The equation for calculating the work performed when a piston in a cylinder expands against a  constant pressure is w = −P ∙ΔV, where ΔV is the change in volume inside the cylinder. How much  work is performed (in joules) when a piston pushes against a constant pressure of 1.21 atm, resulting  in a volume change of 2.56 mL? (Hint: First determine the units that must be used for each term in the  equation.)(101,325 Pa = 1 atm)

An Olympic-size swimming pool is 50 m long, 25 m wide, and 2 m deep. In terms of volume, this pool, when full, holds how many kilogallons of water? Use the following equivalences: 1 gallon = 3.8 L     1 kilogallon = 103 gallon      1 L = 103 mL     for water: 1 mL = 1 cm3      1 m = 100 cm   [Numerical Problem: Just write the numerical answer without units. Express your answer to 2 significant figures in standard notation]

If g(v) is the fuel efficiency, in miles per gallon, of a car going at v miles per hour, what are the units of g′(90)? What is the practical meaning of g′(55)=−0.54?

Still think that unit conversion isn't important? Here is a widely publicized, true story about how failing to convert units resulted in a huge loss. In 1998, the Mars Climate Orbiter probe crashed into the surface of Mars, instead of entering orbit. The resulting inguiry revealed that NASA navigators had been making minor course corrections in SI units, whereas the software written by the probe's makers implicitly used British units. In the United States, most scientists use Sl units, whereas most engineers use the British, or Imperial, system of units. (Interestingly, British units are not used in Britain.) For these two groups to be able to communicate to one another, unit conversions are necessary. The unit of force in the SI system is the newton (N), which is defined in terms of basic Sl units as 1 N=1 kg · m/s?. The unit of force in the British system is the pound (lb), which is defined in terms of the slug (British unit of mass), foot (ft), and second (s) as 1 lb =1 slug ·…

Please use one of the following formulas: F=-k∆d   f=(1/2π)(√(k/m))    T=2π√(m/k)   f=(1/2π)(√(g/L))    T=2π√(L/g)   v=d/t   v=λf   fd=fs(v+vd)/(v-vs)   f=1/T   T=1/f   v=4Lf   v=2Lf   f=(1/2L)√(FT/μ)

A hot tub with a surface area of 28 ft2 is filled with water to a depth of 29 in . Hint: volume is calculated as area × height (A × h). A) What is the volume of water in the tub, in liters? Express your answer to two significant figures and include the appropriate units. B) How many kilojoules are needed to heat the water from 59∘F to 103 ∘F? Express your answer to two significant figures and include the appropriate units. C) If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 59∘F to 103∘F? Express your answer to two significant figures and include the appropriate units.

A relationship is found between the number density of cars on a freeway during rush hour, N, and distance. The relationship can be written as k a'N No dr? From this you can conclude that O w = V No O v = No No O v =