A block with mass of 4.94 kg is attached to a horizontal spring with spring cons

Question

A block with mass of 4.94 kg is attached to a horizontal spring with spring constant k = 3.84 102 N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to xi = 0.0550 m and released.

(a) Find the speed of the block at the equilibrium point.
(b) Find the speed when x = 0.024 m.
(c) Repeat part (a) if friction acts on the block, with coefficient ?k = 0.120.

Explanation / Answer

(a) at the equilibrium point 1/2 Kxi^2 = 1/2 mv^2 ===> v^2 = Kx^2/m ===> v = 0.485 m / s (b) at x = 0.024 . 1/2 Kxi^2 = 1/2 mv^2 + 1/2 Kx^2 ===> 0.581 = 1/2 mv^2 + 0.1106 ===> v = 0.4364 m/s (c) at the equilibrium point 1/2 Kxi^2 = 1/2 mv^2 + ?mgxi ===> 1/2 mv^2 = 0.581 - 0.32 ===> v = 0.3254 m/s

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