- #1
Ascendant0
- 177
- 37
- 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?
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?
