8. [16 pts] a. Convert the following to the base SI units (m, kg, s or appropria

Question

8. [16 pts] a. Convert the following to the base SI units (m, kg, s or appropriate combinations) with correct number of significant digits i. 80.0 mph- iii. 25.0 inimin:- b. A student performed an activity to determine the density of a rectangular solid, which then provides some idea of the metal that the solid is made of. Perform all calculations taking into account SIGNIFICANT FIGURES and show all relevant calculations i. He made the following measurements of the dimensions of the solid length: 0.05200 m width: 0.02053 m height:0.00948 m 0.05190 m 0.02050 m 0.00950 m 0.05195 m 0.02050 m 0.00945 m ii. Determine the average value of the following dimensions: ength_ height width iii. Calculate the volume Volume iv. He measured the mass of the cylinder using the electronic balance: v. Determine the density of the cylinder in kg'm again with appropriate Mass: 112.0g significant figures Density-

Explanation / Answer

i)80 mph

we know that 1mph = 0.447 m/s

80 mph = 80 x 0.447 = 35.76 m/s

Hence, 80mph = 35.76 m/s

iii)25 in/min^2

1 in/min^2 = 7.056 x 10^-6 m/s^2

25 in/min^2 = 25 x 7.056 x 10^-6 m/s^2 = 1.76 x 10^-4 m/s^2

Hence, 25 in/min^2 = 1.76 x 10^-4 m/s^2

b)Lav = (0.05200 + 0.05190 + 0.05195)/ 3 = 0.05195 m

Wav = (0.02053 + 0.02050 + 0.02050)/3 = 0.02051 m

Hav = (0.00948 + 0.00950 + 0.00945)/3 = 0.009747 m

Hence, Lav = 0.05195 m ; Wav = 0.02051 m ; Hav = 0.009747 m

iii) V = l w h

V = 0.05195 m x 0.02051 m x 0.009747 m = 1.0385 x 10^-5 m^3

Hence, V = 1.0385 x 10^-5 m^3

iv)we know that density is given by:

density = mass/volume

density = 112 x 10^-3/(1.0385 x 10^-5) = 10784.786 kg/m^3

Hence, density = 10784.786 kg/m^3

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