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    Question

    A block of mass m rests on a smooth wedge of mass M,

    which in turn rests on a smooth horizontal surface. The wedge is accelerated horizontally with acceleration a. Find the normal force acting on the block by the wedge if the wedge makes an angle θ with the horizontal.
    A N=m(acosθ + gsinθ) Correct Answer Incorrect Answer
    B N=m(gcosθ - asinθ) Correct Answer Incorrect Answer
    C N=m(gcosθ + asinθ) Correct Answer Incorrect Answer
    D N=m(acosθ - gsinθ) Correct Answer Incorrect Answer

    Solution

    To find the normal force N acting on the block by the wedge, consider the forces in a non-inertial frame attached to the accelerating wedge. In this frame, the block is at rest. The forces acting on the block are:

    • Gravity (mg) downwards.
    • Normal force (N) perpendicular to the wedge's surface.
    • Pseudo force (ma) horizontally to the left.
    Resolve these forces perpendicular to the surface of the wedge. The components acting perpendicular to the wedge are:
    • Component of mg: mgcosθ (into the wedge).
    • Component of ma: masinθ (into the wedge).
    • Normal force N (out of the wedge).
    Since the block is at rest relative to the wedge, the net force perpendicular to the wedge is zero: N−mgcosθ−masinθ=0 Therefore, the normal force is: N = mgcosθ+masinθ N=m(gcosθ + asinθ)

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