Practice · Unlimited problems

Practice Lab

Fresh problems on everything in the module, as many as you like: Newton's second law, free-body diagrams and elevators, friction, inclines, cords and pulleys, forces that vary, curves and pendulums, banked curves, crests and loops, and systems of particles. Each one comes with hints and a worked solution built from its own numbers, and once you have solved it you can see its force picture: the forces, bar by bar, landing on \(ma\).

Practice problems

Choose a topic, or Mixed for a bit of everything. Type your answer and press Check (or Enter). Stuck? Take a hint, or open the worked solution, then try another problem of the same kind.

Topic

Streak 0 Best 0 Solved 0

Problem code …

Figure P.1 The picture behind the current problem: usually a force ledger, in which the forces along one direction, bar by bar, land on \(ma\) (or on \(mv^2/\rho\) toward the center of a curve), or a graph whose shaded area gives the change in the motion. It stays hidden until you solve the problem or open its solution, so it never gives the answer away.

Load a problem by its code

Every problem has a code such as incline-40718, shown above the problem and in the page address. The same code always gives the same problem, so you can send one to a classmate or your instructor, or come back to it later.

Problem code

Your progress

Your streak counts problems solved on the first try, in a row. Hints are fine. A wrong answer, or opening the solution before you answer, starts the streak again.

Problems by topic. Rate = first-try solves as a share of problems tried.
Topic	Tried	First try	Solved	Rate

Typing answers

Answer boxes understand arithmetic, so you can type the expression you wrote on paper instead of working it out on a calculator first. Each box shows how it read your input (for example = 1.962), so you can catch a typo before you check.

What you can type
You type	It reads
`(4-0.28)9.81/12`	\((4 - 0.2 \times 8)(9.81)/12 = 1.962\)
`129.81sin(25°)`	\(12(9.81)\sin 25^\circ = 49.75\)
`sqrt(0.69.8180)` or `√(0.69.8180)`	\(\sqrt{470.9} = 21.70\)
`1200*(9.81-20^2/50)`	\(1200(9.81 - 400/50) = 2172\)
`-2.5`	\(-2.5\): an acceleration to the left, when right is positive
`atan(25^2/(9.81*120))`	\(\tan^{-1}(0.531)\), in radians: for an angle answer, type it in degrees, e.g. `27.96`

Give each answer in the unit shown next to its box: newtons or kilonewtons, meters per second, meters per second squared, kilograms, seconds, meters or degrees; a coefficient of friction has no unit. Signs matter where the problem names a positive direction: type the minus sign for a velocity or an acceleration the other way. Inside cos, sin and tan, mark degrees with °; a bare number there is read as radians.