Answer:
(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
