MAPÚA UNIVERSITY
SCHOOL OF MECHANICAL AND MANUFACTURING ENGINEERING
EXPERIMENT NO. 7
PLATFORM BALANCE
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NAME: CATAPANG, JAMIEL S. Date of Performance: October 19, 2020
ME139L-2 – A4 Date of Submission: October 19, 2020
STUDENT No. - 2016142388
Engr. Teodulo A. Valle
Instructor
GRADE
TABLE OF CONTENTS
OBJECTIVE 1
THEORY AND PRINCIPLE 1
LIST OF APPARATUS 4
PROCEDURES 6
SET-UP OF APPARATUS 8
FINAL DATA SHEET 11
SAMPLE COMPUTATION 12
TEST DATA ANALYSIS 13
QUESTIONS AND ANSWERS/PROBLEMS WITH SOLUTIONS 14
CONCLUSION 17
REFERENCES 18
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OBJECTIVES:
1. To learn the principle behind the operation of a weighing scale.
2. To learn how to calibrate platform balance.
3. To determine the accuracy and sensitivity of a weighing scale.
4. To determine the leverage ratio.
THEORY AND PRINCIPLE:
Laboratory balances are used to measure an object’s mass to a very high degree of
precision. They consist of a beam with a friction-free fulcrum, a pointer which attaches to the beam
and amplifies deviation from the balance position, and fractional weights which are applied along
the beam’s measuring arm. Laboratory balances provide high readability, a broad weighting range,
and a high degree of accuracy.
Often, the weighing pan is sealed to prevent the ingress of dust or other contaminants.
Samples are maintained at room temperature to prevent the formation of air currents inside the
enclosure. Other sources of error for laboratory balances include:
Buoyancy
Friction
Improper miscalibration
Misalignment
Evaporation
Gravitational abnormalities
Seismic disturbances
Accuracy vs. Precision
Accuracy refers to the closeness of a measured value to a standard or known value. For
example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual
or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement
is not close to the known value.
Precision refers to the closeness of two or more measurements to each other. Using the
example above, if you weigh a given substance five times, and get 3.2 kg each time, then your
measurement is very precise. Precision is independent of accuracy. You can be very precise but
inaccurate, as described above. You can also be accurate but imprecise.
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For example, if on average, your measurements for a given substance are close to the
known value, but the measurements are far from each other, then you have accuracy without
precision.
The measurement of quantity of materials can be made directly by weight or volume or
inferred from some other property such as pressure or velocity. The inferential methods are used
mainly for fluid-quantity measurements.
Weighing is a primary method of measuring forces, and volumetric devices are calibrated
initially by direct weighing. Scales have been constructed to weigh a million pounds or more
(testing machines), while the chemical balance, at the opposite extreme, will easily weigh a
millionth of a pound.
Figure 1. Diagram of platform
Platform scales are widely used in engineering work particularly in power plants for
measuring weights. It consists of levers and graduated beams which are arranged so that when a
load is applied on the platform, it can be balanced by a weight applied at the end of the graduated
beam or by shifting the poise along the length of the graduated beam. If the balancing is perfect,
then the magnitude is if the weight should be equal to the magnitude of the applied load. The ratio
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of the applied weight at the end of the graduated beam and the magnitude of applied load on the
platform is known as the leverage ratio.
Weighing scales are a measuring instrument for determining the weight or mass of an
object. Weighing scales are used in many industrial and commercial applications, and products
from feathers to loaded tractor-trailers are sold by weight. Specialized medical scales and
bathroom scales are used to measure the body weight of human beings.
The name scales derives from the pair of scales or dishes in which objects to be weighed
and the weights / masses against which to weigh them are placed. The Oxford English Dictionary
defines scales as "Apparatus for weighing. The pan, or each of the pans, of a balance. Spring
balances or spring scales measure force or weight by balancing the force due to gravity against the
force on a spring, whereas a balance or pair of scales using a balance beam compares masses by
balancing the force of gravity (weight) due to the mass of an object against the force due to gravity
(weight) of a known mass. Either type of balance or scales can be calibrated to read in units of
force (weight) such as Newton, or in units of mass such as kilograms, but the balance or pair of
scales using a traditional balance beam to compare masses will read correctly for mass even if
moved to a place with a different (non-zero) gravitational field strength (but would then not read
correctly if calibrated in units of force), while the spring balance would read correctly in force in
a different gravitational field strength (but would not read correctly if calibrated in units of mass).
In calibrating platform scales against known weights, the scales should first be thrown out
of adjustment; that is, the “adjusting” counterpoise (on the threaded rod of the graduated beam)
should be moved from its present setting. To readjust the platform scales, the “adjusting”
counterpoise is moved until a balance is obtained. This should be done without any weight on the
scales. Standard weights now should be placed on the scale in 5-pound increments and the scales
calibrated. The weights should be removed in a similar manner and the scales calibrated as the
weights are removed. It is also well to calibrate the scales with weights placed at the four corners
and compare these values with those obtained with weights at the center.
In order to obtain the leverage ratio by direct measurement, the platform must be removed.
Then, carefully measure the distances between the knife edges of the various levers and also the
length occupied by the 50 or 100 divisions on the graduated beam. One will save considerable time
if these measurements are made with a decimal scale. From these data and the equation given, the
leverage ratio can be obtained.
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LIST OF APPARATUS
1. Analog Platform Balance
2. Digital Platform Balance
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3. Set of Counter weights
4. Set of Standard Weights
5. Screw Driver
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PROCEDURES
A. TEST FOR ACCURACY (Analog & Digital)
1. Set the scale to a zero reading by means of position and placing the beam at the center of
the lower and upper limits by way of using the moving poise. Note also that this may also
be applied through making proper screw adjustments.
2. For the start of the test (i.e. trial 1), initially put a 15 kg standard weight on the center of
the platform. For the analog platform balance, adjust the movable poise for determining
the weight of the standard weight. Also, adjusting the movable poise will be able to center
the beam. Record the weight reading afterwards. Note: For digital platform balance, simply
read the weight reading being displayed by the apparatus.
3. Remove the first standard weight and set, once again, the scale to zero. Place and transfer
the standard weight in one of the corners of the platform balance. Here, adjust the poise
again if needed for obtaining the new reading. Repeat this step for the remaining corners
4. For the next following trials, add a 15 kg load on the platform and then follow the steps 1
to 3. Note: If the weight for the next few trials exceeds 50 kg (i.e. 60 kg, 75 kg and 90 kg),
replace three 15 kg standard weights into one 50 kg for the purpose of minimizing the
number of stacked standard weights on the platform. This will be able to ensure more on
the safety of the performers and care for the pieces of equipment used. Also, this will be
able to have a safer flow of operation. Additionally, add counterweights on the weighing
pan if the moving poise cannot be centered because of the excess load.
5. Calculate the average reading for each trial, determine the difference between the center
reading and average reading and determine the percent error between them.
B. TEST FOR SENSITIVITY
1. Set the scale to a zero reading by means of position and placing the beam at the center of
the lower and upper limits by way of using the moving poise. Note also that this may also
be applied through making proper screw adjustments.
2. In trial 1, place first the 15 kg standard weight on the center of the platform. For the analog
platform balance, adjust the movable poise for determining the weight of the standard
weight. Record the weight reading afterwards. The reading will serve as the initial reading
for this part.
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3. Again, slowly adjust the movable poise to the left until the beam touches the upper stops.
Record the new reading. This reading will serve as the final reading.
4. Remove the standard weights and repeat step no. 1 until step no. 2.
5. Slowly adjust and move the poise to the right and stop as soon as the beam touches the
lower stops. This will be able to obtain the new reading. The new reading will, again, serve
as the final reading.
6. For the next following trials, add a 15 kg load on the platform and then follow the steps 1
to 3. Note: If the weight for the next few trials exceeds 50 kg (i.e. 60 kg, 75 kg and 90 kg),
replace three 15 kg standard weights into one 50 kg for the purpose of minimizing the
number of stacked standard weights on the platform. This will be able to ensure more on
the safety of the performers and care for the pieces of equipment used. Also, this will be
able to have a safer flow of operation. Additionally, add counterweights on the weighing
pan if the moving poise cannot be centered because of the excess load.
7. Calculate the difference between the final and initial reading obtained for each of the trials
done.
C. LEVERAGE RATIO
1. Set the scale to a zero reading by means of position and placing the beam at the center of
the lower and upper limits by way of using the moving poise. Note also that this may also
be applied through making proper screw adjustments.
2. Load a 50 kg standard weight on the center of the platform balance. Afterwards, add the
counterweights on the weighing pan until the beam will be at the centers between the lower
and upper stops.
3. Remove the counterweight and the standard weight, accordingly. Place, again, only the
counterweights on the center of the platform. Then, record the weight reading by means of
adjusting the movable poise at the center of the lower stops and upper stops
4. Settle the counterweights that were used in the analog platform balance on the center of
the digital platform balance. After that, record the weight reading.
5. Calculate the leverage ratio by means of dividing the equivalent weight by the counter
weight.
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SET-UP OF APPARATUS
In summary, in order to determine the accuracy and calibration of each measurement, a set
of weights with known values were placed at different portions across the platform. Each weight
value was placed, one at a time, on each of the four corners and on the middle of the platform. The
precision is verified by measuring the values at these five different spots and checking for the
differences in the measurement at each portions. In the experiment, it was also noted on how to
calibrate the analog platform balance by moving the adjustment screw until the reference value is
detected by the balance. Meanwhile, the sensitivity of the analog platform balance was also
verified through the measurement of the weight interval until the upper and lower stops were
approached by the lever. Furthermore, the leverage ratio was also determined.
A. ACCURACY (Analog)
Figure 2. Test of Accuracy using Analog Platform Balance
For each trial, the standard weights are placed in each corner and center. The varying values
are determined by checking if the beam is balanced. The said values are then averaged and the
difference was determined with respect to the actual weight.
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B. ACCURACY (Digital)
Figure 3. Test of Accuracy using Digital Platform Balance
In this part, the same process with part A is done. The only difference is the platform used,
a digital platform balance instead of an analog platform balance.
C. SENSITIVITY
Figure 4. Test of Sensitivity (Lower Stop)
A standard weight was positioned on a platform balance. The initial reading was then
recorded in the data sheet. The poise was moved slowly to the left until the beam touches the upper
stops. Once it reaches the upper stops, the reading will also be recorded and will serve as the final
reading.
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D. LEVERAGE RATIO
Figure 5. Getting the Leverage Ratio using Analog Platform Balance
Lastly, the weight of the counterweight that was used for the standard load was divided by
the reading on the balance of the standard weight. This is done for the purpose of obtaining the
leverage ratio.
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FINAL DATA SHEET (TABLE OF DATA)
A. Accuracy (Analog)
BEAM READINGS
PLATFORM ERROR
TRIAL CORNERS AVERAGE DIFF.
LOAD (kg) CENTER (%)
1 2 3 4
1 15 14.9 14.9 15.1 15.1 14.9 15 0.1 0.671
2 30 29.9 29.9 30 30.5 29.99 30.75 0.175 0.585
3 45 44.8 44.8 44.8 44.8 44.8 44.8 0 0
4 60 59.4 59.7 59.44 59.4 59.99 59.475 0.425 0.710
5 75 74.2 74.7 74.3 74.3 74.7 74.425 0.275 0.368
6 90 89.4 89.5 89.1 89.6 89.6 89.4 0.2 0.223
B. Accuracy (Digital)
BEAM READINGS
PLATFORM ERROR
TRIAL CORNERS AVERAGE DIFF.
LOAD (kg) CENTER (%)
1 2 3 4
1 15 14.9 14.9 14.95 14.95 14.9 14.925 0.025 0.168
2 30 29.9 29.95 29.9 29.9 29.9 29.913 0.0113 0.043
3 45 44.8 44.88 44.8 44.8 44.8 44.8 0 0
4 60 59.8 59.8 59.85 59.85 59.8 59.825 0.025 0.042
5 75 74.65 74.65 74.7 74.7 74.7 74.675 0.025 0.033
6 90 89.45 89.4 89.45 89.45 89.45 89.438 0.012 0.013
C. Sensitivity
STD. UPPER STOPS LOWER STOPS
TRIAL WTS. INITIAL FINAL INITIAL FINAL
DIFF. DIFF.
(kg) READING READING READING READING
1 15 15.2 14.8 0.4 15.2 15.8 0.6
2 30 29.9 29.5 0.4 29.9 30.5 0.6
3 45 44.9 44.4 0.5 44.9 45.9 1
4 60 59.5 58.8 0.7 59.5 60.2 0.7
5 75 74.4 73.9 0.5 74.4 75.4 1
6 90 89.1 88.4 0.7 89.1 89.9 0.8
D. Leverage Ratio
COUNTER DIGITAL ANALOG
WTS. READING L.R. READING L.R.
50 0.5 kg 0.01 0.5 kg 0.01
100 0.95 kg 0.0095 0.9 kg 0.009
100 0.95 kg 0.0095 0.9 kg 0.009
200 2 kg 0.001 2 kg 0.01
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SAMPLE COMPUTATION
A. Accuracy (Analog)
𝐺𝑖𝑣𝑒𝑛: 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚 𝑙𝑜𝑎𝑑 = 15 𝑘𝑔; 𝐹𝑖𝑟𝑠𝑡 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.9 𝑘𝑔; 𝑆𝑒𝑐𝑜𝑛𝑑 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.9 𝑘𝑔;
𝑇ℎ𝑖𝑟𝑑 𝑐𝑜𝑟𝑛𝑒𝑟 = 15.1 𝑘𝑔; 𝐹𝑜𝑢𝑟𝑡ℎ 𝑐𝑜𝑟𝑛𝑒𝑟 = 15.1 𝑘𝑔; 𝐶𝑒𝑛𝑡𝑒𝑟 = 14.9 𝑘𝑔
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
𝑇𝑜𝑡𝑎𝑙 𝑏𝑒𝑎𝑚 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑟𝑛𝑒𝑟 (14.9 + 14.9 + 15.1 + 15.1) 𝑘𝑔
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = =
𝑁𝑜. 𝑜𝑓 𝐶𝑜𝑟𝑛𝑒𝑟𝑠 4
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 = 𝟏𝟓 𝒌𝒈
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = |𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝐶𝑒𝑛𝑡𝑒𝑟| = |15 − 14.9| → 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = 𝟎. 𝟏
|𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝐶𝑒𝑛𝑡𝑒𝑟| |15 − 14.9|
% 𝑒𝑟𝑟𝑜𝑟 = × 100 = × 100 → % 𝒆𝒓𝒓𝒐𝒓 = 𝟎. 𝟔𝟕𝟏 %
𝐶𝑒𝑛𝑡𝑒𝑟 14.9
B. Accuracy (Digital)
𝐺𝑖𝑣𝑒𝑛: 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚 𝑙𝑜𝑎𝑑 = 30 𝑘𝑔; 𝐹𝑖𝑟𝑠𝑡 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.9 𝑘𝑔; 𝑆𝑒𝑐𝑜𝑛𝑑 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.9 𝑘𝑔;
𝑇ℎ𝑖𝑟𝑑 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.95 𝑘𝑔; 𝐹𝑜𝑢𝑟𝑡ℎ 𝑐𝑜𝑟𝑛𝑒𝑟 = 14.95 𝑘𝑔; 𝐶𝑒𝑛𝑡𝑒𝑟 = 14.9 𝑘𝑔
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
𝑇𝑜𝑡𝑎𝑙 𝑏𝑒𝑎𝑚 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑟𝑛𝑒𝑟 (14.9 + 14.9 + 14.95 + 14.95) 𝑘𝑔
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = =
𝑁𝑜. 𝑜𝑓 𝐶𝑜𝑟𝑛𝑒𝑟𝑠 4
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 = 𝟏𝟒. 𝟗𝟐𝟓 𝒌𝒈
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = |𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝐶𝑒𝑛𝑡𝑒𝑟| = |14.925 − 14.9| → 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = 𝟎. 𝟎𝟐𝟓
|𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝐶𝑒𝑛𝑡𝑒𝑟| |14.925 − 14.9|
% 𝑒𝑟𝑟𝑜𝑟 = × 100 = × 100 → % 𝒆𝒓𝒓𝒐𝒓 = 𝟎. 𝟏𝟔𝟖 %
𝐶𝑒𝑛𝑡𝑒𝑟 14.9
C. Sensitivity
𝐺𝑖𝑣𝑒𝑛: 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 = 15.2; 𝐹𝑖𝑛𝑎𝑙 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 = 14.8
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = |𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 − 𝐹𝑖𝑛𝑎𝑙 𝑅𝑒𝑎𝑑𝑖𝑛𝑔| = |15.2 − 14.8| → 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = 𝟎. 𝟒
D. Leverage Ratio
𝐺𝑖𝑣𝑒𝑛: 𝐶𝑜𝑢𝑛𝑡𝑒𝑟 𝑊𝑒𝑖𝑔ℎ𝑡 = 50 𝑘𝑔; 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 = 0.5 𝑘𝑔
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 0.5 𝑘𝑔
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜 = = → 𝑳𝒆𝒗𝒆𝒓𝒂𝒈𝒆 𝑹𝒂𝒕𝒊𝒐 = 𝟎. 𝟎𝟏
𝐶𝑜𝑢𝑛𝑡𝑒𝑟 𝑊𝑒𝑖𝑔ℎ𝑡 50 𝑘𝑔
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TEST DATA ANALYSIS
In this experiment, the student has followed the laboratory manual provided by the
instructor. The experiment four objectives: (1) To learn the principle behind the operation of a
weighing scale; (2) To learn how to calibrate platform balance; (3) To determine the accuracy and
sensitivity of a weighing scale; and (4) To determine the leverage ratio. Moreover, it was divided
into four categories. The first part is a data sheet for the accuracy of the analog platform balance.
The second part is a data sheet for the accuracy of the digital platform balance. The third part is
for the sensitivity. The last part is for the leverage ratio.
In the first and second part of the experiment, they both dealt with the test for the accuracy
of the analog platform balance and the accuracy of the digital platform balance. The difference
between them is that the analog platform balance can be calibrated by rotating the screw found at
one end of the beam opposite of the pan. In addition, the screw is rotated with no standard weight
placed on the platform and will cause the beam to move upward and downward. Also, the beam
must be centered between the two stops, upper and lower stops in order to obtain accurate results.
As observed, the results for all trials have shown that the percent errors for both analog and digital
platform are below one percent. With this, it shows that the measurements and observed standard
weights are accurate.
In the third part of the experiment, it concerns about the test for sensitivity for the analog
standard weight onto. Here, the observed weight readings are recorded. In the process, the poise is
moved away from the pan, causing the beam to move upwards. It must be noted that the reading
of the weight should be the first moment that the beam will touch the upper stops. The initial
reading for the observed weight will then be subtracted with that of the final reading when the
beam first touched the upper stop. The absolute value of this value will serve as the data for the
difference column. The results showed that the differences for the upper stops are smaller than the
differences for the lower stops. This shows that the beam has lesser sensitivity with regard to the
movement toward the lower stops.
In the last part of the experiment, it dealt with determining the leverage ratio, a weight of
fifty kilogram was placed on the platform. The reading will serve as the denominator for the
leverage ratio. Afterwards, the center weight having a value of fifty kilogram is placed on the
platform in order to get the reading mass. This mass serves as our numerator for the determination
of the leverage ratio.
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QUESTIONS AND ANSWERS/PROBLEMS WITH SOLUTIONS
1. What is the difference between accuracy and precision?
‐ Accuracy refers to the closeness of a measured value to a standard or known value. For
example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but
the actual or known weight is 10 kg, then your measurement is not accurate. In this case,
your measurement is not close to the known value.
‐ Precision refers to the closeness of two or more measurements to each other. Using the
example above, if you weigh a given substance five times, and get 3.2 kg each time, then
your measurement is very precise. Precision is independent of accuracy. You can be very
precise but inaccurate, as described above. You can also be accurate but imprecise.
To summarize, accuracy tells how close a scale gets to the real value. An inaccurate scale
is giving a reading not close to the real value. Precision and accuracy are unrelated terms. A precise
scale will give the same reading multiple times after weighing the same item. A precise scale can
be inaccurate by repeatedly giving values that are far away from the actual value. For another
instance, a scale that reads 5.2 g three times in a row for the same item is very precise but if the
item actually weighs 6.0 g the scale is not accurate.
2. What is the definition of mass?
Mass is the amount of matter something is made from. Big things are generally more
massive than small ones. If you have a lump 15 of iron or copper and you take it to different places
on Earth (or even on the moon) to measure its mass, you will always get the same result.
3. What is the definition of weight?
Weight is a measurement of how much the force of gravity acts on a given amount of mass.
The force of gravity varies slightly all over earth. For an instance above, while your lump of iron
has the same mass, its weight varies: it might weigh a little bit more in Bangladesh than it does in
Tibet. With regard to the moon, gravity is about one sixth the strength on the moon as it is on earth.
Even though every object’s mass is exactly the same in both places, they only weight one sixth as
much on the moon as they do on earth.
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4. Using the data from the experiment, determine the leverage ratio using moment method.
𝑳𝒆𝒕:
𝑀𝐿 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐿𝑜𝑎𝑑
𝑀𝐶𝑊 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐶𝑜𝑢𝑛𝑡𝑒𝑟 𝑊𝑒𝑖𝑔ℎ𝑡
𝐿𝐿 = 𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚 𝑜𝑓 𝑙𝑜𝑎𝑑
𝐿𝐶𝑊 = 𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚 𝑜𝑓 𝑐𝑜𝑢𝑛𝑡𝑒𝑟 𝑤𝑒𝑖𝑔ℎ𝑡
𝐿𝐿
𝐿𝑅 =
𝐿𝑐𝑤
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
∑ 𝑀 = 0 → 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚
𝑀𝐿 = 𝑀𝐶𝑊 → 𝑊𝑒𝑖𝑔ℎ𝑡 × 𝐿𝑒𝑣𝑒𝑟 𝐴𝑟𝑚 = 𝑊𝑒𝑖𝑔ℎ𝑡 × 𝐿𝑒𝑣𝑒𝑟 𝐴𝑟𝑚
𝑊𝐿 𝐿𝐿 = 𝑊𝐶𝑊 𝐿𝐶𝑊
𝐿𝐿 𝑊𝐶𝑊 0.5 𝑘𝑔
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜 (𝐿𝑅) = = = → 𝑳𝒆𝒗𝒆𝒓𝒂𝒈𝒆 𝑹𝒂𝒕𝒊𝒐 (𝑳𝑹) = 𝟎. 𝟎𝟏
𝐿𝐶𝑊 𝑊𝐿 50 𝑘𝑔
5. When a 4 kg mass is hung vertically on a certain light spring that obeys Hooke's law, the spring
stretches 2.5 cm. If the 4 kg mass is removed, (a) how far will the spring stretch if a 1.5 kg mass
is hung on it?
𝑮𝒊𝒗𝒆𝒏: 𝑚1 = 4 𝑘𝑔; 𝑚2 = 1.5 𝑘𝑔; 𝑥1 = 2.5 𝑐𝑚 = 0.025 𝑚; 𝑔 = 9.8 𝑚/𝑠 2
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏:
𝑚
𝐹𝑔1 = 𝑚1 𝑔 = (4 𝑘𝑔) (9.8 ) = 39.2 𝑁
𝑠2
𝐹 39.2 𝑵
𝐹 = 𝑘𝑥 → 𝑘 = = → 𝒌 = 𝟏𝟓𝟔𝟖
𝑥 0.025 𝑚 𝒎
∗ 𝑁𝑜𝑤,
𝑚
𝐹𝑔2 = 𝑚2 𝑔 = (1.5 𝑘𝑔) (9.8 ) = 14.7 𝑁
𝑠2
∗ 𝑇ℎ𝑢𝑠,
𝐹 14.7 𝑁
𝐹 = 𝑘𝑥 → 𝑥 = = → 𝒙 = 𝟎. 𝟎𝟎𝟗𝟑𝟕𝟓 𝒎 = 𝟎. 𝟗𝟕𝟓 𝒄𝒎
𝑘 1568 𝑁/𝑚
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6. Define the spring scale.
A spring scale, also known as the spring balance or newton meter, is a type of weighing
scale. It consists of spring fixed at one end with a hook to attach an object at the other. It works by
Hooke's Law, which states that the force needed to extend a spring is proportional to the distance
that spring is extended from its rest position. Therefore, the scale markings on the spring balance
are equally spaced. A spring scale cannot measure mass, only weight.
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CONCLUSION
In conclusion, the objectives of the experiment were: (1) To learn the principle behind the
operation of a weighing scale; (2) To learn how to calibrate platform balance; (3) To determine
the accuracy and sensitivity of a weighing scale; and (4) To determine the leverage ratio. These
objectives were successfully met and accomplished. With the instructor’s guidance and laboratory
manual, the researcher was able to learn the basics of calibrating two types of platform balance,
the analog and the digital platform balance, respectively.
Based on the results, it can be concluded that the analog platform balance can be calibrated
through the use of a screw driver by rotating the screw found at the column supporting the beam.
Rotating the screw clockwise or counter clockwise moves the beam upward or downward and
enable the user to place it exactly at the center of the upper and lower stops. Furthermore, the
accuracies of the analog and digital platform balance were tested by measuring the weights of the
standard sample placed at different spots on each of the platforms. The difference between the
standard weight value and observed weight value shows how accurate the measurements are.
Moreover, it can be concluded that the measurement for the accuracy of a specific load is
more accurate through using a digital platform balance. This type of platform balance is the one
that provides almost a 100% exact measurement of the weight. The values for this part are near to
the true value by putting the load on the center. Also, the four corners of the platform helps in
knowing if the platform balance is being calibrated. The load on the platform must be distributed
so that the value of the weight are the same regardless of the position of the specimen or load. With
that, it can be stated that a properly calibrated platform balance exhibits this condition. In this
experiment, the results vary, which means that the device used is somehow not properly calibrated.
Leverage ratio is the ratio between the weights of the standard counter relative to the weight
of the pan. Also, it represents the actual weight of the counter weight and the action of the lever
and the mechanical advantage gained by it. Concurrently, the reference or counter weight
represents the ratio of the actual weight of the load to the experimental.
Lastly, the possible sources of errors in this experiment are the inaccurate reading or
movement of the analog platform balance, as well as mechanical problem regarding the balance
because of possibly being old. Another possible source of error is the inaccurate reading of the
measured value of the load. Aside from these, most sources of errors are related to human reading
errors.
17
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*Mechanical Engineering Laboratory 1 Manual
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