Hi,
The question is really long, so ill type it all out, and ill show my working below it, im not sure whether what ive done is right...
A website "urban myth" claims that a man in California tied a number of balloons filled with helium to his chair in the garden with a view to gently hovering above the neighborhood. The moment he cut the anchoring cord he shot upwards to a height of about 4000m. Several hours later he was rescued by a helicopter after being spotted by an airline pilot.
a) If the combined masses of the man and the chair was 70kg, calculate their weight
b) what is meant by the term upthrust
c) Show that the upthrust in N from the balloons is about 1.3 V where V is the total volume of balloons in cubic metres. The Density of air is 1.29 kg/m³
d) Write down an expression, in terms of V, for the weight of the helium in the balloons. The density of helium is 0.18 kg/m³
e) Calculate total volume of the balloons required to just lift the man and his chair from the ground. Assume weight of balloon material is negligible.
f) Explain why any viscous drag force can be ignored in previous calculationa) W = mg
==> 70 x 9.81 = 686.7 N
b) Upthrust is the upward force acting on objects moving through fluids and is equal to, according to the Archimedes Principle, the weight of the fluid displaced.
c) I DONT SEEM TO GET THIS ?? :S My answer doesnt match theirs....
Upthrust = Weight of fluid displaced
=> Mass of fluid displaced x Gravity
=> Volume of fluid displaced x Density of fluid displaced x Gravity
Because our balloons had a total volume of V m³ surely the volume of air displaced is V m³.
Density of air => 1.29 kg/ m³
Gravity = 9.81 N / kg
Upthrust = V x 1.29 x 9.81
=> 12.65V
d) Volume x density = mass
=> V x 0.18
Weight = mg
=> 0.18V x 9.81
=> 1.7658V
e) Upthrust = Weight + Viscous Drag (because he is moving upwards the stoke's term acts downwards)
Ignore Viscous Drag
Upthrust = Weight
12.65V = 1.7658V + 686.7
V = 63.09 m³
f) We are calculating the volume of balloons required to lift the man and the chair. At this point the upthrust is just about greater than the total weight, and because the system is hardly moving there isn't much of viscous drag and hence can be ignored.
Correct or Wrong
