Practice · Unlimited problems

Practice Lab

Fresh problems on everything in the module, as many as you like: the work of a force, weight, springs and friction, speeds and distances, power and efficiency, potential energy, conservation of energy and curved paths. Each one comes with hints and a worked solution built from its own numbers, and once you have solved it you can see its energy 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 energy picture of the current problem: usually a work ledger, in which the starting energy plus each work, bar by bar, lands on the final energy, or a force–displacement graph whose shaded area is the work. 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 speed-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 = 7.672), so you can catch a typo before you check.

What you can type
You type	It reads
`sqrt(29.813)` or `√(29.813)`	\(\sqrt{2(9.81)(3)} \approx 7.672\)
`0.5204.08^2`	\(\tfrac12(20)(4.08)^2 \approx 166.5\)
`-0.3509.81*4`	\(-0.3(50)(9.81)(4) = -588.6\)
`1506cos(30°)`	\(150(6)\cos 30^\circ \approx 779.4\)
`2e3` or `2000`	\(2000\)
`4.09`	\(4.09\), a decimal: accepted when it is within 1% of the exact value

Give each answer in the unit shown next to its box: joules, newtons, meters, meters per second or kilowatts. Signs matter for work: a force that opposes the motion does negative work, so type the minus sign. Inside cos, sin and tan, mark degrees with °; a bare number there is read as radians.