Classical Mechanics
Classical Mechanics
5th Edition
ISBN: 9781891389221
Author: John R. Taylor
Publisher: University Science Books
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Question
Chapter 9, Problem 9.1P
To determine

The reason for the balloon to tilt forward and also the angel of the tilt in equilibrium.

Expert Solution & Answer
Check Mark

Answer to Problem 9.1P

The angel of the tilt in equilibrium is θ=tan1(Ag)

Explanation of Solution

When the car is at the rest the balloon floats up in a direction opposite to the pull of the gravity g.when the car accelerates, the car defines a frame of references with some acceleration a0 to the right.

From the equivalence principle, a frame accelerating to the right is equivalent to a non- accelerating frame with an artificial gravity g0 to the left, where g0=a0. In this non-accelerating frame, there are actually two gravitates, the real gravity g downward and the artificial gravity g0 to the left.

Then the effective gravity is the vector sum of these two and directs as shown in the figure 1.

Classical Mechanics, Chapter 9, Problem 9.1P , additional homework tip  1

The balloon will float in a direction opposite to this geff as shown in the figure 1. The balloon will move forward tilting towards the front of the car as shown in the figure 2.

Classical Mechanics, Chapter 9, Problem 9.1P , additional homework tip  2

 By the equivalence Principle, it will do the same thing in the actual, accelerating car towards the right.

Conclusion:

Write the expression from the figure 3,

Classical Mechanics, Chapter 9, Problem 9.1P , additional homework tip  3

  tanθ=mAm(g)θ=tan1(Ag)

Here, m is the mass of the helium balloon, A is the acceleration of the helium balloon, g is the true gravity on the helium balloon and geff is the effective gravity on the helium balloon.

The angel of the tilt in equilibrium is θ=tan1(Ag)

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