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    Vehicle on sloped road: Worked out problem

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    A lorry travelling on the level road at 40 km/h can be stopped by its brakes in a distance 16 m. Find the speed from which it can be brought to rest in the same distance when descending a hill whose angle of slope is Sin^-1 [1/15]

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf
    https://brainmass.com/physics/work/vehicle-sloped-road-worked-problem-7554

    SOLUTION This solution is FREE courtesy of BrainMass!

    The speed of the lorry = 40 km/h

    = 40 x 5/18 m/s = 100/9 m/s

    Distance in which it is stopped = 16 m

    Using, V^2 = U^2 + 2aS to find the retardation 'a'

    V = 0, U=(100/9) m/s, S = 16m, and a = ?

    Substituting

    0 = (100/9)^2 + 2 a x 16

    from this, a = -3.86m/s^2

    This is the acceleration on the wheels when break is applied
    (note that it is negative)

    Therefore force of brakes F = M a = 3.86xM Newton

    where M is the mass of the lorry

    When the lorry is descending the slope, the gravitational force has a component mgSin(A)

    The resultant force on the lorry = 3.86M - (9.8/15)M

    = 3.21 M Newton

    hence retardation = 3.21 m/s^2

    Let U1 be the velocity required

    we can write,

    0 = U1^2 - 2 x 3.21 x 16

    U1 = [2 x 3.21 x 16]^(1/2)

    = 10.14 m/s

    You can convert it to Km/h by multiplying with (18/5)

    To convert km/h to m/s, multiply by (5/18)

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

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf>
    https://brainmass.com/physics/work/vehicle-sloped-road-worked-problem-7554

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