Ronaldo Degazon Sat 05/05/12 Physics Lab #7 Planning & Design

Situation: A student is asked to calibrate a beam balance using the principle of moments and use

their calibration to find the density of a liquid P.

NB: Assume that he mass of 1 ml of water is 1g.

Hypothesis: The density of the liquid methylated spirit can be found using a makeshift calibrated

beam balance and a measuring cylinder.

Aim: To obtain the density of a liquid using a makeshift beam balance to find the mass.

Apparatus: A meter ruler, nail or stiff wire, 200g mass, methylated spirit, 100 cm3 measuring

cylinder, paper towel, 100 ml of water, length of stick

Diagram:

Above: Diagram illustrating how the beam balance was set up.

Procedure:

1. The ruler was used to find the mid point (balance point) of the piece of wood and

was marked with a pencil.

2. The length of stiff wire was cut in 2 pieces, attaching each to the 200 gram mass and

the measuring cylinder.

3. The cylinder was fixed 20 cm away from the pivot and using a pencil, the point was

marked off on the ruler as the starting point. The 200 gram mass was placed to the

other side of the pivot and was adjusted until the system was at equilibrium. Using a

pencil, the position of the mass on the ruler was marked off as the starting point.

4. 10 cm3 of water was added carefully to the measuring cylinder.

5. The 200 gram mass was moved further away from the starting point until the

system returned to equilibrium and its position on the ruler was marked with a

pencil.

6. Steps 4 & 5 were repeated 7 more times and the results were recorded in a table. A

graph of distance versus mass was also drawn.

7. The measuring cylinder was emptied and the apparatus was re-set as shown in the

diagram.

8. 10 cm3 of methylated spirit was carefully added to the measuring cylinder.

9. The 200 gram mass was moved further away from the starting point until the

system returned to equilibrium. The meter ruler was used to measure the distance

of the mass away from the pivot.

10. The volume of the liquid and distance of the mass were recorded.

11. Steps 8-10 were repeated 7 more times.

12. The graph was used to find the mass of liquid at each point. The density of the

methylated spirit was then calculated.

Results:

I. Below: Table showing distance moved by the 200 g mass for each 10 cm3 of water

added.

Volume of Water (cm3)

Mass of Water (g)

Distance of 200g mass away from the starting point (cm)

10 cm3 10 g 1 cm 20 cm3 20 g 2 cm

30 cm3 30 g 2.5 cm

40 cm3 40 g 4 cm 50 cm3 50 g 5 cm

60 cm3 60 g 6.5 cm 70 cm3 70 g 7 cm

80 cm3 80 g 8 cm

II. Below: Table showing the distance moved by the 200 g mass for each 10 cm3 of

methylated spirit added.

Volume of Methylated Spirit (cm3)

Distance of 200g mass away from the starting point (cm)

Mass of Methylated Spirit (g)

Density (g/cm3)

10 cm3 0.8 cm 8 g 0.8 g/cm3 20 cm3 1.6 cm 16 g 0.8 g/cm3

30 cm3 2 cm 20 g 0.7 g/cm3

40 cm3 3.2 cm 32 g 0.8 g/cm3 50 cm3 4 cm 40 g 0.8 g/cm3

60 cm3 5.2 cm 52 g 0.9 g/cm3 70 cm3 5.6 cm 56 g 0.8 g/cm3

80 cm3 6.4 cm 64 g 0.8 g/cm3

Calculations:

- Sample calculation of cm3 to grams conversion.

1 ml = 1 cm3 = 1 g

Hence: Conversion rate for cm3 to grams = 1g/1 cm3 = 1g/ cm3

Hence 10 cm3 = 10 x 1 = 10 g

- Sample calculation for the density of the methylated spirit.

Density = mass / volume

= 40 g / 50 cm3

= 8 g / cm3

- Calculation used to find the average of the densities of the methylated spirit.

Total Density = (0.8 + 0.8 + 0.7 + 0.8 + 0.8 + 0.9 + 0.8 + 0.8) g/cm3

= 6.4 g/cm3

Total No. of Values = 8

Average = 6.4 g/cm3 / 8

= 0.8 g/cm3

- Calculations used to prove the positions of the starting points.

According to the principle of moments:

Anticlockwise moments – Clockwise Moments

Assuming that each object was a starting point (total moments = 0)

Hence: d x (200 x 10-3 g) x 10 N/kg = 0 x m x 10 N/kg

Where: d = distance from starting point

m = mass of measuring cylinder

10 N/kg = gravitation field strength

0 x (0.2 kg) x 10 N/kg = 0 x m x 10 N/kg

0 = 0

So Anticlockwise moments = Clockwise Moments

- Calculations used as proof of results

Again using the principle of moments:

let d= initial distance of 200 g mass away from pivot

x = distance moved by 200 g mass

mc = mass of measuring cylinder alone

ml = mass of water in measuring cylinder

0.2 kg x 10 N/kg x (d+x) = 0.2m x 10 N/kg x (mc + ml )

2 (d +x) = 2 (mc + ml )

2 (d +x) = 2 (mc + ml )

d + x = mc + ml (Since both d and mc = 0.2)

x = ml

Hence the distance moved by the 200 g mass is equal to the mass of the water in

the measuring cylinder.

Taking one set of results from the table

x = 4 cm ml = 40g

Converting to SI units:

4 x 10-2 cm = 0.04 m 40 x 10-3 g = 0.04 kg

Hence: 0.04m = 0.04 kg

x = ml

Discussion:

Using the principle of moments, a makeshift beam balance constructed from a nail,

stick, 200 gram mass and measuring cylinder was used to find the density of a liquid

(methylated spirit).

The principle of moments states that “For systems in equilibrium the sum of the

clockwise moments about a point equals the sum of the anti -clockwise moments about

that same point.

Since the moment of a force is equal to mass times ten times distance away from pivot,

the beam balance was expected to be able to be used to find the mass of an object. The

200 gram mass had to be moved a certain distance away from the pivot each time the

water was added to return the balance to equilibrium and remember that mass and

distance are proportional to the moment of a force. Hence, since the moments on either

side of the pivot are the same, the distance moved by the 200 gram mass would be

proportional to the mass of the water added.

Since the distance moved by the mass is proportional to the mass of the water added,

the scale could be calibrated in terms of the distance moved per 10 grams of water

added. Hence, when using the balance to find the mass of the methylated spirit, the

mass would be found by finding the values corresponding to the distance moved by the

200 g mass. For those distances which fell between the graduations on the scale, the

graph was used to find the mass of the spirit.

Sources of Error:

- There was a possibility that the initial distance of the 200g mass from the pivot

would throw off the results since the distance moved away from the mass is not the

same as the distance away from the pivot.

Precautions:

- To prevent the initial distance of the 200 g mass from the pivot to throw off the

results, the initial distance was used as the lower fixed point (starting point) for the

scale instead of the pivot.

- To increase the accuracy of the value for the density of the liquid, several readings

were recorded and the results were averaged.

Conclusion: The density of a liquid (methylated spirit) was found using a makeshift beam balance

constructed from a nail, stick, measuring cylinder and 200 gram mass.