A 2 kg block is sliding on a frictionless surface when it strikes a spring with

Question

A 2 kg block is sliding on a frictionless surface when it strikes a spring with a spring constant of 75 N/m. The block compresses the spring by 16 cm when it comes to a stop. a) What was the speed of the block when it first encountered the spring? b) What was the speed of the block when the spring was compressed to half its maximum compression? c) Suppose, instead, the block was sliding on a rough surface and the spring was compressed by only 10 cm. Find the work done by friction if the speed of the block was the same as in part a when it first encountered the spring.

Explanation / Answer

2. (A) Applying energy conservation,

k A^2 /2 = m Vmax^2 / 2

(75) (0.16^2) = (2) Vmax^2

Vmax = 0.98 m/s

(b) k A^2 / 2 = k x^2 /2 + m v^2 /2

(75) (0.16^2) = (75)(0.08^2) + 2 v^2

v = 0.85 m/s

(c) Initially energy, Ei = (75) (0.16^2)/2 = 0.96 J

final energy Ef = (75)(0.10^2) / 2 = 0.375 J

Work done = Ef - Ei

= - 0.585 J

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