# A high schooler looking for some complicated physics problems

#### Bassir

I'm in high school and am very frustrated by how easy "physics" is. I really enjoy the subject but feel it's watered down in my school, and apparently my state.

I would like to do some more complicated problems that only cover intro to physics, but are very complicated in that you need to actually think.

I'm bored with physics in my school. My calculus is not good enough yet to do complicated calculus, so I can't do that.

I want to challenge myself.

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#### Superstring

If $$x=2sin(9t)$$ expresses a mass on a spring in simple harmonic motion, what is its maximum velocity?

Not exactly difficult, but it requires some thought.

#### Bassir

Are there any books with physics thought problems?

I need problems that challenge my logic, not my ability to plug and chug. Your problem is good.

I hear about SHCAUM's 3,000 Physics problems, but I don't wanna waste money on something that isn't very challenging.

#### Andy Resnick

have you checked out Jearl Walker's "Flying Circus of Physics"?

#### Bob S

Here is an interesting problem.

Consider a point A in space at x1, y1, and another lower point B at x2, y2 (not directly below the upper point). A bead slides on a stiff frictionless wire between the two points. Find the shape (curve) of the wire such that the transit time from a bead released at point A to point B is a minimum. Note: The shortest distance (direct line) is not the quickest. If you want specific numbers; use y1-y2 = 1 meter, and x2 - x1 = 1 meter.

Bob S

#### Stonebridge

I'm in high school and am very frustrated by how easy "physics" is. I really enjoy the subject but feel it's watered down in my school, and apparently my state.

I would like to do some more complicated problems that only cover intro to physics, but are very complicated in that you need to actually think.

I'm bored with physics in my school. My calculus is not good enough yet to do complicated calculus, so I can't do that.

I want to challenge myself.
Try this

The bicycle is on a rough surface and is being gently supported so that it doesn't fall over sideways. It is a standard pedal bicycle.
You tie a string to the pedal as shown and pull horizontally.
In which direction does the cycle move?

#### DavidSullivan

Go to Amazon and search “Schaum’s Physics” and have your folks buy you a book. I have the “3000 Solved Problems..” and find it invaluable. They work from simple to hard in each category and solutions to all problems are given so you can learn if you get stumped. (Note – you need to cover the solutions as you work through the problems.)

The only thing I don’t like about the book is the problems assume you’ve mastered what’s come before. I like to skip around, so that’s kind of a pain, but you’ll probably be sticking to the first chapters so you should be ok.

Good luck!

-David

#### yuiop

Try this. You have a wheel of radius (r) with a mark on the rim that is in contact with another mark on the road. The wheel is rolled forward by less than half a turn (theta degrees) so that the distance the base of the wheel moves along the road is x= 2*Pi*r*(theta/360). What is the vertical and horizontal distance that the mark on the rim of the wheel moves by?

Warning. Despite its simple appearance this is a very difficult problem.

#### DavidSullivan

Are there any books with physics thought problems?

I need problems that challenge my logic, not my ability to plug and chug. Your problem is good.

I hear about SHCAUM's 3,000 Physics problems, but I don't wanna waste money on something that isn't very challenging.
Go to a bookstore and thumb through it. If you can knock out all 3,000 problems "plugging and chugging" you're ready to start your masters thesis in physics!

-David

#### Bassir

Are they all 3000 problems a good difficulty or do I have to weed out the easy ones to get to the hard ones?

#### cragar

your in a room with 2 iron bars , one is a magnet and the other is not ,
how do u tell which one is the magnet , you can only use the two iron bars to tell which one is the magnet.

another one , i light 2 candles one candle on each end of the merry go round then i put a glass chimney around the candles to protect the flame from getting blown out when it goes around . but they are still open to the top
and i spin the merry go round , which way do they candle flames lean , or do they lean at all .
do they lean out , lean in , fall behind , angle back at a diagonal . lean forward .

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#### vin300

Try this. You have a wheel of radius (r) with a mark on the rim that is in contact with another mark on the road. The wheel is rolled forward by less than half a turn (theta degrees) so that the distance the base of the wheel moves along the road is x= 2*Pi*r*(theta/360). What is the vertical and horizontal distance that the mark on the rim of the wheel moves by?

Warning. Despite its simple appearance this is a very difficult problem.
The vertical distance is r-rcos(theta) and the horizontal distance is
2*pi*r(theta/360) - rsin(theta)

#### vin300

Here is an interesting problem.

Consider a point A in space at x1, y1, and another lower point B at x2, y2 (not directly below the upper point). A bead slides on a stiff frictionless wire between the two points. Find the shape (curve) of the wire such that the transit time from a bead released at point A to point B is a minimum. Note: The shortest distance (direct line) is not the quickest. If you want specific numbers; use y1-y2 = 1 meter, and x2 - x1 = 1 meter.

Bob S
Could you provide the answer to that? According to my calculation, the shortest distance is the quickest

#### A.T.

Could you provide the answer to that? According to my calculation, the shortest distance is the quickest
Nah, I'm pretty sure the quickest is somewhere below the straight line. You want to gain speed first, so initially you go down with higher slope.

But I'm to lazy to [STRIKE]google it[/STRIKE] derive it. ;)

#### Flat

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#### Borek

Mentor
Consider concrete block lying on the surface, mass m, friction coefficient f. What is the minimum force required to pull it from the place. Assume Earth surface (that is, g).

#### vin300

Nah, I'm pretty sure the quickest is somewhere below the straight line. You want to gain speed first, so initially you go down with higher slope.

But I'm to lazy to [STRIKE]google it[/STRIKE] derive it. ;)
I got it at 35.26° to the vertical

#### Andy Resnick

Here is an interesting problem.

Consider a point A in space at x1, y1, and another lower point B at x2, y2 (not directly below the upper point). A bead slides on a stiff frictionless wire between the two points. Find the shape (curve) of the wire such that the transit time from a bead released at point A to point B is a minimum. Note: The shortest distance (direct line) is not the quickest. If you want specific numbers; use y1-y2 = 1 meter, and x2 - x1 = 1 meter.

Bob S
Bob S didn't explicitly say this, but there's gravity present.

Mentor

#### Bob S

Good for Borek. This deceivingly simple classical mechanics problem is actually a very challenging one. It is not a "plug and chug" problem. The straight-line transit time (y=1-x) is t=sqrt(4/g), but y=(1-x)2.5 is shorter. But is it the shortest? What about
y=1-sin(pi*x/2)?
Isaac Newton was challenged to solve this minimum-transit-time problem ~1697, and rumor has it that in one day he found a unique solution (inverted cycloid) which he proved was the shortest transit-time solution, using calculus of variations. Newton "invented" calculus of variations.

Fermat's Law of minimum transit time in optics is eerily similar to this one. Is there a connection?

Bob S

#### Borek

Mentor
After seeing how vin is struggling I decided to push him in a right direction.

#### bjacoby

I'm in high school and am very frustrated by how easy "physics" is. I really enjoy the subject but feel it's watered down in my school, and apparently my state.

I would like to do some more complicated problems that only cover intro to physics, but are very complicated in that you need to actually think.

I'm bored with physics in my school. My calculus is not good enough yet to do complicated calculus, so I can't do that.

I want to challenge myself.
I know what you mean. I suggest you go find a couple sets of college freshman physics books and dig in. Usually they have quite a few thoughtful problems at the end of each chapter. They also start out assuming that you know nothing of calculus and are learning it concurrently. Get a head start on college. I did. You are planning on studying science in college, right?

#### espen180

I'm in high school and am very frustrated by how easy "physics" is. I really enjoy the subject but feel it's watered down in my school, and apparently my state.

I would like to do some more complicated problems that only cover intro to physics, but are very complicated in that you need to actually think.

I'm bored with physics in my school. My calculus is not good enough yet to do complicated calculus, so I can't do that.

I want to challenge myself.
Here are the examination problems of last year's IPhO. They require some physics beyond high school. Dig in. :)

http://ipho2009.smf.mx/home

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#### Matterwave

Gold Member
You can take a look at the GRE physics, and just skip the physics you haven't learned yet. Do all the mechanics questions...imo they are quite difficult (at least I usually fail at doing them XD).

#### issacnewton

I have a book by Mir publishers ,Moscow in english in djvu format.

"Problems in general physics" by I.E.Irodov . PM me . I can send it by email.

The book has really challenging problems as well as easy ones.

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