Motivating high school Physics students with Popcorn Physics

[BRUCE A RATCLIFFE]

How did you find PF?: Quiet Desparation prompted me to search for "Electronic forums"

I've been teaching physics for forty five years (quadruple alliteration : ) Though I would dearly love to teach a rigorous, math-based course, if I did so, my clientele would be lost, bored and gone. My students taking Calculus are oft times stopped cold by 1/2 X 1/3 = ?

My solution? ACTION! Projects where students are cooperating, building, testing, deploying and analyzing some project seems just the thing to keep students eager to come to class. (see Egg Drop preparation: ). These sorts of "lessons" last a lifetime:

Popcorn Physics? It was an accident that we spent two months on. Turns out a whole lot of physics was involved, but it started out with a microwave popcorn thief:

[Personal information removed]
45 years into it, and hoping for 20 more!

 

[Charles Link]

The problem I like to give non-physics students involving popcorn is: If Bob can eat a bag of popcorn in twenty minutes, and Mary can eat a bag in thirty minutes, how long does it take Bob and Mary to eat one bag when they both eat it together?

Many do not get this one correct, but most understand the solution when I tell it to them.

When they get stuck, sometimes I will give them the hint of how many bags can they eat in an hour?

 

[berkeman]

The problem I like to give non-physics students involving popcorn is: If Bob can eat a bag of popcorn in twenty minutes, and Mary can eat a bag in thirty minutes, how long does it take Bob and Mary to eat one bag when they both eat it together?

That's a trick question. Just sayin'.

 

[BRUCE A RATCLIFFE]

I'm not sure if this is what you call an elegant solution. Maybe cumbersome would be a better descriptor. But here's my solution: It is a rate problem.
Bob: 1 bag/20 min
Mary: 1 bag/30 minutes.
To add fractions you need a common denominator:
Bob: 1bag/20 min = 3 bag/60 min
Mary: 1 bag/30 min = 2 bag/60 minutes
Team B&M together will finish off 5 bag/60 minutes.
Which is (5/5 bags) / (60/5 minutes)
So 1 bag will be gone in 60/5 minutes = 12 minutes
QED

 

[Charles Link]

It is much easier solved with what is probably not the best mathematical technique in that it switches back and forth with units, but still fairly easy to follow:

Bob can eat 3 bags in an hour, and Mary two, making for 5 bags in an hour, or twelve minutes per bag.

Sticking with minutes only and working the rates is more systematic, but the arithmetic becomes more difficult then, so the lay person usually prefers the simpler albeit unsystematic approach.

Edit: Computing it more systematically by computing rates per minute, adding the rates, and then setting $rate_{total} \times time= 1$ and computing the time makes for a more difficult arithmetic exercise.

 

[BRUCE A RATCLIFFE]

TOO funny, Charles! I was proud of my solution, featuring units analysis AND fractions--the terror of my students. And then I see your oh-so-simple solution.
Bruce

 

[PeroK]

I sometimes like the random approach. By the time Mary has eaten one bag, Bob has eaten 1.5 bags. That's 2.5 bags in 30 minutes, or 12 minutes a bag.

 

[PAllen]

I sometimes like the random approach. By the time Mary has eaten one bag, Bob has eaten 1.5 bags. That's 2.5 bags in 30 minutes, or 12 minutes a bag.

Similar to my immediate approach, but I used Bob. After 20 minutes, Bob has eaten one bag and Mary 2/3 of a bag. That’s 5/3 bags in 20 minutes, so 3/5 of that time for one bag, so 12 minutes.

 

[symbolipoint]

The exercise work rates problem in post #2 is or seems like a typical routine exercise being so many like that one. But I did not look into that particular one very carefully; just it seems so familiar in type.

 

[symbolipoint]

My solution, still a typical way to solve:

my solution: combined constant rates, eating bag of popcorn

Spoiler: my solution: work rates combined -- 1 bag popcorn

Maybe slightly differently arranged but like this:
rate=quantity/time

from it find that (rate)(time)=quantity


Bob's rate, 1/20 the unit in bag per minutes

Mary's rate, 1/30

Bob and Mary Combined, 1/20+1/30



and to simplify

30/(30*20)+20/(20*30)

(30+20)/600

50/600 and this is bags per minutes;

5/60

But you want how much time for 1 bag,
then the reciprocal of the rate

60/5

12 MINUTES per BAG

 

[Charles Link]

See https://www.physicsforums.com/threa...ns-around-a-central-coin.971465/#post-6176083 for another fairly simple problem that I try to motivate students with. It's a good application of the law of cosines. See also post 4 where the 8 pennies are close to a perfect fit around the JFK 50 cent piece.

 

[WWGD]

Since Bob eats 1.5 times as fast, he'll eat 60% of it, while Mary finishes the remaining 40%. Since Bob eats 1 bag in 20 min, he'll eat 60% of the bag in 12 minutes.
Then I'll ruin it by saying neither eats at a uniform rate.