JBug asked in Science & MathematicsPhysics · 9 years ago

A 2.0-kg solid cylinder and 2.5-kg solid sphere are released from rest at the top of a ramp and allowed to...?

A 2.0-kg solid cylinder and 2.5-kg solid sphere are released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.79 m high and 5.0 m long.

Which object do you expect to have the greater speed at the bottom of the ramp?

cylinder or sphere?

Verify your answer to part A by calculating the speed of the cylinder and of the sphere when they reach the bottom of the ramp.

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  • 9 years ago
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    For the cylinder

    As there is no slipping,

    The kinetic energy due to rotation is half of the linear kinetic energy.

    M g h = 0.5 M U² + 0.5 (0.5 M R²) U² / R²

    g h = 0.5* U² + 0.5*0.5 U²

    9.8* 0.79 = 0.5* U² + 0.5*0.5 U²

    Uc = 3.21 m/s

    ---------------------------------------------------------

    For the sphere

    As there is no slipping,

    The kinetic energy due to rotation is two fifth of the linear kinetic energy.

    M g h = 0.5 M U² + 0.5 (0.4 M R²) U² / R²

    g h = 0.5* U² + 0.5*0.4 U²

    9.8* 0.79 = 0.5* U² + 0.5*0.4 U²

    Us = 3.33 m/s

    ======================================

    Since Us > Uc sphere reaches first at the bottom of the ramp .

    ======================================

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