# Indirect measurement

In this section,we discuss indirect measurement of:-

• (i) Distance
• (ii)Volume
• (iii)Mass

# 1.Indirect measurement of Distance

Concepts to investigate:
Similar ratios,triangles and indirect measurement of distance.
Materials:
Book,ruler measuring tape or meter stick
Principles and Procedures:

Part 1:Thickness of a sheet of paper


Suppose we want to measure the thickness of a page in a book. It is impossible to measure the thickness of a page directly with your ruler because the thickness is much less than the distance be the mm mark. We can however obtain an indirect measurement. Use a ruler to measure the width of all the pages(excluding the covers),divide the number by the total number of sheets. For example,if a book of 800 pages has a width of 40mm then the with of one sheet is 40mm/400 sheets=0.10mm

Part 2:Height of a tree


You can find the hieght of a tall tree using the following procedure and an understding of simple similar triangles. Two triangles are similar if they contain equal triangles and their corresponding sides are proportional.

# 2.Indirect measurement of Volume

Concepts to investigate:
Displacement method of measuring volume,indirect measurement of volume.
Materials:
Eye dropper or pipette,graduated cylinder,milk carton or similar container
Principles and Procedures:

Part 1:Determining the volume of a single drop


Suppose you want to find the volume of one drop of water from a small eye dropper. If you place one drop of water in a calibrated measuring cylinder you will find that it is hardly visible. How possibly can this measurement be done?
Method
1. Use the dropper to fill a 10-ml graduated cylinedr,counting the number of drops required to completely fill the cylinder to the 10ml mark.
2. Divide the volume of the water by the nomber of drops to find the vol. of a drop. For example,suppose 200 drops are required to fill the cylinder to the 10-ml mark,then the vol of one drop is =$frac {10}{200}$ml Now try it yourself with with the liquids shown below:-

• Why do you think the size of the rop varies from liquid to liquid?
• What does the size of the drop tell you about a liquid?
Liquid No. of drops to fill 10 ml Vol of single drop
Water, cell 1 ..........ml
Water with detergent, cell 1 ..........ml
Rubbing alchol ..........ml
Part 2:Determining the volume of an irregular object


Two substances cannot occupy the same space at the same time.If you place your hand in a bowl that is filled with water,some of the water spills over the hands because for the same reason. This fact can be used to find the volume of an irregular object such as your hand.
Method:
1. Obtain a 1-litre milk carton or similar container,cut off the top and cut a spout
2. Pour water in the container untill it pours from the spout.
3. Once the water has stopped dripping,put a beaker or measuring cylinder under the spout
4. Carefully submerge your hand up to the wrist and wait untill all the displaced water has flowed into the container. The amount of the water collected represents the volume of your hand.
5. Repeat this 3 times each time making sure the hand is submerged to the same point and find the average of your measurements.This is the volume of the hand.

# Reflection

 1. Which is larger,a drop of fresh water or soapy water? What does this tell you about soap's ability to help water penetrate fabrics? 2. How would you measure the volume of an irregulary shaped object such as wrench? 3. Is the method used in part 2 a form of direct or indirect measurement 4. How could you determine if a gem is authentic or artificial,having nothing more than a sensitive balance and a graduated cylinder? Clickhere for answers

# 3.Indirect measurement of Mass

Concepts to investigate::
Indirect measurement of mass,ratios
Materials:
Sand,rice,goggles,large rock,hammer,string,meter stick or tape.
Principles and procedures:

Part 1: Estimating the mass of a very small object


Although the mass of a single grain of sand may be too small to register on a standard classroom balance,we can use the balance to estimate the mass using an indirect measurement. Count 100 grains of sand and use a balance to determine their mass to the nearest 10th of a gram. Divide this mass by 100 to determine the average mass of an individual grain of sand. Repeat this procedure to determine the mass of an individual grain of rice.

Part 2:Estimating the mass of a very large object


Suppose there is a rock that is too large to be placed on a balance,how could one find its mass?
Method:
1. Cut off a small piece from the rock using a hammer.
2. Determine the mass of this mass using aclassroom balance and its volume using a measuring cylinder( The volume of the rock chip is equal to the diference in volume of water before and after the rock chip is submerged)
3. Wrap a string round the middle of the rock. Staraighten the string out and lay it next to a measuring tape to obtain a measure of the rock's circumfrence.
4. Wrap the string around the rock on two additional directions and determine the average circumfrence C. Although the rock is not perfectly spherical,this technique produces fairly good result if the rock is relatively round.
Calculation:
The radius r$=\frac{C}{2 \pi}$ and the volume of a sphere V$=\frac{4 \pi r^2}{3}$

Using proportionality $\frac{Mass of rock}{Volume of rock}$=$=\frac{Mass of piece of rock}{Volume of piece of rock}$ from which the mass of the rock can be determined For the sake of neatness,your results could be entered in a table as shown below:-

Equation Trial 1 Trial 2
Average circumfrence of rock crock=$\frac{c\ltsub\gt1\lt/sub\gt+c\ltsub\gt2\lt/sub\gt+c\ltsub\gt3\lt/sub\gt}{3}$ .......cm .......cm
Radius of rock $r\ltsub\gtrock\lt/sub\gt$=$\frac {c\ltsub\gtrock\lt/sub\gt{2 \pi}$ .......cm .......cm
Volume of rock $V\ltsub\gtrock\lt/sub\gt$=$\frac{4 \pi r^3}{3}$ .......cm^3 .......cm^3
Mass of piece of rock $m\ltsub\gtrock\lt/sub\gt$ .......g .......g
Vol of water displaced by piece of rock $v\ltsub\gtrock\lt/sub\gt$ .......cm^3 .......cm^3
Mass of rock $m\ltsub\gtrock\lt/sub\gt$=$\ frac{(m\lt/sub\gtpiece of rock\lt/sub\gtV\lt/sub\gtrock\lt/sub\gt{V\ltsub\gtpiece of rock\lt/sub\gt}$ .......kg .......kg