A spring lies along X axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at X = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement X max .
(i) During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block –
Text Solution
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(i) : Applying W-E theorem on the block for any compression X:
W ext + W g + W spring = Δ KE ⇒ FX + 0 – 
kX 2 = 
mv 2 ⇒ KE vs X is inverted parabola.
(ii) : W ext = FX ⇒ linear variation
(iii) : From beginning to end of motion: Δ KE = 0
⇒ X = 2F/k. (from W-E theorem)
∴ first half corresponds to 0 ≤ X ≤ (F/k)
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