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## Homework Statement

A small weight of mass 'm' hangs from a string in an automobile. Initially, the car is at rest with the weight hanging vertically. Then, the car SUDDENLY accelerates to a rate 'A'. Find the maximum angle [tex]\varphi_{max}[/tex] through which the weight swings by analyzing the motion of the pendulum WITHIN AN

**INERTIAL**REFERENCE FRAME.

## Homework Equations

In my book they derive the solution to this problem using an analysis within a NON-INERTIAL reference frame. The answer is:

[tex]\varphi_{max}[/tex] = 2*arctan(A/g) (1)

If you instead try to find the static angle the pendulum makes with the vertical in a car that is already accelerating at a constant rate A you will find that the static angle is half of the maximum angle given by equation (1).

The problem we are being asked though is to try and derive equation (1) using a non-inertial frame and I cannot figure out how to carry out the calculation.

## The Attempt at a Solution

I am assuming that the best way to solve this problem is to use a classic Newton's 2nd Law analysis using an inertial reference frame that is stationary with respect to the car. Or is it better to solve this problem using an energy approach? Note that when I say an energy approach I do NOT mean forming the Lagrangian and solving that way. In my class we have only been doing classical analyses using Newton's formulation of mechanics so Lagrangian and Hamiltonian analyses are not acceptable for my class. By energy approach I simply mean that the weight increases in potential energy as it approaches the max angle, thus the corresponding increase in the kinetic energy of the bob must equal the increase in grav. potential so maybe there is a way to connect the kinetic energy of the bob with the acceleration of the car?

By the way this is not a homework question. Instead my professor challenged us to attempt to solve this problem in an inertial frame. I hope that I am not posting this question in the wrong forum. If I am I am sorry but I am new here so just let me know and I will move it.

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