1. Consider a physical constant we will call B that has units of Joules per Farad. If the dimensions of this constant are expressed as [A]ª[T] [M]°[L]d then what are the values of a, b, c, and d?
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![1. Consider a physical constant we will call B that has units of Joules per Farad. If the dimensions of this
constant are expressed as [A]ª[T] [M]°[L]d then what are the values of a, b, c, and d?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcba434d-76d4-4036-80a1-f05d1bad2e8d%2F178980ff-f38c-48da-8486-bf4ee942aaa7%2Forkty5i_processed.jpeg&w=3840&q=75)
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- What is the area of a circle which has a diameter equal to 3.138 cm? Hint The area is cm².Now you will use the ruler to measure the dimensions of a block of pure aluminum metal. Make sure you report both the uncertainty and an estimated digit with your answers. V [ Select ] 1 21 1.5 cm +/- .1 cm cm 1.38 cm +/- .01 cm What is the best measurement of the length of this block? 1.35 cm +/- .01 cm 1.3 cm +/- .1 cm 1.40 cm +/- .05 cmIf B is added to A, the result is 8.8î + 3.0ĵ. If B is subtracted from A, the result is -4.61 + 5.6ĵ. What is the magnitude of A? Number i Units
- 2abSoccer fields vary in size. A large soccer field is 144 meters long and 84.4 meters wide. Hint a. What are its dimensions in feet? o Its length is ft. o Its width is b. What are its dimensions in inches? o Its length is o Its width is ft. in. in.a) Acceleration is described as space divided by time squared. Determine the dimensions of acceleration and its SI units.b) Kinetic Energy K has dimensions kg m2/s2. It can be written in terms of momentum p and mass m following the equation below. Determine the dimensions of the momentum and its SI units. c) The unit of force is the newton N, where 1 N = 1 kg m/s2. Determine the dimensions and the SI units of the momentum in terms of newtons.d) Newton’s law of universal gravitation is F =Gm1m2/r2 , where F is the magnitude of the gravitational force exerted by one object on another, m1 and m2 are the masses of the objects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G.
- 3. A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and in cubic centimeters? [1 foot 0.305 m]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 ·…b) In an equation (P+) (V - b) = RT, where P is the pressure, V is the volume, T is the temperature and a, b, R are constants. What is the dimensional formula of ?