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20 August, 18:39

A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s^2. (a.) What is the acceleration of the bolt relative to the train car? (b.) What is the acceleration of the bolt relative to the earth?

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  1. 20 August, 20:06
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    Refer to the diagrams shown below.

    Define

    a₁ = 2.5 m/s², acceleration of the car (north)

    a₂ = the acceleration of the bolt relative to the car

    g = 9.8 m/s²

    Relative to the car, the acceleration of the bolt is

    a₂² = 9.8² + 2.5² = 102.29

    a₂ = 10.1 m/s²

    The direction of a₂ is

    θ = tan⁻¹ (2.5/9.8) = 14.3° south of the vertical.

    Relative to the earth, the acceleration of the bolt is

    a₂ = 10.1 m/s²

    θ = 14.3°, north of the vertical.

    Answer:

    (a) 10.1 m/s² at a vertical angle of 14.3° southward.

    (b) 10.1 m/s² at a vertical angle of 14.3° northward
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