Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

A 400N bag of cement starts from rest and slides 12m down a roof with slope of 3 horizontal to 1 vertical and a coefficient ..?

Cont..

of friction of 0.20. If the vertical distance from the edge of roof to the ground is 10 m, how far from the wall will the bag of cement strike the ground?

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  • 2 months ago
    Favourite answer

    Given: W = mg = 400 N = 400/9.8 kg = 40.82 kg & tanθ = 1/3

    =>sinθ = 1/√{(3)^2 + (1)^2} = 1/√10 = 0.32

    =>cosθ = 3/√{(3)^2 + (1)^2} = 3/√10 = 0.95By F(net) = F(gravity) - F(friction)=>ma = mgsinθ - µk x N=>ma = mgsinθ - µk x  mgcosθ=>ma = W(sinθ - µk x cosθ)=>40.82 x a = 400(0.32 - 0.20 x 0.95)

    =>a = 1.28 m/s^2

    Thus by v^2 = u^2 + 2as

    =>v^2 = 0 + 2 x 1.28 x 12

    =>v = √30.64

    =>v = 5.53 m/s 

    Now v(X) = vcosθ = 5.53 x 0.95 = 5.26 m/s

    & v(Y) = vsinθ = 5.53 x 0.32 = 1.77 m/s

    Let the bag take t sec to cover 10 m under v(Y), by s = ut + 1/2gt^2

    =>10 = 1.77 x t + 1/2 x 9.8 x t^2

    =>4.9t^2 + 1.77t - 10 = 0

    =>t = [-1.77 +/-√{(1.77)^2 - 4 x 4.9 x (-10)}]/(2 x 4.9)

    =>t = 1.26 sec

    Thus distance covered on X-axis (Let R) under v(X), by s = ut

    =>R = v(X) x t

    =>R = 5.26 x 1.26 = 6.62 m ----------The required Answer.

    • J2 months agoReport

      But why 10 m sir? The problem says its 12 m

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  • oubaas
    Lv 7
    2 months ago

    mass =400/9.80665 = 40.79 kg 

    tan Θ = 1/3 ; 

    Θ = 18.435 ° ; sin Θ = 0.316 ; cos Θ = 0.949

    acceleration a = 400*(0.316- 0.949*0.20)/40.79 = 1.238 m/sec^2

    V = √ 2ad = √ 2*12*1.238 = 5.45 m/sec 

    Vy = -5.45*0.316 = -1.72 m/sec 

    -12 = -1,72*t-9,80665*t^2

    falling time t = (1,72-√ 1.72^2+48*9.80665)/-19,613 = 1.022 sec 

    distance d = 5.45*0.949*1.022 = 5.28 m 

     

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