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A block of mass m initially at x = 0 is pulled along X-axis by applying the force F = b - cx, where b andcare positive constant.m →FEx = 0 |
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Answer» n-> The block of mass m initially at x=0 is acted UPON by a horizontal force F = b -cx² (where b > μmg) as shown in the figure. The coefficient of friction between the SURFACE is μ. The net work done on the block is ZERO, if the block travels a distance of ..Solution : according to QUESTION, Net workdone on the block is zero.so, Workdone by friction + workdone by force = 0Let distance covered by the block is x⇒-μmgx + ∫F(x) dx = 0⇒-μmgx + ∫(b - cx²)dx = 0⇒-μmgx + bx - cx³/3 = 0⇒-(μmg - b)x - cx³/3 = 0⇒(b - μmg) = cx²/3 ⇒x = √{3(b - μmg)/c} Therefore the distance covered by the block is √{3(b - μmg)/c} |
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