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    Workign with Boxes going down a belt

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    Boxes are transported by a conveyor belt with a velocity v_0 to a fixed incline at A where they slide and eventually fall off at B. Knowing that u_k=0.40, determine the velocity of the conveyor belt if the boses leave the incline at B with a velocity of 2m/s.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf
    https://brainmass.com/physics/conservation-of-energy/working-boxes-going-down-belt-13272

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    SOLUTION This solution is FREE courtesy of BrainMass!

    we will use the conservation of energy here,

    the initial energy of the box E = Kinetic+ Potential

    = (1/2)mv^2 + mgh

    from the figure, h = 6*sin15 = 1.55

    final enrgy = (1/2) m U^2

    where u = 2 m/s our final velocity

    thus some enrgy is lost in transition and it is used for doing work
    againist the force of friction.

    Frictional force = mu * normal force = 0.4 * m g cos15, from figure

    workdone againist this force = force * distance = 6 * 0.4 * m g cos 15

    now we can write, (1/2)mv^2 + mgh - (1/2) m U^2 = 6 * 0.4 * m g cos 15

    cancel m throughout and multiply by 2 throughout

    V^2 = - 2* 9.8 * 1.55 + 2^2 + 12 * 0.4 * 9.8* cos 15

    = -30.38 + 4 + 45.44

    or V = 4.36 m/sec

    see the attached figure also.

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

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf>
    https://brainmass.com/physics/conservation-of-energy/working-boxes-going-down-belt-13272

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