applicable to elastic spring instrument for measuring Mass

Example

If a standard mass of  500g is used in a beam balance as shown in the FIG 1. Given that L=50cm while A=30cm. What is the value of Mass M2 ?

Solution

Remember always do your calculations in SI units.

M1 =500g =0.5kg,   L=50cm = 0.5m,   A=0.3m

Then  M2= 0.5 x 0.5/0.3 = 0.8333kg = 833.3g

WEIGHT MEASUREMENT

Weight can be defined as the earth pull on a substance

The weight  W of a substance is directly proportional to extension E on an elastic spring when allow to hang freely on air space, provided the elastic limit is not exceeded.

WɤE,  W=KE  where k  is the elastic constant of the spring.

K can be known by using a known mass to obtain an extension E.

Example

If a known mass of 500g is used for calibration and graduating scale purpose of an instrument designed to measure weight and this mass produce extension of 10cm . What is the value of K for the spring. Hence do a scale graduation for this instrument from 1g to 1kg at 100g interval.

Solution

M=500g =0.5kg

E=10cm=0.1m

W=Mg=0.5 x 9.8 = 4.9N

Where g = gravitational constant or Acceleration due to gavity

W=kE therefore

k=W/E=4.9/0.1 = 49N/m

E=W/k

When Mass=1g=0.001kg, W=0.001x9.8, = 0.0098N,  E=0.0098/49m =0.0002m =0.02cm

See fig 2

Whenever this instrument read 10cm the MASS is 500g

MEASUREMENT OF TIME

Stop watch, wall clock, and wrist watch  are common instruments to measure TIME.

They measure Time in seconds, minutes and hours

60 seconds = 1 minutes

60 minutes = 1 hour

24 hours = 1 day

Example

Convert   1megaseconds to hours and days

Solution

1 megaseconds = 1000000seconds =1000000/60 minutes =16666.67/60 hours = 277.78 hours

= 277.78/24 days  =  11.57 days  = 11days +13hour +46minute +34seconds

INSTRUMENTS ACCURACY

Reading accuracy of an instrument is the nearest decimal place we can measure with the instrument. It is the uncertainty in the measure quantity.

The accuracy of Vernier caliper is 0.01cm

The accuracy of Meter Rule is 0.1cm

The accuracy of Micrometer Screwgauge is 0.001cm

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