A rough incline of angle θ rises rightward and accelerates horizontally leftward with acceleration a. A block of mass m is attached to a spring of force constant k along the plane. A positive spring extension x pulls the block up the incline. The coefficient of static friction between block and incline is μ. For the block to remain at rest relative to the accelerating incline, the allowed values of x can be written as [mD-μmN′]/k ≤ x ≤ [mD+μmN′]/k. The correct D and N′ are:
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Question

A rough incline of angle θ rises rightward and accelerates horizontally leftward with acceleration a. A block of mass m is attached to a spring of force constant k along the plane. A positive spring extension x pulls the block up the incline. The coefficient of static friction between block and incline is μ. For the block to remain at rest relative to the accelerating incline, the allowed values of x can be written as [mD-μmN′]/k ≤ x ≤ [mD+μmN′]/k. The correct D and N′ are:

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G1 Physics · Accepted Answer

In the accelerating frame, pseudo force ma acts rightward. Without spring and friction, the net tendency down the plane is mD = m(g sinθ-a cosθ). The normal reaction is N = mN′ = m(g cosθ+a sinθ). Equilibrium requires |mD-kx|≤μmN′, which rearranges to the stated interval.