- #1
bananabandana
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Homework Statement
A balloon stands upright in a stationary truck. The truck then accelerates forwards. What direction does the balloon move in?
Homework Equations
Just Newton 1&2.
The Attempt at a Solution
1) A Free body diagram on the balloon. We know the balloon accelerates at the same rate as the truck in the x direction. There's no reason for there not to be equilibrium in the y, so (please see attached file) I choose the positive theta direction as shown (which happens to be the same direction as acceleration)
$latex mg =Tcos\theta (F_{y}) $
$latex ma=Tsin\theta = ma $
$latex a=gtan\theta $
Since a is in the positive theta direction, it is positive in the third equation. This implies that theta must be greater than 0, (i.e the balloon does actually move as shown.)
The issue is, I'm not sure if this is acceptable as a solution! The method given in my book suggests that the approach is along the lines of
(1) Newton's first law implies you would expect the balloon to move backwards while the truck accelerates.
(2) But, the movement of all the air in the truck to the back (by Newton's first law) creates a pressure gradient that causes the balloon to move forward.
So my question is, are these two approaches equivalent or not? If not, why, please!
Many thanks for all your help.