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    Acceleration, Friction Force, Coefficient of Friction

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    A hollow, spherical shell with mass 2.00 kg rolls without slipping down a slope angled at 34.0 degrees

    A) Find the acceleration (take free fall to be 9.8 m/s^2)

    B) Find the friction force

    C) Find the minimum coefficient of friction needed to prevent slipping

    © BrainMass Inc. brainmass.com December 24, 2021, 9:11 pm ad1c9bdddf
    https://brainmass.com/physics/torques/acceleration-friction-force-coefficient-friction-352719

    SOLUTION This solution is FREE courtesy of BrainMass!

    Since the sphere doesn't slip;

    torque = (moment of inertia of sphere)(angular acceleration) = (force due to friction)(radius of sphere)

    Iα = (Ff)(r)

    where;

    I=2mr^2/3
    α=a/r

    if we substitute and solve for Ff;
    (2mr^2/3)(a/r) = (Ff)(r)
    Ff = 2ma/3

    Net force acting on the system is;

    Fnet=(force due to gravity along slope) - (force due to friction)

    Fnet = (force due to gravity along slope) - (force due to friction)

    Fnet = mgsinθ - Ff

    Fnet = mgsinθ - 2ma/3 = ma

    a=gsinθ - 2a/3

    a=3gsinθ/5

    sin 34=0.56

    a=3x9.81x0.56/5

    a=3.29m/s2

    Now we can calculate Ff;

    Ff=2ma/3=2x2x3.29/3

    Ff=4.38N

    Minimum friction coefficient for the non-slip condition can be calculated from;

    Ff = μmgcosθ

    cos 34=0.83

    4.38=μx2x9.81x0.83

    μ=4.38/16.28

    μ=0.27

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:11 pm ad1c9bdddf>
    https://brainmass.com/physics/torques/acceleration-friction-force-coefficient-friction-352719

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