A block of mass 1 kg is released from top of a rough incline having $μ = \frac{1}{3}$ . The initial speed of block is 2m/s. The incline plane is of unknown length and has a spring of constant $k = 1 N / m$ connected at base as in figure. Find the maximum compression of spring. (answer in meter).

Question

incline with spring

TestHub · Accepted Answer

Sliding down: ma = m g sin 3 0 ∘ − 3 ​ 1 ​ m g cos 3 0 ∘ = 0 , so the block reaches the spring at constant v = 2 m/s . During compression gravity and friction work cancel ( W m g ​ = − W f r ​ ), so 2 1 ​ k x 2 = 2 1 ​ m v 2 . With m = k = 1 : x = v m / k ​ = 2 m .

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