91Ó°ÊÓ

What is the percent uncertainty in the measurement $5.48Â\pm 0.25\mathrm{m}$?

You measure the radius of a wheel to be 4.16 cm. If you multiply it by 2 to get the diameter, should you write the result as 8 cm or as 8.32 cm? Justify your answer.

Accuracy represents

(a) repeatability of a measurement, using a given instrument

(b) how close a measurement is to the true value

(c) an ideal number of measurements to make

(d) how poorly an instrument is operating

Estimate the number of days it would take to walk around the earth, assuming 12 h walking per day at$4{\mathrm{kmh}}^{-1}$.

One liter ($1000{\mathrm{cm}}^3$) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick of just one molecule thick, with adjacent molecule just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of$2×{10}^{-10}\mathrm{m}$.

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

An angstrom (symbol$\stackrel{∘}{A}$) is a unit of length, defined as${10}^{-10}\mathrm{m}$, which is on the order of the diameter of an atom.

(a) How many nanometres are there in 1.0 angstrom?

(b) How many femtometers or fermis (the common unit of length in nuclear physics) are there in 1.0 angstrom?

(c) How many angstroms are there in 1.0 m?

(d) How many angstroms are there in 1.0 light-year (See problem 19)?

Jim stands beside a river and wonders how wide it is. He spots a large rock on the bank directly across from him. He then walks 65 strides upstream and judges that the angle between him and the rock, which he can still see, is at${30}^o$downstream (See below figure). Jim measures his stride to be about 0.8 m long. Estimate the width of the river.

Determine the percent uncertainty in$\mathrm{θ}$,and in$\sin \mathrm{θ}$, when (a)$\mathrm{θ}=15°Â\pm 0.5°$, (b)$\mathrm{θ}=75°Â\pm 0.5°$.

If you walked north along one line of longitude until you had changed the latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? (This distance is called a nautical mile.)