Question

Four bodies are located in a region where g = 9.67 m/s2

.Body1 = 750 gm; Body2 = 4 poundals; body3 = 4.5 N and body4 = 32.2 lbf.

a) What is the total mass expressed in lbm?

b) What will be the total weight (lbf) if the bodies are located 15,000 ft above

the earth’s surface? (gravitational acceleration decreases by 0.003 ft/s2

for every 1000 ft ascent above sea level)

c) At what distance (miles) from the earth’s surface will these objects weigh

zero.

Answer 1

$1m/s^6 = 3.28fts^{-2}\\ 1lbf=1lbm \times 31.72fts^{-2}(9.67ms^{-2})\\1kg=2.205lbm\\1ms^{-2}=3.28fts^{-2}\\1poundas=0.128235N\\9.67ms^{-2}=31.72fts^{-2}\\5280ft=1mile$

$(a)~Body~1=750g=0.75kg\\ ~~~~~~~~~~~~~=(0.75 \times2.205)lbm=1.6537lbm$

$~Body~2=4~poundals\\~~~~~~~~~~~~~~~~~~~=(4\times 0.138235)N=0.55294N\\\therefore0.55294N\div9.67=0.0572kg=(0.0572\times2.205)lbm=0.1261lbm$

$~Body~3=4.5N\\ ~~~~~~4.5\div 9.67=0.4654kg=(0.4654\times 2.205)lbm=1.1262lbm$

$~Body ~4=32.2lbf\\~~1lbf=1lbm \times 31.72fts^{-2}\\ \implies32.2\div31.72=1.0151ibm$

$Total~mass=1.6537+0.1261+1.1262+1.0151=3.9211lbm$

$(b) ~at~15~000ft~g~decreses~by=\frac{0.003\times15~000}{1000}=0.045fts^{-2}\\g~at~that~location=31.72-0.045=31.675fts^{-2}\\the~total~weight~at ~=the~location=3.9211\times31.675=124.2lbf$

$(c)~for~the ~object~to weigh~zero, g=0\\\therefore decrease~in~gravity~\frac{0.003\times h}{1000}=31.72\\h=10~573~333.33ft=(10~573~333.33\times5280)miles=2002.53miles$