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AP Physics C: Mechanics and E&M

Practice that brings back the problems you miss.

Original problems with new numbers every time, feedback that names the exact mistake, and a review schedule that keeps every unit fresh until the exam in May.

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Unit 3 Conservation of energy 4 of 8

A 4.0 kg block slides from rest down the full 3.0 m length of a frictionless ramp inclined at 30°. What is its speed at the bottom?

A3.83 m/s
B5.42 m/s
Not quite. Kinetic energy is missing its ½.
With K = mv² instead of ½mv², the speed comes out too small by a factor of √2. This problem comes back tomorrow with new numbers.

Each visit takes about fifteen minutes and picks up where you left off.

01
Practice your unit

Tell us which unit your class is on. Problems come from that unit and the ones before it, with fresh numbers every time.

02
Learn from the miss

Every wrong answer choice comes from a real student error. Pick one and you see which error it was and how to fix it.

03
Review on a schedule

A missed problem returns after one day, then three, then seven, until you get it right without help.

See what you get

Five problems from the bank, shown with what happens after you answer. Every problem gets new numbers each time it comes up.

Multiple choiceUnit 1, Kinematics

The graph shows the velocity v of a cart moving along a straight track as a function of time t. What is the displacement of the cart from t = 0 to t = 9 s?

12345678910−4−3−2−10123456t (s)v (m/s)
A9.00 m
B13.0 mCorrect
C17.5 mYour pick
D22.0 m
What you see after a wrong pick
Area below the axis left out
While the velocity is negative, the cart is still moving, just backward. Count the area below the time axis as negative displacement instead of stopping where the graph crosses zero.
This exact problem returns in tomorrow’s review with a new graph.
Multiple choiceUnit 11, Circuits

Four identical light bulbs, A, B, C, and D, 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?

ABCDε
AA > B > C = DCorrect
BA = B = C = D
CA > B > C > DYour pick
DA = B > C = D
What you see after a wrong pick
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 C and D must be equally bright.
Every wrong choice in the bank comes from a real student error like this one.
Typed expressionUnit 3, Energy

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

Your answer
(1/2)*k*x^2/(m*g)Accepted
Preview: h = 12kx2 / mg
Other answers students type
k*x^2/(2*m*g)Accepted
k*x^2/(m*g)Spring energy without the ½
x*sqrt(k/m)Found a speed instead of a height
What you see after you check
Accepted. Any correct form counts.
Your answer matches h = kx22mg. The checker tests your expression at random values, so you never lose credit for writing it a different way.
A typed answer that matches a common mistake gets that mistake’s feedback, just like a wrong choice.
Typed numberUnit 8, Electric fields

Point charge q1 = +2 nC is h = 8.0 cm directly above point P, and point charge q2 = −2 nC is w = 6.5 cm directly to the right of P, as shown. What is the magnitude of the net electric field at P?

hw+q1−q2P
Your answer
5.1e3N/CAccepted
What you see after you check
Accepted: 5.1 × 103 N/C
Anything within 2% of 5100 N/C counts. Type numbers the way you would on a calculator, scientific notation included.
Stuck? Two hints come first, then the full worked solution.
Free responseUnit 8, Gauss’s law

A solid insulating sphere of radius R carries total charge Q spread evenly through its volume.

  1. (a)Use Gauss’s law to derive the field at r < R.Checked
  2. (b)Derive the field at r > R.Checked
  3. (c)Compare the field at R/2 with the field at 2R.Checked
  4. (d)Justify your answer to part (c).Self scored
  5. (e)Sketch E as a function of r from 0 to 3R.Self scored
Score part (e) against the rubric
2 of 3 points
Straight line from the origin rising to a maximum at r = R.
Continuous at r = R, with no jump.
Decreasing, concave up curve for r > R, near one quarter of the peak at 2R.
Parts with a value or an expression are checked for you. Explanations and sketches are scored with a rubric written the way exam readers award points.
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Built for the way the exam is written

Every unit, both exams

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

Write your justification, then score it point by point. Sketch graphs and compare 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

Each topic levels up only with correct answers given without hints, and slips back if you stop practicing it.

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Questions

Who writes the problems?

An AP Physics C teacher. Every problem is original, and every answer is checked by a second reviewer before it goes live.

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No. It is an independent practice site.

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