Practice · Unlimited problems

Practice Lab

Fresh problems on everything in the module, as many as you like: momentum and the impulse of a force, force–time graphs, constant and time-varying forces, conservation of momentum, direct and oblique impact, restitution, and problems in stages. Each one comes with hints and a worked solution built from its own numbers, and once you have solved it you can see its impulse and momentum bookkeeping.

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 an impulse ledger, in which the starting momentum plus each impulse, bar by bar, lands on the final momentum (or, for problems in stages, an energy ledger), or a force–time graph whose shaded area is the impulse. 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 impact-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 = 13.05), so you can catch a typo before you check.

What you can type
You type	It reads
`0.145*(50+40)`	\(0.145(50 + 40) = 13.05\)
`13.05/1.2e-3`	\(13.05/0.0012 = 10\,875\)
`(26+30)/5`	\(\left[2(6) + 3(0)\right]/5 = 2.4\)
`-1.2`	\(-1.2\): a velocity to the left, when right is positive
`sqrt(0.96/1.5)` or `√(0.96/1.5)`	\(\sqrt{0.64} = 0.8\)
`atan(0.6*tan(50°))`	\(\tan^{-1}(0.6\tan 50^\circ)\), in radians unless you add °: type the angle in degrees, e.g. `35.57`

Give each answer in the unit shown next to its box: newton-seconds, kilogram-meters per second, newtons, meters per second, seconds, meters, joules or degrees. Signs matter for velocities after an impact: use the positive direction the problem gives, and type the minus sign for a velocity the other way. Inside cos, sin and tan, mark degrees with °; a bare number there is read as radians.