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AP Physics C: Mechanics and E&M

Practice AP Physics C problems and review the ones you miss.

The problems are original, and the numbers change each time you see one. A wrong answer tells you which mistake you made, and the problems you miss go into a daily review until you can solve them on your own.

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Unit 3 Conservation of energy 4 of 8

A 4.0 kg4.0\ \text{kg} block slides from rest down the full 3.0 m3.0\ \text{m} length of a frictionless ramp inclined at 30∘30^\circ. What is its speed at the bottom?

A3.83 m/s3.83\ \text{m/s}
B5.42 m/s5.42\ \text{m/s}
Incorrect: kinetic energy without the 12\tfrac{1}{2}
Using K=mv2K = mv^2 instead of K=12mv2K = \tfrac{1}{2}mv^2 makes the speed too small by a factor of 2\sqrt{2}. You will get this problem again in tomorrow’s review, with different numbers.

A typical session takes about fifteen minutes, and the site saves your place.

01
Practice your unit

Choose the unit your class is on. You get problems from that unit and the earlier ones, and the numbers change every time.

02
See what went wrong

Each wrong answer choice is based on a mistake students actually make. If you pick one, the site tells you which mistake it was and how to fix it.

03
Review on a schedule

If you miss a problem, you get a new version of it one day later, then three days later, then a week later, until you solve it without hints.

Example problems

Here are five problems from the site and what you see after you answer each one. The numbers change every time a problem is shown.

Multiple choiceUnit 1, Kinematics

The graph shows the velocity vv of a cart moving along a straight track as a function of time tt. What is the displacement of the cart from t=0t = 0 to t=9 st = 9\ \text{s}?

12345678910−4−3−2−10123456t (s)t\ (\text{s})v (m/s)v\ (\text{m/s})
A9.00 m9.00\ \text{m}
B13.0 m13.0\ \text{m}Correct
C17.5 m17.5\ \text{m}Your pick
D22.0 m22.0\ \text{m}
What you see after a wrong answer
Area below the axis left out
While the velocity is negative, the cart is still moving, but backward. Count the area below the time axis as negative displacement instead of stopping where the graph crosses zero.
You will get this problem again in tomorrow’s review, with a different graph.
Multiple choiceUnit 11, Circuits

Four identical light bulbs, AA, BB, CC, and DD, are connected to an ideal battery as shown. Each bulb acts as a resistor with the same constant resistance. Which ranking from brightest to dimmest is correct?

AABBCCDDε\varepsilon
AA>B>C=DA > B > C = DCorrect
BA=B=C=DA = B = C = D
CA>B>C>DA > B > C > DYour pick
DA=B>C=DA = B > C = D
What you see after a wrong answer
Thought current is used up along the path
A bulb converts electrical energy, but it does not consume current. Bulbs in series carry exactly the same current, so CC and DD must be equally bright.
Each wrong choice on the site is based on a real student mistake like this one.
Typed expressionUnit 3, Energy

A block of mass mm on a frictionless horizontal surface is pushed against a spring with spring constant kk, compressing it a distance xx. The block is released and slides up a frictionless ramp. What maximum height does it reach? Answer in terms of mm, kk, xx, and constants.

Your answer
(1/2)*k*x^2/(m*g)Accepted
Reads as 12kx2mg\displaystyle \frac{\frac{1}{2} k x^{2}}{m g}
Other answers students type
k*x^2/(2*m*g)Accepted
k*x^2/(m*g)Spring energy without the 12\tfrac{1}{2}
x*sqrt(k/m)Found a speed instead of a height
What you see after you check
Correct. Any equivalent form is accepted.
Your answer is equal to h=kx22mgh = \dfrac{kx^2}{2mg}. The checker compares expressions by plugging in random values, so an equivalent form is never marked wrong.
If a typed answer matches a common mistake, you get the same feedback you would get for that wrong choice.
Typed numberUnit 8, Electric fields

Point charge q1=+2 nCq_1 = +2\ \text{nC} is h=8.0 cmh = 8.0\ \text{cm} directly above point PP, and point charge q2=−2 nCq_2 = -2\ \text{nC} is w=6.5 cmw = 6.5\ \text{cm} directly to the right of PP, as shown. What is the magnitude of the net electric field at PP?

hhww+q1q_1−q2q_2PP
Your answer
5.1e3N/C\text{N/C}Accepted
What you see after you check
Correct: 5.1×103 N/C5.1 \times 10^{3}\ \text{N/C}
Any answer within 2% of 5100 N/C5100\ \text{N/C} is accepted. You can type numbers the way you would on a calculator, including scientific notation.
If you are stuck, you can open two hints and then the full worked solution.
Free responseUnit 8, Gauss’s law

A solid insulating sphere of radius RR carries total charge QQ spread evenly through its volume.

  1. (a)Use Gauss’s law to derive the field at r<Rr < R.Checked
  2. (b)Derive the field at r>Rr > R.Checked
  3. (c)Compare the field at R/2R/2 with the field at 2R2R.Checked
  4. (d)Justify your answer to part (c).Self scored
  5. (e)Sketch EE as a function of rr from 00 to 3R3R.Self scored
Score part (e) against the rubric
2 of 3 points
Straight line from the origin rising to a maximum at r=Rr = R.
Continuous at r=Rr = R, with no jump.
Decreasing, concave up curve for r>Rr > R, near one quarter of the peak at 2R2R.
Parts with a number or an expression are checked automatically. You score your own explanations and sketches with a rubric written the way exam readers award points.
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Matched to the AP Physics C exams

Both courses, unit by unit

Problems are sorted into the units of Mechanics (Units 1 to 7) and Electricity and Magnetism (Units 8 to 13), in the order most classes teach them.

Free response with scoring guides

You write your justification and then score it point by point. You can also sketch graphs and compare them with the key.

Answers in your own form

Type expressions like 1/2 mv^2 or sqrt(2gh). Any equivalent form is accepted.

A map of what you know

A topic moves up a level only when you answer correctly without hints, and it moves down if you stop practicing it.

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Questions

Who writes the problems?

An AP Physics C teacher writes them. Every problem is original, and a second reviewer checks each answer before it goes on the site.

Is FivePhysics connected to the College Board?

No. It is an independent practice site.

Can I use it on my phone and my school computer?

Yes. When you sign in, your reviews and progress are available on any device.

What does it cost?

Practice, review, and the mastery map are free. Premium will add a set builder, timed exams, and full worked solutions.