# Review of 2008 AP Physics C E&M Free Response | Student's Perspective

In summary, the rod swings up and down due to the gravitational force pulling it down (Fgravity), the tension in the cord (Tension), and the force of friction between the hinge and the support (Ffriction).
What did people think? It may have been the hardest thing I've ever seen, and I am a very prolific calc and phys student.

The E&M free response was very very ridiculous, especially #2 where you had to plug in different devices at the terminal and find the current in the parallel resistor. I was completely lost.

For anyone that took it, what did you think?

Well, it was what I was expecting, to be quite honest. Found E&M #3 to be the hardest problem on the whole thing (mainly the first part) but other than that... just another day in AP Physics.

I thought the E&M FRQ's were really straightforward. #1 was ridiculously simple. #2 was just like any other circuit problem, didn't even require much analysis. I think I screwed up #3's first part though. Forgot to square root something.

Everyone was complaining about the mechanics FRQ's but I thought they weren't terribly difficult. Knowing E&M actually helped me with the first problem.

Anyway, we probably shouldn't talk about it until two days.

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I tried doing the entire course independent study as my school doesn't offer it, and my senior year ended up being considerably busier than I anticipated, so I didn't get to finish the material. By Friday I only had done about half of mechanics and less than 1/4 of E&M, so over the weekend I studied for about 15 hours covering the rest of mechanics through my Princeton Review book and completely ignoring E&M. Needless to say, that didn't work very well! The Princeton Review book was insanely difficult, and had me really worried for the test, but I was actually surprised at how relatively easy the exam seemed. I'm expecting a 3 in mechanics and an almighty 1 in E&M (my first and only 1 on an AP exam, and probably only non-passing one, was in physics, my intended major ), so yeah I found it difficult, but I think if I had studied diligently throughout the year the exams wouldn't be too difficult to score a 5 on.

So, overall, challenging AP exams, but I think if someone has good preparation over the year (unfortunately I hear of all the AP Physics teachers who have no idea what they're doing, and sometimes skip over major concepts) they are not at all insurmountable. The generous curve assures that: in 2004 you only needed a 54.4% in mechanics for a 5! And E&M traditionally is curved even more than mechanics!

is it just me or wasnt the multiple choice for E&M insanely difficult...time juz flew for me...and I was left with 5 mins for 10 ten questions!
"wht happens to the enrgy/voltage of a capacitor as blah blah"...this question took soo much of my time!

AP Physics C 2008 FRQ1

Okay, 48 hours have passed, so we can now discuss the FRQs.

here is the first mechanics FRQ:
1. A skier of mass M is skiing down a frictionless hill that makes an angle θ with the horizontal, as shown in the diagram. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F= -bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M, b, θ , and fundamental constants.
(a) On the dot below that represents the skier, draw a free-body diagram indicating and labeling all of the forces that act on the skier while the skier descends the hill.
(b) Write a differential equation that can be used to solve for the velocity of the skier as a function of time.
(c) Determine an expression for the terminal velocity V(sub T) of the skier.
(d) Solve the differential equation in part (b) to determine the velocity of the skier as a function of time, showing all your steps.

I have a couple of questions. For the free-body diagram, should the drag force point back horizontally or back up the slope? Also, what's the differential equation in part (b)? How do you solve it?

Here's what I got, but I think it's wrong.
(b) m(d^2x/dt^2)=mgsinθ-b(dx/dt)
(c) bv=mgsinθ ===> v=(mgsinθ)/b
(d) ma=mgsinθ-bv ===> mv=mgt*sinθ-bx ===> v=(mgt*sinθ -bx)/m

AP Physics C 2008 FRQ2

The horizontal uniform rod shown above has length 0.60 m and mass 2.0 kg. The left end of the rod is attached to a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is supported by a cord that makes an angle of 30 with the rod. A spring scale of negligible mass measures the tension in the cord. A 0.50 kg block is also attached to the right end of the rod.
(a) On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force vector originating at its point of application.
(b) Calculate the reading on the spring scale.
(c) The rotational inertia of a rod about its center is (1/12)ML^2 , where M is the mass of the rod and L is its length. Calculate the rotational inertia of the rod-block system about the hinge.
(d) If the cord that supports the rod is cut near the end of the rod, calculate the initial angular acceleration of the rod-block system about the hinge.

Here's what I got:
(a) If I made a mistake, I think I made it here. I only drew vectors for F(sub T), W(sub rod), and W(sub block). Here's my question: Does the contact point at the hinge provide a force? If so, everything else I did was wrong.

(b) ma=0=F(sub T) - W(sub rod) - W(sub block) ===> F(sub T) = W(sub rod) + W(sub block) = 25N.

(c) I = I(sub rod) + I(sub block) = I(sub rod, center) + M(1/2L)^2 + M(sub block)L^2 = 1/3ML^2+M(sub block)L^2=.42 kg*m^2

(d) torque=I*alpha ===> alpha=torque/.42 kg*m^2
torque = L(F(sub T) - 1/2W(sub rod) - W(sub block))=(.6m)(25N - 10 N - 5 N) = 6 N*m ===> alpha = 6/.42=14.29rad/s^2

AP Physics C 2008 FRQ3

Here's the third FRQ:

In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord
from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student
allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded
in the table below:
Weight (N) 0 10 15 20 25
Length (m) 0.60 0.97 1.24 1.37 1.64

(a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through the data.
(b) Use the best-fit line you sketched in part (a) to determine an experimental value for the spring constant k of the cord.
The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at
which the top of the cord is tied to the rod, as represented above. When the object is released from rest, it falls
1.5 m before stopping and turning around. Assume that air resistance is negligible.
(c) Calculate the value of the unknown mass m of the object.
(d) i. Calculate how far down the object has fallen at the moment it attains its maximum speed.
ii. Explain why this is the point at which the object has its maximum speed.
iii. Calculate the maximum speed of the object.

AP Physics C 2008 FRQ3 (continued)

Part (b) was the easiest thing ever: 0=mg-ky ===> ky=mg, so k is the the slope of the graph. However, I can't think of how to do parts (c) and (d) right now. I haven't taken the test yet, since my school ordered the wrong test. I'm going to take it during the late testing, and I'd like to use these as practice. Any ideas on how to do these FRQs?

For reference, here are the original problems:

http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_mech_frq.pdf

here is the first mechanics FRQ:
I have a couple of questions. For the free-body diagram, should the drag force point back horizontally or back up the slope? Also, what's the differential equation in part (b)? How do you solve it?

Here's what I got, but I think it's wrong.
(b) m(d^2x/dt^2)=mgsinθ-b(dx/dt)
(c) bv=mgsinθ ===> v=(mgsinθ)/b
(d) ma=mgsinθ-bv ===> mv=mgt*sinθ-bx ===> v=(mgt*sinθ -bx)/m

Drag force goes back up the slope. The force equation is really a vector equation, $\vec{F} = -b \vec{v}$. v is down the slope, so F must point exactly up the slope due to the negative sign.

(b) You're solving for velocity, so you need the equation in terms of v, not x. And solving (this is exactly like an RC or LC circuit if you've done E&M. I only remembered how to do it for the test because we recently covered solving this type of diff eq. in E&M.):
$$m\frac{dv}{dt} = m g \sin(\theta) - b v$$
$$\frac{dv}{dt} = g \sin(\theta) - \frac{b}{m} v$$
Seperating variables (divide both sides by RHS and multiply the dt to the right) and integrating both sides:
$$\int_0^{v_f} \frac{dv}{g \sin(\theta) - \frac{b}{m} v} = \int_0^{t}dt$$
u-substitution:
$$u = g \sin(\theta) - \frac{b}{m} v$$
$$du = -\frac{b}{m}$$
Note that I put the negative sign to the right. This saves a bunch of annoying algebra later on (I forgot to do this during the test, wasted time). I'm also going to move the constant introduced from du to the right.
$$\left[ \log\left(g \sin(\theta) - \frac{b}{m} v\right) \right]_{0}^{v_f} = \log\left(\frac{g \sin(\theta) - \frac{b}{m} v}{g \sin(\theta)}\right) = -\frac{b}{m}t$$

Do the algebra yourself, I'm too lazy to finish.

(a) On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force vector originating at its point of application.

If I made a mistake, I think I made it here. I only drew vectors for F(sub T), W(sub rod), and W(sub block). Here's my question: Does the contact point at the hinge provide a force? If so, everything else I did was wrong.
(a) Yes. The rod must be in equilibrium. Therefore all torques and forces must balance out. The tension force has an x-component that points left. Therefore the hinge must only provide a force to the right that balances it out. It doesn't affect any of the later answers though. For part d, the tension force torque should be multiplied by sin(30 deg). In fact, there shouldn't even be a tension force, since the rope is cut.

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Continuing, forum downtime made me miss the edit window.

#3:

Part c is definitely a conservation of energy problem. At the top, it has mgh potential energy, and at the lowest point, it has maximum spring potential energy and zero gravitational potential energy. Both points have no kinetic energy. This allows us to relate mass and height it fell.

Part d:
$$0 = kx^2 + mgx + \frac{1}{2} m v^2$$
To maximize v based on x, solve for v, set $dv/dx = 0$ and solve for x. The denominator of $dv/dx$ is going to be pretty long but I just ignored it and found the numerator only.
$$-mg - 2 k x = 0$$

Then just plug x back into the equation for v.

Hope this helps. And I'm not 100% I'm right for any of this, of course.

It's pretty surprising. I think two of the hardest parts of the FRQ's (#1 solving the diffeq, #3 finding the spring compression that maximized velocity) were pretty standard problems that any textbook should have (or teacher have you do).

Now back to studying for economics tomorrow..

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On the Mechanics the first problem is an easy give me because it's just like all of the other drag force problems from the past.

The second problem is very unlike the typical rotation problems you usually see on the AP exam. However it's not atypical in the sense of being harder, it's atypical in the sense of being easier. The rotation problems are usually either collision problems or dynamics problems. Until the last part this was a statics problem. In the class that I taught, we did a lab just like that problem... and boy do I hope that my students remembered it!

Most of the third problem is a breeze provided that you can follow instructions, make plots and find best fit lines. I make my students use a ruler just because even if you think your line is straight and thin enough, the reader might disagree. Play it safe. Especially since you have to use your best fit line to find the slope.

I forgot to include part (e) of the first FRQ.

(e) On the axes below, sketch a graph of the acceleration a of the skier as a function of time t, and indicate the initial value of a. Take downhill as positive.

I just made a piecewise graph: a straight line with negative slope from the initial a to some point on the t-axis, and then a straight line at a=0 from then on.

As for the initial value of a, I used mgsinθ, since the initial velocity is zero, making the drag force zero.

Okay, I've corrected my mistakes (I think). The correct answers (unless you can find any other mistakes) are:
1. b) dv/dt=gsinθ-(b/m)v
c) v(sub T)=Mgsinθ/b
d) v=(mgsinθ-me^(-bt/m))/b
2. b) F(sub T) = 50N
c) I = .42 kg*m^2
3. b) k = slope

I forgot to include part (e) of the first FRQ.

(e) On the axes below, sketch a graph of the acceleration a of the skier as a function of time t, and indicate the initial value of a. Take downhill as positive.

I just made a piecewise graph: a straight line with negative slope from the initial a to some point on the t-axis, and then a straight line at a=0 from then on.

As for the initial value of a, I used mgsinθ, since the initial velocity is zero, making the drag force zero.

You screwed the plot up, but I bet you'll get full credit. Your plot reflects your wrong solution, and they grade based on consistency and not correctness (that is to ensure that they don't penalize repeatedly for the same mistake).

The acceleration is an exponential decay. You could have reasoned it through even if you did the math wrong before because as you reach terminal velocity the acceleration goes to zero, also the equation never changes so the curve needs to be everywhere continuous. Initially since it starts from rest, there is no drag force, and the initial value should be simply gsin. If you drew a curve with everywhere positive concavity that was continuous everywhere, started at gsin and asymptotically reaches 0 at infinity you would have had it.

Limiting behavior is the key to do all of those sketch a plot or identify a plot without breaking a sweat.

I have a question. The derivative of the velocity function (as determined by solving the differential equation) is e^(-bt/m). As DavidWhitbeck stated, this function asymptotically reaches 0 at infinity. However, from part (b), a=gsinθ-(b/m)v, which reaches 0 whenever (b/m)v is equal to gsinθ. The graph of the first is consistent with DavidWhitbeck's exponential decay description, and the graph of the second is consistent with my piecewise continuous graph, since after reaching the terminal velocity, acceleration is zero. Which one is correct? Maybe my original equation for part (b) is wrong. Any opinions?

I have a question. The derivative of the velocity function (as determined by solving the differential equation) is e^(-bt/m). As DavidWhitbeck stated, this function asymptotically reaches 0 at infinity. However, from part (b), a=gsinθ-(b/m)v, which reaches 0 whenever (b/m)v is equal to gsinθ. The graph of the first is consistent with DavidWhitbeck's exponential decay description, and the graph of the second is consistent with my piecewise continuous graph, since after reaching the terminal velocity, acceleration is zero. Which one is correct? Maybe my original equation for part (b) is wrong. Any opinions?

Yeah I screwed up my graph on the test. Drew a linearly downsloping line and made it zero after it hit the axis. Terminal velocity is never actually achieved, acceleration actually never hits zero, only in the limit as time goes to infinity.

They want acceleration as a function of time, not as a function of velocity.

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Ohhh... I see what you mean. Thanks!

In regards to the FRQs of Electricity and Magnetism,
for number one, how would you determine the charge induced on the inner and outer surfaces?
is it simply a matter of surface area?

im not allowed to post the url, but the questions are available at apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_em_frq.pdf

jderm said:
In regards to the FRQs of Electricity and Magnetism,
for number one, how would you determine the charge induced on the inner and outer surfaces?
is it simply a matter of surface area?

im not allowed to post the url, but the questions are available at apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_em_frq.pdf

The positive inner sphere polarizes the outer sphere, pulling negative charges to the inner surface, and leaving positive charges on the outer surface.

if part c is asking for a graph of E as a function of r,

from origin to a
=zero

from a to b
=zero

from b to c
=zero

from c to d
decreasing 1/r^2

this is the only thing i can conclude based on the field within a charged sphere being equal to zero

Do you know Gauss's law? Between the two spheres, there is still a net charge enclosed so therefore there's an electric field. It's only zero inside the conductors.

how were the FR questions in the late physics C mechanics exam?

The FRQs were ok... very few calc questions, but heavy on the physics intuition. One part was surprisingly easy: I kept thinking I must have overlooked something or done something wrong. The question involved a wheel rolling down an inclined plane, and it asked for the translational acceleration. I put a = g*sin(theta).

they were easier than expected. and i got that answer too! what about the other questions?

i thought it was easy! i got a 5 on both E&M and Mechanics! :]

Yep, I got a 5 on mine too. Too bad the FRQs aren't released for late testers... I'd really like to see what I wrote.

## 1. What is the purpose of a review of the 2008 AP Physics C E&M Free Response from a student's perspective?

The purpose of a review of the 2008 AP Physics C E&M Free Response from a student's perspective is to gain insight into the experience of taking the exam and to learn from the mistakes and successes of others in order to improve one's own performance.

## 2. What were the most challenging concepts or questions on the 2008 AP Physics C E&M Free Response?

The most challenging concepts or questions on the 2008 AP Physics C E&M Free Response varied from student to student, but some common ones included topics such as electromagnetic waves, Gauss's Law, and electric potential.

## 3. How can reviewing the 2008 AP Physics C E&M Free Response help with studying for the exam?

Reviewing the 2008 AP Physics C E&M Free Response can help with studying for the exam by providing a real-life example of what to expect on the exam and allowing students to identify areas of weakness that they can focus on in their studying.

## 4. What tips or strategies can be learned from a student's perspective on the 2008 AP Physics C E&M Free Response?

From a student's perspective, tips and strategies that can be learned from the 2008 AP Physics C E&M Free Response include managing time effectively, showing all work and calculations clearly, and practicing with past exams to get a feel for the format and types of questions.

## 5. How can a student use the 2008 AP Physics C E&M Free Response review to improve their overall performance on the exam?

A student can use the 2008 AP Physics C E&M Free Response review to improve their overall performance on the exam by analyzing their mistakes and understanding where they went wrong. They can also use the review to identify their strengths and weaknesses and focus on studying those areas in preparation for the exam.

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