# Biggest Physics Bloopers

1. Jul 4, 2004

### JohnDubYa

I have read oodles of physics textbooks and have come across many topics that are rarely discussed correctly or clearly (at least in my opinion). Here are some of my favorites.

1. Impulse. Authors continually ascribe the impulse to an individual force, not a net force. Why? The force in the equation $$\Delta p = F\Delta t$$ is clearly the net force.

2. Systems, such as the rocket ship, that supposedly change mass, producing some mysterious force that has no definable source. Nope, not in my book.

3. Reversible/irreversible cycles. I have seen these two issues screwed up on many occassions. At some point I begin to wonder if the authors really understand thermodynamics.

4. Work/energy. Most authors do not have a clear, uniform way of relating conservative and non-conservative forces to changes in energy.

5. Too many equations. You should only need about a dozen equations to cover the entire first semester of classical physics. Any more than that simply confuses the students.

Any others?

2. Jul 4, 2004

### AKG

Only a dozen? Which would those be? In my first semester of classical physics, I covered
• projectile motion
• Galilean transformation
• Perfectly Inelastic Collisions
• Rocket Propulsion
• Gyroscopes
• Kepler's Laws
• Resistive Forces
• pendulums
• orbits and gravitation
• springs
• damped oscillations
• forced oscilations
• and all the basic equations with force, momentum, velocity, acceleration, angular velocity, torque, angular momentum, etc.

You're telling me you could cover all of those in 12 equations?

3. Jul 4, 2004

### JohnDubYa

I was mainly referring to algebra-based physics and those formulas that need to be remembered for exams (and not easily deduced from other formulas). The calculus-based courses probably need a few more. (Although I suspect not as many as everyone thinks.)

So what formula do you associate with resistive forces? Orbits? Forced oscillations? Galilean transformations? Perfectly inelastic collisions? Projectile motion?

Or is your physics class merely a memorization/plug & chug fest?

4. Jul 4, 2004

### AKG

The Physics exam (in fact most of my exams) were pretty easy, but throughout the year the assignments and tests did pose some interesting problems, so it wasn't a "plug and chug fest" by any means. Also, since the tests and exams permitted an aid sheet, it wasn't memorization (there were a lot of formulas; you didn't need to memorize them but you needed to know how to apply them, and you needed to have problem solving skills).

I don't really care to get out my aid sheet right now, but with resistive forces, for example, I believe we had some equations describing laminar flow, Reynolds number, some stuff with terminal velocity I believe, etc. As for "Orbits," that section in the book was supposedly covered, so I wrote down some equations for it, but I never went to lecture, and no discussion of oribts came up on tests, assignments, the exam, or in tutorial but I believe it could have come up in any of those places and we may still have needed to know the formulas. They had to do with the kinetic and potential energies of objects in orbits and such. For "Projectile Motion," it's nice to have a quick equation (not have to derive it) to find out the range and maximum height and time taken for an object on a level surface with given initial velocity and angle.

I think if you're able to solve problems well, then as long as you're given the formulas, if you truly understand the concept you should be able to solve a given problem. Since they want to test whether you understand the concepts, they let you have the formulas, and make sure you can prove you know how to use them, and thus prove you know the concept. And I think it makes sense to cover a lot of topics, but not test on all, because that way students still have to learn all the concepts well (any of the topics may be on the tests), and this way they're kind of pushed to learn more concepts well. It also depends on what pace the class can go at, and what you can expect of the students. Of course, it doesn't make sense to push students past the point of learning, and force them to cram, which is one benefit of allowing students to bring an aid sheet with formulas, removing the focus from memorizing formulas.

5. Jul 5, 2004

### JohnDubYa

RE: "For "Projectile Motion," it's nice to have a quick equation (not have to derive it) to find out the range and maximum height and time taken for an object on a level surface with given initial velocity and angle."

That's just bad physics. Any projectile motion -- indeed, any linear acceleration problem whatsoever -- can be solved using only two equations as long as you understand vector summation:

$$\vec{d} = \vec{v}_ot + \frac{1}{2}\vec{a}t^2$$

$$\vec{v} = \vec{v}_o + \vec{a}t$$

(And for calculus-based courses, only the first equation is necessary since the second is trivially derived from the first. In fact, that should be part (a) of the exam question.)

If you were asked to find the maximum range in a problem and were given a formula for calculating the maximum range, then you learned nothing about projectile motion.

Of what value is it to ask for the maximum range when all the student has to do is find the corresponding formula on their cheat sheet and dump in the numbers? I can teach a monkey to do that.

My policy has always been to only provide those formulas learned since the last exam. This way I rarely have to place more than five formulas on an exam. After all, if I have to write down the equations of motion for linear acceleration on their exam, then they haven't been doing their homework. And if Newton's second law appears on a final exam cheat sheet, I really begin to wonder if any learning has taken place, whatsoever.

6. Jul 5, 2004

### AKG

Seeing as how finding the range and maximum height are trivial problems, being able to derive the formula to get it is really not indicative of any learning. It would be better to have a really challenging problem which requires you to find the maximum range, but also do much more than that. If you're asked to find the maximum range of a projectile, whether you're given the formula or not, it's just a bad question. It's grade 11 physics, and testing whether people can derive a projectile motion formula from one of those kinematics equations is pretty pointless (if they can't do it by their first physics college phyiscs course, I was perhaps incorrectly assuming we're talking about college, they shouldn't be there). They should be able to derive the formula, but it's pointless to waste time testing them on that, so may as well give them the formula and let them use it to solve a harder problem, one that will really let you see if they've learnt the harder concepts.

Now that I think about it, if you're talking about gr. 11 physics, maybe a dozen equations will do. What topics do you cover in that course?

7. Jul 5, 2004

### LURCH

Don't understand what you mean by this one.

8. Jul 6, 2004

### JohnDubYa

LURCH,

Some textbooks treat the rocket ship + remaining fuel as a system. Such a system is badly defined and produces a notion of force that is not only abstract but counter-intuitive.

RE: "Seeing as how finding the range and maximum height are trivial problems, being able to derive the formula to get it is really not indicative of any learning."

Having a student derive a formula is certainly better than handing them the formula. At least there is SOME learning in the former. The latter is brainless.

And never overestimate student skill. WE think that deriving the range formula is easy. But 25% of the class will struggle to do it.

I don't have my students derive formulas, but rather solve the system numerically from the get-go. All projectile motion problems are straightforward and solved identically. (Some require a little more algebra than others, but the setup is the same.)

Here is a problem that was on my final exam. (This is an algebra-based physics course for non-technical majors.)

A rock is projected at 45 degrees at a initial speed of 10 m/s. If the rock was originally located at the bottom of a 30 degree incline, how far up (that is, along the incline) will it strike?

Now look over your cheat sheet and find an equation that solves this problem. :)

9. Jul 6, 2004

### arildno

Great question!
I thought all projectile motion problems had lost their charm years ago, but this had a delightful twist to it..

10. Jul 6, 2004

### AKG

Well then you didn't read what I wrote, because I said basically that deriving a simple formula is trivial compared to having the simple formula and solving a tough question. Of course, deriving a simple formula may not be so easy in a purely introductory physics classes, which is I guess (but didn't guess at first) what you're talking about.

What requires more thinking deriving a simple formula or solving a tough problem? It depends on what we consider a simple formula. From my perspective, I was thinking of a first year physics course in university for engineering students, in which case a projectile motion formula would be too simple to derive, and so it makes sense to let them have it, and give them really tough problems. In an introductory, grade 11 high school physics class, deriving one of those formulas is perhaps a worthwhile problem, and not so simple, and so handing it to them so they can plug in numbers requires little compared to having them derive it. In a university setting, handing them the formula and giving them a simple problem where they need only to plug in numbers is totally out of the question.

11. Jul 6, 2004

### JohnDubYa

I agree with you, AKG.

RE: "From my perspective, I was thinking of a first year physics course in university for engineering students, in which case a projectile motion formula would be too simple to derive, and so it makes sense to let them have it, and give them really tough problems."

But here is another question:

In the displacement equation of motion,

$$\vec{d} = \vec{v}_ot + \frac{1}{2}\vec{a}t^2$$

what is the physical significance of each of the two terms on the right hand side. After all, both terms are displacements. What displacements are they, exactly?

I wonder how many introductory physics students would know how to answer that question? How many could really explain the solution to the monkey-gun problem?

This tends to be my approach. Not formula memorization, utilization, or derivation, but rather dissection.

12. Jul 6, 2004

### AKG

My professor for first year physics actually demonstrated the monkey-gun problem, it was pretty interesting (no animals were harmed, it was a plastic model monkey). Technically, I don't see why you couldn't have them dissect the formula, but still give it to them on a test (and offer a challenging problem that forces them to prove that they really understand it). Of course, in a purely introductory class, you're right that only perhaps a dozen equations are necessary, and giving the formulas really shouldn't be necessary, and those who need it probably don't understand, so giving the formula only gives them a possibility to succeed on the exam even though they haven't really learnt.

13. Jul 6, 2004

### Zorodius

Is the answer 5.0 meters? (along the incline, not horizontally or vertically)

14. Jul 6, 2004

### salamander

I think it is 5.9 m (along the incline). But hell, what do I know?
JohnDubYa, enlighten us!

15. Jul 6, 2004

### AKG

$$\Delta d_v = v_{0v}\Delta t + \frac{1}{2}a\Delta t^2$$

$$\Delta d_v = \frac{10}{\sqrt{2}}\Delta t - 4.9\Delta t^2\ \dots \ (1)$$

$$\Delta d_h = v_{0h}\Delta t = \frac{10}{\sqrt{2}}\Delta t\ \dots \ (2)$$

$$\frac{\Delta d_v}{\Delta d_h} = \tan \frac{\pi}{6}\ \dots \ (3)$$

3 equations, 3 unknowns; simply solve. I solved for $\Delta d_h$, and noting that the distance up the incline, $\Delta d = \Delta d_h \sec \frac{\pi}{6}[/tex], we get (assuming we need only two significant digits, I didn't bother to actually make sure of that) [itex]\Delta d = 5.0 m$.

Last edited: Jul 6, 2004
16. Jul 6, 2004

### JohnDubYa

The ramp problem solution:

The motion of the ball is modelled by the displacement equation of motion:

$$\vec{d} = \vec{v}_ot + \frac{1}{2}\vec{a}t^2$$

We know that the displacement vector $$\vec{d}$$ points up the ramp. It has a length d, and a direction of 30 degrees.

The acceleraration vector points downwards and has a magnitude of roughly 10 (I use 10 in my courses rather than 9.8).

The velocity vector has a magnitude of 10 and a direction of 45 degrees.

So all we have to do is replace these vectors with two vectors that point along the preferred direction. So we replace our original displacement vector $$\vec{d}$$ with

$$d\cos(30^\circ)\;({\rm for\; the\; x \;direction})\qquad d\sin(30^\circ)\;({\rm for\; the\; y\;direction})$$

and our original velocity vector with

$$10\cos(45^\circ)\;({\rm for\;the\;x\;direction})\qquad 10\sin(30^\circ)\;({\rm y\;direction})$$

Along the x-direction our displacement equation of motion becomes

$$\vec{d}_x = \vec{v}_{ox}t + \frac{1}{2}\vec{a}_xt^2$$

$$d \cos(30^\circ) = 10\cos(30^\circ)t + \frac{1}{2}(0)t^2$$

Along the y-direction:

$$\vec{d}_y = \vec{v}_{oy}t + \frac{1}{2}\vec{a}_yt^2$$

$$d\sin(30^\circ) = 10\sin(45^\circ)t + \frac{1}{2}(-10)t^2$$

Two equations, two unknowns. And this exact methodology can be used to solve any projectile motion problem.

Last edited: Jul 6, 2004
17. Sep 26, 2004

### Alkatran

First make the problem a lot less ominous: Rotate everything 30 degrees. The mind works so much better with a level plane.

Then:
Calculate the new 'downward' force of gravity
Calculate the upward launch speed (with 15 degree launch angle, of course)
Get time via accel, speed change
Calculate sideways force of gravity
Calculate sideways launch speed
Get distance via time, accel, speed

QED, and I didn't use any 'weird' formulas except for a little rotation