Question

A block of mass m initially at x = 0 is pulled along
X-axis by applying the force F = b - cx, where b and
care positive constant.
m →F
E
x = 0
​

Answer 1

Question-> 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 = 0

Let 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}

Answer 2

Answer:-

Question->

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 = 0

Let 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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