A rock is hanging downwards from the top of a bus accelerating at 16 m/s^2. What is the angle of the string made with the vertical?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A rock is hanging downwards from the top of a bus accelerating at 16 m/s^2. It is assumed that the acceleration is in the horizontal direction. The angle that the string by which the rock is hanging makes with the vertical is a function of all the forces accelerating the rock.

There is an acceleration of 9.8 m/s^2 acting vertically downwards and an acceleration of 16 m/s^2 acting in the horizontal direction. Let the angle made with the vertical by the string be X.

The tangent of this angle is equal to the magnitude of the horizontal acceleration divided by the magnitude of the vertical acceleration. tan X = 16/9.8

=> X = arc tan (16/9.8)

=> X = 58.51 degrees

The angle of the string by which the rock is hanging makes an angle of 58.51 degrees with the vertical.

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