A block with mass of 5.99 kg is attached to a horizontal spring with spring cons

Question

A block with mass of 5.99 kg is attached to a horizontal spring with spring constant k = 3.92 102 N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to xi = 0.0520 m and released.

Suppose the spring system in the last example starts at x = 0 and the attached object is given a kick to the right, so it has an initial speed of 0.59 m/s. (a) What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless?
m

(b) How does the answer change if the answer if the coefficient of kinetic friction is ?k = 0.160? (Use the quadratic formula.)
m

Thank you so much

Explanation / Answer

a) mv2/2 = kx2 /2

5.99 x 0.592 = 392x2

x = 0.0729m



b) now work done by friction will also come in action.

mv2 /2 = kx2 /2 + mgx

5.99 x 0.592 /2 = 392x2 /2 + 0.160 x 5.99 x 9.81x

196x2 + 9.40x - 1.043 = 0

x = 0.0528 m

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