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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 Īø with the horizontal.
    A N=m(acosĪø + gsinĪø) Correct Answer Incorrect Answer
    B N=m(gcosĪø - asinĪø) Correct Answer Incorrect Answer
    C N=m(gcosĪø + asinĪø) Correct Answer Incorrect Answer
    D N=m(acosĪø - gsinĪø) 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: mgcosĪø (into the wedge).
    • Component of ma: masinĪø (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: Nāˆ’mgcosĪøāˆ’masinĪø=0 Therefore, the normal force is: N = mgcosĪø+masinĪø N=m(gcosĪø + asinĪø)

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