An inclined plane that makes an angle of \(30^{\circ}\) with the horizontal has a spring of spring constant \(4500 \mathrm{~N} / \mathrm{m}\) at the bottom (Figure P10.91). A 2. 2-kg block released near the top of the plane moves down the plane and compresses the spring a maximum of \(0.0240 \mathrm{~m}\) from its relaxed length.

(a) Ignoring any frictional effects, calculate the distance the leading edge of the block travels from the instant the block is released to the instant it briefly stops against the compressed spring.

(b) Now suppose there is friction between the block and the surface of the plane, with \(\mu_{k}=0.10\). If the block is again placed somewhere on the plane and allowed to slide down and compress the spring by the same \(0.0240 \mathrm{~m}\), how far does the leading edge of the block travel now?

Data from Figure P10.91

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