A horizontal spring has spring constant k = 360N/m. (a) How much work is require

Question

A horizontal spring has spring constant k = 360N/m. (a) How much work is required to compress it from its uncompressed length (x = 0) to x = 11.0 cm? (b) If a 1.85-kg block is placed against the spring and the spring is released, what will be the speed of the block when it separates from the spring at x = 0? Ignore friction. (c) Repeat part (b) but assume that the block is moving on a table and that some kind of constant drag force FD = 7.0N is acting to slow it down, such as friction (or perhaps your finger).

(Please explain and show steps)

Explanation / Answer

k = 360 N/m

(A) Work done = k (xf^2 - xi^2) / 2

= 360 (0.11^2 - 0^2) / 2

= 2.18 J

(B) Applying work done= change in KE

2.18 = 1.85(v^2 - 0) / 2

v = 1.53 m/s

(C) Work done by spring + work done by friction = change in KE

2.18 - (7 x 0.11) = 1.85 v^2 /2 - 0

v = 1.23 m/s

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