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A solid block of mass `m = 1 kg` is reasting on a horizontal platform as shown in figure. The `z` direction is vertically up. Coefficient of friction between the block and the paltform is `mu = 0.2`. The platform is moved with a time dependent velocity given `vec(V) = (2that(i) + that(j) + 3hatk) m//s`. Then the magnitude of the net force exerted by the block on the platform is : (Take `g = 10 m//s^(2)`) A. `sqrt(168)N`B. `sqrt(174)N`C. `sqrt(194)N`D. None of these |
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Answer» Correct Answer - B Acceleration of the platform `overset(vec)(a_(p) ) - (doverset(vec)v)/(dt) - 2hati + hat(j) + 3hat(k)` Horizontal force on the block Normal force on the block `a_(H) = sqrt(4 + 1) = sqrt(5) m//s^(2)` `a_(v)= 3 m//s^(2)` Normal force on the block `N = m (g + a_(v)) = 1 xx 13 = 13N` Maximum acceleration that friction can positive `a_(mass) = mu(g + a_(y)) = 0.2 xx 13 = 206 m//s^(2)` `:. a_(max) gt a_(H)` `:.` Value of frication force on the block `f = ma_(H) = sqrt(5)N` `:.` Force by the platform on the block is `F = sqrt(N^(2) t^(2)) = sqrt(169 + 5) = sqrt(174)N` |
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