Question
Can you help me set up calculations for A mountain climber friend with a mass of 80 kg pondersthe idea of attaching a helium balloon to himself to effectivelyreduce his weight by 25% when he climbs. He wonders what heapproximate size of such a balloon would be. Can you help me set up calculations for A mountain climber friend with a mass of 80 kg pondersthe idea of attaching a helium balloon to himself to effectivelyreduce his weight by 25% when he climbs. He wonders what heapproximate size of such a balloon would be.
Explanation / Answer
You have requested that only hints beprovided. We shall declare the downward direction to be negative, upwardto be positive. M = mass of man m = mass of helium air in balloon ---- Mass of man = M = 80 kg g = 9.8 m/s2 Weight of Man = Fm = -Mg = -784 N Direction of man's weight is downward, towards center ofEarth. --- Man wisher to reduce weight by 25% F = M25%g = (784N)0.25 = 196 N Net Force of balloon must be 196 N Direction of balloon's net force is upward. ---- Net force on balloon is: Fnet = M25%g = 196 N = -mg +Fbouy where -mg is the downward weight of the helium air inballoon, Fbouy is the upward bouyant force ------ ------ Fbouy = hVg where h is the density of helium air = 0.179 g/L =0.000179 kg/L V is the volume of the balloon, or the volume of airdisplaced, which we are solving for, once you have the volume use V = (4/3)r3 to solve for radius to describethe size of the balloon. -----