Menu Close

A-rescue-cable-attached-to-a-helicopter-s-weighs-2-lb-ft-A-man-180-lb-grabs-the-end-of-the-rope-and-his-pulled-from-the-ocean-into-the-helicopter-How-much-work-is-done-in-lifting-the-man-if-th




Question Number 125052 by bramlexs22 last updated on 08/Dec/20
 A rescue cable attached to a   helicopter′s weighs 2 lb/ft.   A man 180−lb grabs the end   of the rope and his pulled   from the ocean into the helicopter.  How much work is done in   lifting the man if the helicopter  is 40 ft above the water ?  (a) 8800 lb−ft  (b) 1780 lb−ft  (c) 7280 lb−ft  (d) 10,400 lb−ft
$$\:{A}\:{rescue}\:{cable}\:{attached}\:{to}\:{a}\: \\ $$$${helicopter}'{s}\:{weighs}\:\mathrm{2}\:{lb}/{ft}.\: \\ $$$${A}\:{man}\:\mathrm{180}−{lb}\:{grabs}\:{the}\:{end}\: \\ $$$${of}\:{the}\:{rope}\:{and}\:{his}\:{pulled}\: \\ $$$${from}\:{the}\:{ocean}\:{into}\:{the}\:{helicopter}. \\ $$$${How}\:{much}\:{work}\:{is}\:{done}\:{in}\: \\ $$$${lifting}\:{the}\:{man}\:{if}\:{the}\:{helicopter} \\ $$$${is}\:\mathrm{40}\:{ft}\:{above}\:{the}\:{water}\:? \\ $$$$\left({a}\right)\:\mathrm{8800}\:{lb}−{ft} \\ $$$$\left({b}\right)\:\mathrm{1780}\:{lb}−{ft} \\ $$$$\left({c}\right)\:\mathrm{7280}\:{lb}−{ft} \\ $$$$\left({d}\right)\:\mathrm{10},\mathrm{400}\:{lb}−{ft} \\ $$
Commented by mr W last updated on 08/Dec/20
W=180×40+2×40×((40)/2)=8800 lb−ft  ⇒answer (a)
$${W}=\mathrm{180}×\mathrm{40}+\mathrm{2}×\mathrm{40}×\frac{\mathrm{40}}{\mathrm{2}}=\mathrm{8800}\:{lb}−{ft} \\ $$$$\Rightarrow{answer}\:\left({a}\right) \\ $$
Commented by benjo_mathlover last updated on 08/Dec/20
sir please what your formula
$${sir}\:{please}\:{what}\:{your}\:{formula} \\ $$
Commented by mr W last updated on 08/Dec/20
man:  weight =180 lb  distance moved=40 ft  work done=180×40 lb−ft    rope:  length=40ft  weight=2×40 lb  distance moved=((40)/2) ft  (center of mass of rope is ((40)/2) beneath  the helicopter)  work done=2×40×((40)/2) lb−ft
$${man}: \\ $$$${weight}\:=\mathrm{180}\:{lb} \\ $$$${distance}\:{moved}=\mathrm{40}\:{ft} \\ $$$${work}\:{done}=\mathrm{180}×\mathrm{40}\:{lb}−{ft} \\ $$$$ \\ $$$${rope}: \\ $$$${length}=\mathrm{40}{ft} \\ $$$${weight}=\mathrm{2}×\mathrm{40}\:{lb} \\ $$$${distance}\:{moved}=\frac{\mathrm{40}}{\mathrm{2}}\:{ft} \\ $$$$\left({center}\:{of}\:{mass}\:{of}\:{rope}\:{is}\:\frac{\mathrm{40}}{\mathrm{2}}\:{beneath}\right. \\ $$$$\left.{the}\:{helicopter}\right) \\ $$$${work}\:{done}=\mathrm{2}×\mathrm{40}×\frac{\mathrm{40}}{\mathrm{2}}\:{lb}−{ft} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *