Question

Figure shows a block of mass 'm' resting on a smooth horizontal surface. It is
connected to rigid wall by a massless spring of stiffness 'k' The spring is in its natural length. A constant horizontal force F starts acting on the block towards right.
Find (1) speed of the block as it moves through a distance x, (ii) speed when the block is in equilibrium and (ii) maximum extension produced in the spring.

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Answer 1

When the block has moved through 'x' its speed is v(say) .

[i] By work - Energy principle ,

W = ∆K

Wf + Wsp = 1/2 mv^2 - 0

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[ii] At the equilibrium, net force is zero .

∴ F = kx or x= F/k

•v = √ (2 Fx - kx^2) / m

•v = √ [(2F^2/ k ) - ( F ^2/k )] / m

•v = F/ √mk

[iii] At the maximum extension, speed of the block becomes zero .

∴ v = 0

or, √ (2Fx - kx^2) / m = 0

=> x = 2F/ K

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Answer 2

Answer:

X=2F/k is the correct answer!!!..

Hope it will be helpful ☺️ thank you!!