A ball hangs from the ceiling of a car accelerating horizontally at a. In the same car, a block on a smooth fixed incline remains at rest. The inclination angle θ of the plane with the horizontal satisfies:
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Question

A ball hangs from the ceiling of a car accelerating horizontally at a. In the same car, a block on a smooth fixed incline remains at rest. The inclination angle θ of the plane with the horizontal satisfies:

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G1 Physics · Accepted Answer

In the accelerating car frame, effective gravity has horizontal component a and vertical component g. Both the hanging string and the normal to the equilibrium incline align with effective gravity, so tanθ=a/g.