A 100 kg (when empty) cylindrical bottle of gas, containing 100 l of air at a pressure of 100 atmospheres, falls over on the lab floor, breaking the valve. This leaves a circular hole of radius 2.0 cm at the end of the bottle, through which the air escapes in a direction parallel to the long axis of the bottle.
(a) Let the friction coefficient between the bottle and the floor be μ = 0.4, and suppose that the air escapes at a constant rate Δ M/Δ t = 2.0 kg/s. What is the acceleration imparted to the bottle by the escaping gas?
(b) Suppose that the acceleration imparted to the bottle by the escaping gas and that you calculated in part (a) remains the same until the air has finished escaping at the constant rate Δ M/Δ t. What would be the total distance covered by the bottle when it finally comes to a stop?
(c) NOTE: BONUS marks will be awarded if you can derive the following expression for the maximum speed the bottle can ever attain once all the air has escaped, and which does not assume that the acceleration of the bottle is constant while the air is escaping:
vf=uMfm−(ΔM/Δt)μg/2(Mi2−Mf2)
where m is the mass of the escaped air, neglecting the air left in the bottle at the end.