Unit conversions.(a) convert 10,000 dynes to units of lbm ∙ ft/s^2 and lbf(b) convert 0.2 atm to units of kpa and lbf/in^2(c) convert 37 °c (physiological temperature) to units of °f and k.(d) convert 50 in 2 ∙ lbm/s^2 units of joules and cal.

(a)  0.72 lbm· ft/s²

(b)  20.3 kPa,  2.94 lbf / in²

(c)  98.6 ºF,  310 K

(d)  1.5 x 10⁻² J,  6.1 x 10⁻² cal

Explanation:

Our strategy here will be to find the conversion factors for the quantities we are asked in each part, and perform the calculations.

(a) 10,000 dynes to lbm ·ft/s²

here we are asked to convert  the  force of 10,000 dynes to lbm ·ft/s². Recall that F= ma ( m= mass, a = acceleration), thus

10,000 dynes = 10 g cm/s²

converting the force

10,000 g cm/s² x (1 lbm/454 g) x (1 ft / 30.48 cm ) /s² = 0.72 lbm· ft/s²

(b)

1 atm = 101.33 pa

0.2 atm x ( 101.33 kPa ) = 20.3 kPa

1 atm = 14.7 lbf / in²

0.2 atm x ( 14.7 lbf / in² /atm ) = 2.94 lbf / in²

(c) The formula for the conversion from ºC to ºF is:

ºF = 9/5 ºC +32

ºF = 9/5 ( 37ºC) + 32 = 98.6 ºF

K = ºC + 273

K = (37 + 273) K = 310 K

(d) 50 in²·lbm/s² to joules and calories

Since the unit in² ·lbm/s² is not that common, lets convert it using their definition.

These are energy units, and we know the energy is the force times distance. In turn force is mass times acceleration so that the units of energy are mass time distance per time squared.

Joules is the unit of energy  in the metric system.

50 in² lbm/s² = 50 in²x ( 2.54 cm/in x 1m /100cm)² x (1lbm x 0.454 Kg/lbm)/s²

= 1.5 x 10⁻² Kg m²/² =  1.5 x 10⁻² J

To convert to cal it wilñl be easier to use the value in joules just calculated:

1.5 x 10⁻² J x  (4.184 cal/J) = 6.1 x 10⁻² cal