Measurements Calculation Problem

In summary, the "Measurements Calculation Problem" involves determining the correct values or units of measurements in various scenarios, often requiring the application of mathematical formulas and conversion techniques. This problem can arise in fields such as engineering, physics, and everyday measurements, necessitating a clear understanding of measurement systems and precision to ensure accurate results. The challenge often lies in identifying the appropriate method to convert or calculate measurements accurately.
  • #1
Ascendant0
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Homework Statement
A vertical container with base area measuring 14.0 cm by
17.0 cm is being filled with identical pieces of candy, each with a
volume of 50.0 mm3 and a mass of 0.0200 g. Assume that the volume
of the empty spaces between the candies is negligible. If the height
of the candies in the container increases at the rate of 0.250 cm/s, at
what rate (kilograms per minute) does the mass of the candies in
the container increase?
Relevant Equations
N/A (It's the "Measurements" chapter, that's focusing on us familiarizing ourselves with implementing measurements into mathematical problems)
I have done this problem three times now, and keep coming up with an answer that is a factor of 10 off from the answer in the solutions manual. The way I'm doing it is MUCH different than how they did it, so I can't use their method to see where I'm going wrong. I want to find out what I'm doing wrong in my method. I can't figure out where I'm converting wrong and it's driving me crazy. Here's what I do:

The base of the container = 14cm x 17cm = 238cm^2
Candy (converted to cm for later) = 5x10^-2cm^3 (volume) ; 1.357cm^2 (area of one side); 0.368cm (length of one side)
Candy (mass converted to kg for later) = 2x10^(-5)kg

To find out how many candies it would take to fill the surface area of the base of the container (238cm^2), I take the surface area of each candy and divide it into it:

238cm^2/1.357cm^2 = 175.387pcs (from my thought process, this is how many pieces it would take to have a layer of candies completely cover the base of the container, so for every 175.387 pieces, the height of the candies would increase by one additional stack/height (length) of candy, which is 0.368cm from my calculation)

Based on that calculation, and that the length of a side of each candy is 0.368cm, that means for every 175.387 pieces of candy, the height in the container would increase by 0.368cm, right? So with that in mind, I then calculate how many pieces it would take to increase the height by 0.25cm/sec:

175.387pcs/0.368cm = (x)pcs/0.25cm +> x = 119.148pcs per second would fill the container at a rate of 0.25cm per second, right?

So then, I take that value and convert it into how much that would cause the weight to increase per minute:

119.148pcs/1sec * (60sec/1min) * (2x10^-5kg) = 0.143kg/min (my answer)

So, my answer I got is at an increase of 0.25cm/sec, the weight would be increasing by 0.143kg/min. However, their answer in the solutions manual is 1.43kg/min. So, I would assume that somehow, I converted my measurements wrong, which shifted my answer one decimal place off. But again, I've done this three times now, and I keep getting the same exact answer every single time.

I know there is other ways to calculate it, as theirs in the solutions manual, but I'd really like to know where I'm going wrong here with this method?
 
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  • #2
Omg, nevermind, I found it. I messed up on the surface area of the candies. One side should be 0.1357cm^2, NOT 1.357^2. How I made that same exact mistake three consecutive times is beyond me. Sorry for wasting anyone's time, I can't believe I messed up math as simple as that...
 
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Likes docnet and BvU
  • #3
No better way to learn and make progress than finding your own mistakes and fixing them :smile:
 
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  • #4
Ascendant0 said:
Omg, nevermind, I found it. I messed up on the surface area of the candies. One side should be 0.1357cm^2, NOT 1.357^2. How I made that same exact mistake three consecutive times is beyond me. Sorry for wasting anyone's time, I can't believe I messed up math as simple as that...
it happens to the best of us.
 
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FAQ: Measurements Calculation Problem

What are the common units of measurement used in scientific calculations?

Common units of measurement in scientific calculations include meters (m) for length, kilograms (kg) for mass, seconds (s) for time, amperes (A) for electric current, kelvin (K) for temperature, moles (mol) for the amount of substance, and candela (cd) for luminous intensity.

How do you convert between different units of measurement?

To convert between different units of measurement, you use conversion factors that relate the two units. For example, to convert from meters to centimeters, you multiply by 100 because there are 100 centimeters in a meter. Similarly, to convert from kilograms to grams, you multiply by 1000. Unit conversion often involves multiplying or dividing by these factors.

What is the significance of significant figures in measurement calculations?

Significant figures are important in measurement calculations because they indicate the precision of a measurement. The number of significant figures reflects the accuracy of the measuring instrument and ensures that calculations do not imply greater precision than the measurements allow. When performing calculations, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation.

How do you handle measurement uncertainties in calculations?

Measurement uncertainties are handled by propagating the uncertainties through the calculations. For addition and subtraction, the absolute uncertainties are added. For multiplication and division, the relative uncertainties (percentage uncertainties) are added. This ensures that the final result reflects the combined uncertainty of all measurements involved.

What is the difference between accuracy and precision in measurements?

Accuracy refers to how close a measured value is to the true value or accepted standard. Precision, on the other hand, refers to the consistency or repeatability of measurements. A measurement can be precise without being accurate if it consistently yields the same result, but that result is far from the true value. Conversely, a measurement can be accurate but not precise if it is close to the true value but varies widely between measurements.

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