Master Physics Formulas with Formula Mania: Tips for First-Year Students!

[marcus]

hello holly
i was enjoying the problems you shared with us about
the rifle hung by string
and the clay blobs
and all
tell us some more if you want

 

[marcus]

does the chinless man have a name
(he's not the same as Bronco is he? I thought not)

 

[holly]

Hmmm. Perhaps I am being baited and mocked by a snide physics expert who enjoys laughing at my tiny brain...on the other hand, maybe I'll get some answers out of it...youse really want more questions? I have some that are stumping me.

Okay, I can get this right, but I can't defend my method. We have a car, going 50 km/h, and it skids 20m with locked brakes. And then, it is going 150 km/h and it has locked brakes, so how far will it skid now?

I say, 150 is to 50 as what is to what? Well, it is 3 to 1. And the first car, it went 20m. So, I am going to square the 3, making it nine. And times this 9 by 20m. Giving me 180m. This is always working for skidding cars where I can find the clear relationship and then square how many times more the speed is, and multiply it by the original skid length. But why did I do that? It seemed right...it seems repeatable, but I don't like it when I don't know what I'm really doing. It seems similar to where the arrow goes twice as fast but four times as far into a hay bale. Is there a formula?

Okay, this is a stumper: The force of gravity acts on some apples up in a tree. Some of the apples are twice as far from the ground as others. These twice-as-high apples, for the same mass, have: a) 1/4 the weight. b) 1/2 the weight or c)practically the same weight. It must be a trick question, otherwise it is entirely too stupid.

And this is a horrible one:
How many kilometers pre liter will a car obtain if its engine is 25 percent efficient and it encounters an average retarding force of 1000N? Assume energy content of the gas to be 40MJ/L.

Thanking you in advance.
An aside: The overbite boy has no name, sadly. The pig-tailed girl is not Nellie Newton. Nellie has curly hair. There is a really, really muscular guy with glasses and a cowlick, a buff physicist, I guess, and he, too, is nameless. But much later in the year, we have Sammie Sodium and Connie Chlorine coming up.

 

[paul11273]

Holly,
For your car question, you are getting the right answer, but kind of for the wrong reason.
You are correct in setting this up as a proportion, but it is not a direct proportion, which is clear because you are having to square the relation (in this example the 3). There may be a simpler way, but here is what I have for you...get a pencil and write it down as you go through.

Use the kinetic energy formula, KE=1/2(mass*velocity^2) This simply means that you square the velocity, multiply by the mass, and divide by 2. I am aware that you are not given the mass of the car, but that's coming up.
Know let KEa and KEb represent the kinetic energy of the car at 50 and 150 km/h, respectively. You can then divide the KEa by the distance it stops in...Da
KEa/Da
And do likewise for the other set, KEb/Db

Now set these two equal and solve:
KEa/Da=KEb/Db
KEa * Db = KEb * Da ( I cross multiplied)
1/2(mass*velocity^2)a * Db = 1/2(mass*velocity^2)b * Da (subbed in the KE formula for a and b)

Now we can see that each side has the mass as a multiplier, so it simply cancels out...
(velocity^2)a/2 * Db = (velocity^2)b/2 * Da

At this point you can plug in your known values and solve...
(50^2)/2 * Db = (150^2)/2 * 20
1250 * Db = 11250 * 20
1250 * Db = 225000
Db = 225000/1250
Db = 180m

When you use the kinetic energy formula, you can see how the velocity is squared, it is not linear. This is what you compensated for by squaring the 3 in your ratio.
So that is how I arrived at 180 meters for the unknown distance. I hope you stuck through that explanation, and see how to apply the formula. It is kind of hard to follow some of this typed text. Print it out, and write every step in you own handwriting and notation, and I think you will realize it is not too bad.

For the apple, I would have to say nearly the same weight. As you increase in altitude, the force of gravity lessens, but for the height of a tree, it is negligible (unless maybe for Jack's Beanstalk).

For your last question, good luck. I will try to work it out tomorrow on the bus.

As for the buff physicist character in your text, would you say he is a cross between Johnny Bravo and Dexter from the Cartoon Channel?
Just trying to get a good visual here...

 

[holly]

Howdy Paul...what a horrid mishmash of equations you gave me to solve that skidding problem! Can't I just keep squaring the number I get for the proportion? It's SO much easier. We get only those easy kinds of numbers, something is almost always half as much, twice as much, 100 times as much, etc. I printed out the real method you did -- thank you -- and will puzzle over it tomorrow. I used to dislike physics, but now I truly loathe it.

I don't watch television, so I am not sure if the Buff Physics Grad looks like those cartoons or not. But his arms are enormous. That's because he has to wrestle with such weighty problems.

Thanks again for the real method, guess I'd better learn it.

 

[marcus]

And this is a horrible one:
How many kilometers per liter will a car obtain if its engine is 25 percent efficient and it encounters an average retarding force of 1000N? Assume energy content of the gas to be 40MJ/L.

a joule is just another name for a Newton-meter
(the work done in pushing with a force of 1 Newton for a distance of one meter)

so put a liter in the car is like
putting in 40 million joule
but engine only delivers 10 million joule (25 percent, the rest is waste like exhaust heat and friction heat and all kinds waste energy)

the car has to push with 1000 Newton to keep moving because that is the retarding force

everytime it advances by one meter it does 1000 Newton meters of pushing work----1000 joules of work to go one meter (because pushing against the damn 1000 Newton retarding force!)

so with a million joules of work it can go 1000 meters (a kilometer)
and with the ten million joules the engine can put out (burning that liter of fuel) it can go 10 kilometers.
-------------------

BTW you were right to see the similarity between the arrow into the strawbale and the car skidding
kinetic energy is proportional to SQUARE of speed
and the energy is shown by the length of the skidmarks times the retarding force of the skidding tires----force x distance.


the apples in top of tree weigh practically the same
because their distance from the center of the Earth is practically the same as that of those at bottom of tree.
variation of gravity depends on distance from Earth center

height of tree makes percentagewise almost no difference at all

 

[marcus]

tell us some more problems holly